UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The crystal chemistry of gorceixite, grandidierite, and traskite Dzikowski, Tashia Jayne 2006

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_2006-0438.pdf [ 3.63MB ]
Metadata
JSON: 831-1.0052713.json
JSON-LD: 831-1.0052713-ld.json
RDF/XML (Pretty): 831-1.0052713-rdf.xml
RDF/JSON: 831-1.0052713-rdf.json
Turtle: 831-1.0052713-turtle.txt
N-Triples: 831-1.0052713-rdf-ntriples.txt
Original Record: 831-1.0052713-source.json
Full Text
831-1.0052713-fulltext.txt
Citation
831-1.0052713.ris

Full Text

THE CRYSTAL CHEMISTRY OF GORCEIXITE, GRANDIDIERITE, AND TRASKITE by T A S H I A J A Y N E D Z I K O W S K I B . S c , The University of Manitoba, 2004 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R OF S C I E N C E in T H E F A C U L T Y OF G R A D U A T E S T U D I E S ^Geological Sciences^ T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A August 2006 © Tashia Jayne Dzikowski , 2006 ABSTRACT This thesis reinvestigates the crystal structures of gorceixite and traskite, and the geometric effects of v F e 2 + for v M g substitution on the crystal structures of the grandidierite-ominelite series. A l l data was measured using using MoKa radiation on an automated Bruker X 8 single-crystal diffractometer with a S M A R T A P E X C C D (charge coupled device) detector. The crystal structure of gorcexite ( B a A l 3 ( P 0 3 0 , O H ) 2 ( O H 6 ) , a 7.0538(3), c 17.2746(6) A, V 744.4(2) A3, space group R 3m, Z=3, has been refined to an R] index of 2.3% based on 253 unique reflections. The results indicate that this specimen has rhombohedral rather than monoclinic Cm symmetry as was previously reported for the species. The crystal-structure refinement shows that the atomic arrangement of gorceixite is similar to that of other members of the plumbogummite group. The chemical compositions and crystal structures of seven members of the grandidierite-ominelite ( M g A l 3 B S i 0 9 - F e 2 + A l 3 B S i 0 9 ) series w i t h X - (Fe 2 + + M n + Zn)/(Fe 2 + + M n + Zn + Mg) ranging from 0.00 to 0.52 were studied to determine the geometric effects of Fe substitution for M g on the crystal structures. Regression equations derived from single-crystal X-ray diffraction data show that b increases by 0.18 for the range X= 0-1. The crystal structure refinements show that the most significant changes involve the (Mg,Fe ) 0 5 polyhedron, which increases in volume by 0.36 A3 (5.0%), largely as a result o f expansion o f the M g F e - 0 5 , - 0 2 , and - 0 6 (x2) bond distances, which increase by 0.09 (4.4%), 0.06, and 0.04 A, respectively. Numerous space groups were tried in an attempt to solve and refine the crystal structure of the traskite (Ba9Fe 2 +2Ti2(Si0 3)i2(F,Cl,OH)6-6H20. The most successful was P3\m, with a 17.863(3), c 12.298(3) A, and Z = 3. The Rm = 5.3% and R{ = 5.3% values indicate that the data are good and that the model is close to being correct; however, split Ba , O, and CI sites indicate that there are missing symmetry elements within the structure. Attempts to refine the structure in P6/mmm, which contains the supposed missing symmetry elements, were unsuccessful. i i TABLE OF CONTENTS A B S T R A C T i i T A B L E OF C O N T E N T S ; i i i LIST OF T A B L E S . v LIST O F F I G U R E S v i A C K N O W L E D G E M E N T S v i i 1.0 I N T R O D U C T I O N 1 2.0 G O R C E I X I T E 2 2.1 Introduction 2 2.2 Experimental 4 2.3 Results 7 2.4 Discussion 17 3.0 G R A N D I D I E R I T E 18 3.1 Introduction 18 3.2 Background 18 3.3 Experimental 22 3.4 Results 27 3.4.1 Electron microprobe analyses 27 3.4.2 Unit cell parameters 40 3.4.3 Bond distances 40 3.4.4 Bond angles 44 3.4.5 Polyhedral edges 48 3.4.6 Polyhedral volumes and distortion parameters 52 3.4.7 Summary 52 i i i 3.5 Discussion 54 3.5.1 Unit-cell parameters 54 3.5.2 Geometric effects 55 3.5.3 Effect of other substituents 57 3.5.4 Ionic radius of v F e 2 + 58 3.5.6 Conclusion: v Fe in minerals 58 4.0 T R A S K I T E 60 4.1 Introduction 60 4.2 Experimental 60 4.3 Results and Discussion 62 R E F E R E N C E S 72 A P P E N D I X A . l Commonly used symbols and terms 80 iv L I S T O F T A B L E S 2.1 Electron-microprobe composition of the gorceixite single-crystal used in this study.... 5 2.2 Gorceixite: Data collection and structure refinement information 8 3.3 Atom parameters for gorceixite 9 3.4 Selected interatomic distances (A) and angles (°) for gorceixite 10 3.5 Bond valence analysis of gorceixite 13 3.6 Sample information for grandidierite and ominelite 23 3.7 Average electron-microprobe compositions of grandidierite and ominelite crystals used in the single-crystal X-ray diffraction study 25 3.8 Data measurement and refinement information for grandidierite and ominelite 28 3.9 Atomic parameters for grandidierite and ominelite 29 3.10 Atomic displacement parameters for grandidierite and ominelite 31 3.11 Interatomic distances (A) and angles (°) for grandidierite and ominelite 34 3.12 Polyhedral edges (A) for grandidierite and ominelite 37 3.13 Polyhedral volumes and distortion parameters for grandidierite and ominelite 39 4.1 Electron microprobe analyses of traskite 63 4.2 Attempted space groups and resulting Flack x parameters, and |E -1 | values of traskite 66 4.3 Traskite: Data collection and structure refinement information 66 4.4 Atom parameters for traskite 67 4.5 Selected interatomic distances (A) for traskite 69 4.6 Selected interatomic angles (°) for traskite ...71 v LIST OF FIGURES 2.1 Coordination polyhedra of cations in the gorceixite structure 11 2.2 The gorceixite structure projected onto (a) (100) and (b) (001) 16 3.1 Projection of the crystal structure of grandidierite and ominelite onto (001) 20 3.2 Coordination polyhedra for the cations in the grandidierite-ominelite structure 21 3.3 (Fe 2 + + M n + Zn)/(Fe 2 + + M n + Z n + Mg) vs. (a) a, (b) b, (c) c, (d) F f o r grandidierite and ominelite 41 3.4 (Fe 2 + + M n + Zn)/(Fe 2 + + M n + Z n + Mg) vs. (a) M g F e - 0 5 a , (b) M g F e - 0 2 , (c) M g F e - 0 6 x 2 for grandidierite and ominelite 42 3.5 (Fe 2 + + M n + Zn)/ (Fe 2 + + M n + Zn + Mg) vs. ( a ) A l l - 0 6 x 2; (b) A12-04 x 2; (c) A 1 2 - 0 7 f x 2 (squares), - 0 5 c x 2 (triangles) for grandidierite and ominelite 43 3.6 (Fe 2 + + M n + Zn)/(Fe 2 + + M n + Z n + Mg) vs. (a) O l - M g F e - 0 2 (squares), 0 6 - M g F e - 0 6 b (triangles); (b) O l - M g F e - 0 6 x 2; (c) 0 2 - M g F e - 0 6 x 2 (squares), 0 1 - M g F e - 0 5 a (triangles); and (d) 0 2 - M g F e - 0 5 a for grandidierite and ominelite 45 3.7 (Fe 2 + + M n + Zn)/ (Fe 2 + + M n + Z n + Mg) vs. (a) 0 6 - A 1 1 - 0 2 x 2 (squares), - 0 2 d x 2 (triangles); (b) 0 1 - A 1 3 - 0 5 a (squares), - 0 2 i (triangles) for grandidierite and ominelite 46 3.8 (Fe 2 + + M n + Zn)/(Fe 2 + + M n + Z n + Mg) vs. (a) 0 4 - S i - 0 6 j x 2 (squares), - O l (triangles); (b) 0 6 j - S i - 0 6 f (squares), - O l x 2 (triangles) for grandidierite and ominelite 47 3.9 (Fe 2 + + M n + Zn)/ (Fe 2 + + M n + Zn + Mg) vs. ( M g , F e 2 + ) 0 5 polyhedral edges: (a) 0 2 - 0 6 x 2 (squares), 0 1 - 0 5 a (triangles); (b) 0 6 - 0 5 a x 2 (squares), -6b (triangles); (c) 0 1 - 0 2 (squares), - 0 6 x 2 (triangles) 49 3.10 (Fe 2 + + M n + Zn)/(Fe 2 + + M n + Zn + Mg) vs. polyhedral edges: (a) A110 6 , 0 6 - 0 2 d x 2; (b) A120 6 , 0 7 f - 0 4 h x 2 (squares), - 0 4 x 2 (triangles); (c) A 1 3 0 5 , 0 2 i - 0 1 50 3.11 (Fe 2 + + M n + Zn)/(Fe 2 + + M n + Z n + Mg) vs. S i 0 4 tetrahedral edges, 0 4 - 0 6 x 2 51 3.12 (Fe 2 + + M n + Zn)/ (Fe 2 + + M n + Zn + Mg) vs. (a) volume o f the (Mg,Fe 2 + )05 (squares) and A130s (triangles) polyhedra, (b) volume of the A l l 0 6 (squares) and A 1 2 0 6 (triangles) octahedra, (c) tetrahedral angle variance for Si04 tetrahedron in grandidierite and ominelite 53 4.1 Structure of traskite projected down (001) 61 v i A C K N O W L E D G E M E N T S I would like to thank Prof. Lee A . Groat for suggesting this project, always being there to listen, discussing and solving mineralogical problems with me, spending endless hours helping me write and edit, collecting data when I could not, and giving me the opportunity to move to Vancouver where I have experienced the most amazing time of my life. I would also like to thank Edward S. Grew and John A . Jambor for their contribution to my work with grandidierite and gorceixite. In addition, I would like to thank Col in Fyfe and Mat i Raudsepp for serving on my committee. I would not have been able to collect electron microprobe data without the help of Mati Raudsepp nor would I have been able to collect X-ray diffraction data without the help of Anita Lam and Brian Patrick. I would also like the thank Anita and Brian for all o f their help with interpreting my results. I would also like to thank Al l i son Brand for helping prepare and revise my manuscripts. M y last two years have gone so smoothly in part because of Alex Allen 's assistance with graduate affairs. I would also like to thank my dear friends Jen, Laura, Megan, Victoria, and Tanya. Your support and friendship over the years means so much to me. I would also like to thank my family for encouraging me to always do my best and to set my goals high. I would not be here without you. Support for this project was provided by N S E R C operating grants to Lee A . Groat. Personal financial support was provided by a Post-Graduate Masters and a Canada Graduate Scholarship Masters N S E R C as well as the University of British Columbia in the form of scholarships and teaching assistantships. v i i 1.0 I N T R O D U C T I O N Here I reinvestigate the crystal structures of gorceixite and traskite, and the geometric effects of v F e 2 + for v M g substitution on the crystal structures of the grandidierite-ominelite series. For data collection I used a Bruker X 8 single crystal X-ray diffractometer with a S M A R T A P E X C C D (charge coupled device) detector in the Center for Higher Order Structure Elucidation ( C - H O R S E ) lab at the University of British Columbia. I was the first to use this instrument this instrument to examine the crystal structures of minerals. I chose to study the crystal chemistry of gorceixite, grandidierite, and traskite with the Bruker X 8 single crystal X-ray diffractometer with a S M A R T A P E X C C D detector primarily because of the advancements of the S M A R T A P E X C C D detector over the former area or serial detectors (Bruker A X S 2000). The X 8 diffractometer with the S M A R T A P E X C C D detector has higher sensitivity, greater precision, resolution, accuracy and shorter collection times than other detectors for a number of reasons. First, the S M A R T A P E X C C D does not have a fiber optic taper, which eliminates spatial distortion and allows the collection of accurate and precise unit cell parameters. This allowed me to see changes in unit cell dimensions on the order of <0.1 A. Second, new electronics read the C C D chip at all four corners resulting in significantly shorter collection times at the same X-ray exposure time. The advancements of this instrument allowed me to collect large and very accurate data sets which allowed me to accurately refine the structures of gorceixite and grandidierite, and attempt to solve and refine the structure of traskite. 1 2.0 THE SYMMETRY AND CRYSTAL STRUCTURE OF GORCEIXITE, BaAl 3(P0 30,0H)2(0H) 6, A MEMBER OF THE ALUNITE SUPERGROUP 2.1 Introduction The Ba,Al-phosphate mineral gorceixite has been described from numerous localities and diverse parageneses worldwide. It occurs as a primary mineral in igneous rocks, an authigenie mineral and a resistate mineral in sediments and sedimentary rocks, a metamorphic mineral in schist, and as a supergene product in weathered iron ore. Examples from the more recent literature include the description by van Hees et al. (2002), who reported gorceixite inclusions in secondary phosphate minerals in carbonate-derived eluvial sediments at the Agr ium phosphate mine, Kapuskasing, Ontario. Baldwin et al. (2000) found gorceixite in brazilianite that replaced montebrasite in rare-element pegmatites in Namibia. Gorceixite has also been described as a replacement product in fossil bones in Brazil (Coutinho et al. 1999), and Rasmussen et al. (2000) pointed out that early-diagenetic phosphatic minerals, including gorceixite, are widespread in Australian shallow-marine sandstones of all ages. Schwab et al. (1990, 1991) synthesized end-member gorceixite [and arsenogorceixite, BaAl 3(As04)(As03-OH)(OH)6]. In natural gorceixite, partial substitution of B a by Sr or Ca is typical; among the rarely detected substitutions, Taylor et al. (1984) reported up to 4.7 wt% F, and Johan et al. (1995) found up to 0.6 mol V 3 + and 0.18 mol C r 3 + (18% of the G site). In the current IMA-approved nomenclature (Scott 1987), gorceixite is a member of the plumbogummite group of the alunite supergroup, which also includes the alunite, hinsdalite, and florencite groups. In members of the plumbogummite group, the T site is dominated by either A s 5 + or P 5 + , and S 6 + is <0.25 mol %, whereas minerals of the alunite group have (sensu stricto) have the T site dominated (> 0.75 mol %) by S 6 + . The primary distinction between the alunite supergroup and the jarosite supergroup rests on whether the proportion of A l is greater than that 2 of Fe or vice versa. O f the more than 25 CNMMN-approved members with A l > Fe, three have B a dominant at D; these are gorceixite, arsenogorceixite, and walthierite Bao.o5Do.5Ai3(S04)2(OH)6. The only other Ba-dominant minerals within the complete series are dussertite BaFe 3 (As0 4 )2 (OH) 6 , and springcreekite B a V 3 3 + [ ( O H , H 2 0 ) 6 ( P 0 4 ) 2 ] . Previous single-crystal X-ray studies of minerals in the alunite and jarosite supergroups have shown that all except a few crystallize in space group R 3m (Jambor 1999). Radoslovich and Slade (1980) determined that gorceixite is structurally similar to alunite, but that its true symmetry is monoclinic with a 12.216(2), b 7.033(2), c 7.046(5) A , and (3 125.4(1)°. The symmetry was observed to be strongly pseudo-trigonal, and to allow comparisons with chemically related minerals the structure was refined in space group i?3w,with a 7.0363(2) and c 17.2819(1) A , to an unweighted agreement factor of R\ = 0.053. Subsequently, the structure of a gorceixite sample from the same locality (Glen Al ice , N e w South Wales) was refined by Radoslovich (1982) to i?i = 0.031 in space group Cm, with a 12.195(8), b 7.040(5), c 7.055(5) A , P 125.19(5)°. The results showed two independent phosphate groups, both having point-group symmetry m but with quite different shapes. The authors stated that in contrast to crandallite, with reported structural formula CaAl 3 (P0 3 -(0 , /2(OH)!/2)2(OH) 6 (Blount 1974), the gorceixite structure accommodates an extra proton at only one apical oxygen site, and the formula B a A l 3 ( P 0 4 ) ( P 0 3 - O H ) ( O H ) 6 was therefore suggested. Blanchard (1989) collected powder X-ray diffraction data from a gorceixite sample from the B i g Fish River-Rapid Creek area in the Yukon Territory, and indexed the reflections in space groups Cm and R 3m, obtaining figures of merit F28 = 7 and 10, respectively. However, because eight out of the 28 reflections in the rhombohedral model had A20 values greater than 0.05°, it was suggested that this result "may be a clue that the [rhombohedral] space group assignment is in error." 3 Interest in the minerals of the alunite supergroup has surged in recent years because of the prominence of some of these minerals both as oxidation products of sulfide-bearing mine wastes and as precipitates from the resulting acidic effluents. Further environmental interest has also focused on the possibility of using these minerals as storage materials for toxic metals (Baron and Palmer 1996, Koli tsch and Pring 2001). As part of a more extensive study of the crystal chemistry of the alunite supergroup, I report here on the crystal structure of gorceixite. 2.2 Experimental The sample used in this study is from Location 1, Area A , Crosscut Creek, in the Rapid Creek area, Yukon Territory, Canada (Canadian Museum of Nature Mineral Collection no. 51269). The crystals occur as thin hexagonal plates that are optically uniaxial. A Philips X L 3 0 scanning electron microscope equipped with a Princeton Gamma-Tech energy-dispersion X-ray spectrometer was used to obtain qualitative chemical data. Compositional data were obtained with a C A M E C A SX-50 electron microprobe operated in the wavelength-dispersion mode. Operating conditions were as follows: accelerating voltage, 15 k V ; beam current, 10 nA; peak count time, 20 s; background count-time, 10 s; spot diameter (standards and specimen), 30 pm. Data reduction was done using the " P A P " <)>(pZ) method (Pouchou and Pichoir 1985). For the elements considered, the following standards, X-ray lines, and crystals were used: grossular, AlKa, T A P ; apatite, ?Ka, CaKa, PET; S r T i 0 3 , SrZa, T A P ; barite, B a l a , PET. Fluorine was sought but was not detected. The formula was calculated on the basis of two P (as recommended by Scott 1987) and seven H atoms. The results are reported in Table 2.1. For single-crystal X-ray diffraction measurements, a gorceixite plate was glued to a glass fiber. The instrument used was a Bruker X 8 A P E X diffractometer with graphite monochromated MoKa radiation. The data were obtained at room temperature to a maximum 29 value of 55.7°. 4 T A B L E 2.1. E L E C T R O N - M I C R O P R O B E C O M P O S I T I O N O F T H E G O R C E I X I T E S I N G L E -C R Y S T A L U S E D IN TH IS S T U D Y Point 1 Point 2 Point 3 P 2 0 5 (wt%) 27.02 27.03 28.79 A l 2 0 3 28.74 28.94 29.09 C a O 0.05 0.02 0.12 F e O 0.12 0.12 0.12 S r O 0.25 0.28 0.26 B a O 29.50 29.43 29.51 N a 2 0 0.17 0.17 0.17 H 2 0* 11.97 11.98 12.78 F 0.07 0.05 0.01 0=F -0.03 -0.02 0.00 T O T A L 97.86 98.00 100.85 P 5 + (apfu) 2.000 2.000 2.000 A l 3 + 2.962 2.981 2.813 C a 2 + 0.005 0.002 0.011 F e 2 + 0.009 0.009 0.008 Si2* 0.013 0.014 0.012 B a 2 + 1.011 1.008 0.949 N a + 0.029 0.029 0.027 H + 6.981 6.986 6.997 F 0.019 0.014 0.003 o2- 13.994 14.005 13.714 Note: Compos i t i ons were reca lcu la ted on the bas is of 2 ( P 5 + ) a toms per formula unit. *Determined by stoichiometry, assum ing 7 ( O H + F) per formula unit. 5 Data were collected in a series of and co scans in 0.50° oscillations with exposures of 7.0. The crystal-to-detector distance was 40 mm. O f the 14,812 reflections that were collected, 253 were unique (Rmt = 0.036). Data were collected and integrated using the Bruker S A I N T software package. The linear absorption coefficient, p, for MoKa radiation was 4.21 m m - 1 . Data were corrected for absorption effects using the multi-scan technique ( S A D A B S ) , with minimum and maximum transmission coefficients of 0.441 and 0.714, respectively. The data were corrected for Lorentz and polarization effects. A l l refinements were performed using the S H E L X T L crystallographic software package of Bruker A X S . Neutral-atom scattering factors were taken from Cromer and Waber (1974). Anomalous dispersion effects were included in Fca\c (Ibers and Hamilton 1964); the values for Af and A/ 7 ' were those of Creagh and McAuley (1992). The values for the mass attenuation coefficients were those of Creagh and Hubbell (1992). The \E -1] value of 0.772 indicated a non-centrosymmetric space group, and refinement was initiated in space group Cm using atomic positions from Radoslovich (1982). With all non-hydrogen atoms modeled anisotropically the refinement converged to an unweighted agreement factor of R\ = 0.0230. However, some of the atoms were non-positive definite, and the Flack x parameter was 0.48(3). The inverted structure was tested and an attempt was made to refine x as a full-matrix parameter using the T W I N and B A S F commands in S H E L X T L . However, this was unsuccessful and the conclusion was reached that Cm was not the correct space group. The structure was next refined in space group R3m, as had been done by Radoslovich and Slade (1980). However, 7?int was high at 0.17(3), there were 229 inconsistent equivalents, R\ = 0.0443, and the Flack x parameter was 0.46(4). It was concluded that R3m was not the correct space group either. 6 The structure was next refined in space group R 3 m using the atomic positions for jarosite from Menchetti and Sabelli (1976). A l l non-hydrogen atoms were refined anisotropically. The A site was initially fixed to full occupancy with Ba, resulting in Ri = 0.0318, but was subsequently allowed to refine. The final cycle of full-matrix least-squares refinement (least-squares function minimized: XwCF 0 2 - F c 2 ) 2 on F2) was based on 253 reflections and 29 variable parameters and converged (largest parameter shift was 0.00 times its esd) with Ri = 0.0231 and a weighted agreement factor of wi?2 = 0.0629. The standard deviation of an observation of unit weight was 1.365. The weighting scheme was based on counting statistics. The maximum and minimum peaks on the final difference Fourier map corresponded to 1.380 and -0.603 e 7 A 3 , respectively. Data collection and refinement parameters are summarized in Table 2.2, positional and displacement parameters in Table 2.3, and bond lengths and angles in Table 2.4. 2.3 Results The energy-dispersion spectra showed peaks corresponding only to those of the expected elements. The electron-microprobe compositions (Table 1) show only trace amounts of substituents and have reasonable totals. The crystal-structure refinement indicates that the atomic arrangement of gorceixite is similar to that of other members of the alunite-jarosite supergroups, e.g., crandallite (Blount 1974); dussertite (Kolitsch et al. 1999b); florencite-(Ce) (Kato 1990); goyazite (Kato 1971, 1987); kintoreite (Kharisun et al. 1997); plumbogummite (Kolitsch et al. 1999c); and springcreekite (Kolitsch et al. 1999a). The coordination polyhedra of cations in the gorceixite structure are shown in Figure 2.1. The atom at the A site, at special position 3b (0,0,'/2) is 7 T A B L E 2.2 G O R C E I X I T E : D A T A C O L L E C T I O N A N D S T R U C T U R E - R E F I N E M E N T I N F O R M A T I O N a (A) 7.0538(3) F 0 > 4 a F 0 253 c ( A ) . 17.2746(6) RM 0.036(3) V(A3) 744.36(5) L.s. parameters 29 S p a c e G r o u p R 3 M 0^°- 166) for F 0 > 4 o F 0 0.0231 Z 3 F?i for all un ique F0 0.0231 Crysta l s i ze (mm) 0.10 x 0.09 x 0.007 wR2 0 .0633 Radiat ion M o K a a (see Note) 0.0235 Monochromator graphite b (see Note) 7.97 Total F0 14812 G o o F (= S) 1.355 Unique F 0 253 Note: w = 1/ [a 2 (F 0 2 ) + (a x P)2 + b x P] where P = [Max ( F 0 2 , 0) + 2 x F c 2 ) ] /3 8 TABLE 2.3 ATOM PARAMETERS FOR GORCEIXITE Site sof x y z L/n* U22 U33 U,2 U23 A (Ba) 0.0735(5) 0 0 1/2 0.0119(3) 0.0119(3) 0.0165(4) 0.0059(1) 0 0 0.0134(2) G(AI) 0.25 1/2 0 0 0.0101(7) 0.0104(9) 0.0238(9) 0.0052(4) 0.0005(3) 0.0010(7) 0.0147(5) 7(P5 +) 0.16667 0 0 0.1987(1) 0.0099(6) 0.0099(6) 0.027(1) 0.0049(3) 0 0 0.0155(5) 01 0.5 0.5477(3) 0.4523(3) 0.1055(2) 0.013(1) 0.013(1) 0.026(1) 0.010(1) -0.0007(6) 0.0007(6) 0.0159(7) 02 0.16667 0 0 0.1082(3) 0.018(2) 0.018(2) 0.023(3) 0.0090(9) 0 0 0.020(1) OH 0.5 0.4600(3) 0.5400(3) 0.3058(2) 0.011(1) 0.011(1) 0.026(2) 0.004(1) 0.0026(6) -0.0026(6) 0.0172(7) H 0.5 0.530(4) 0.470(4) 0.278(5) 0.13(4) TABLE 2.4 SELECTED INTERATOMIC DISTANCES (A) AND ANGLES (°) FOR GORCEIXITE A - 0 1 a x 6 2.825(3) 0 1 a - A - 0 1 f x 6 106.87(6) - O H b x 6 2.859(3) - O l g x 6 73.13(6) <A-0> 2.842 - O H b x 12 124.44(5) - O H h x 12 55.56(5) G - 0 1 c x 2 1.914(3) - O H a x 6 79.19(9) - O H d x 4 1.902(1) - O H i x 6 100.81(8) <G-0> 1.906 O H b - A - O H f x 2 55.9(1) - O H g x 2 124.1(1) T - 0 1 e x 3 1.538(3) < 0 - A - 0 > 90.0 - 0 2 1.563(6) <T-0> 1.544 0 1 c - G - O H d x 4 92.1(1) - G - O H i x 4 87.9(1) O H - H 0.980(1) O H d - G - O H e x 2 89.6(2) H - 0 2 e 1.904(5) -OH j x 2 90.4(2) 0 H - 0 2 e 2.884(4) < 0 - G - 0 > 90.0 0 1 e - T - 0 1 k x 3 109.8(1) - 0 2 x 3 109.1(1) <0 -T -0> 109.5 O H - H - 0 2 C 179(8) Equivalent posi t ions: a = x - y + VS, x - VS, - z + 2A\ b = -x + VS, -y + 2A, - z + 2A\ c = y, -x + y, -z ; d = x - y + 2A, x - 2A, -z + "A; e = -x + 2A, -y + "A, - z + VS; f = y - 2A, -x + y -1/3, - z + 2A\ g = -y + 2A, x - y + Vs, z + VS; h = x - VS, y - 2A, z + VS; i = -x + y + VS, -x + 2A, z - VS; j = x + 1/S, y - VS, z - 1/S; k = y - 1/S, -x + y + 1/S, - z + VS. 10 Figure 2.1 Coordination polyhedra of cations in the gorceixite structure, projected onto (100). The atomic displacement ellipsoids represent 75% probability. 11 coordinated by six O atoms (from six separate PO4 groups) and six O H molecules to form an icosahedron. TheA-0 a n d ^ l - O H distances are 2.825 and 2.859 A (both x 6), respectively (mean 2.842 A), and the §-A-§ = unspecified anion) angles range from 55.9 to 124.44° (mean 90.0°). The bond-length and bond-angle distortion parameters (A and a 2 ; Hawthorne et al. 1989) are 0.0004 and 729.53, respectively, and the polyhedral volume is 55.64 A 3 . Electron-microprobe results indicate that the site is completely occupied by Ba, but the site occupancy refines to 88% B a (and 12% vacancy). Presumably this could be due to an inaccurate absorption correction and (or) scattering curve for Ba; however, Radoslovich (1982) reported a site occupancy of 96% B a (and 4% vacancy) in his Cm refinement. The bond-valence sum (Table 2.5) assuming complete occupancy by B a is 2.70 valence units; this improves to 2.38 valence units i f we assume partial occupancy, but it is important to note that B a compounds in general commonly give poor bond-valence sums (Brown and W u 1976). The atom at the G site, special position 9e ('/2,0,0), is coordinated by two O atoms (from two separate PO4 groups) and four O H molecules to form a distorted octahedron. The G - 0 and G - O H distances are 1.914 (x 2) and 1.902 A (x 4), respectively (mean 1.906 A), and the <j)-G-(|> angles range from 87.9 to 92.1° (mean 90.0°). The O - O H and O H - O H edge lengths are 2.649 and 2.746, and 2.681 and 2.698 A , respectively. The bond-length and bond-angle distortion parameters are 0.00005 and 2.993, respectively. The variance in the octahedron angle is 3.15, the mean octahedral quadratic elongation (Robinson et al. 1971) is 1.0009, and the polyhedral volume is 9.21 A 3 . Electron-microprobe compositions, refined site-occupancy, and bond-valence analysis indicate that the site is completely occupied by A l . The atom at the T site, at special position 6c (0,0, z), is coordinated by three atoms at the 01 site and one at the 0 2 site that together form a tetrahedron. The 7 -01 and 7 - 0 2 distances are 1.538 (x 3) and 1.563 A respectively. The 0 1 - 7 - 0 1 angles are 109.8° and the 12 T A B L E 2.5 B O N D - V A L E N C E * ANALYSIS OF GORCEIXITE Site A ( B A 2 + ) G(ALi+) H ^ \ 01 0.24 x 6 l 0 . 4 9 x 2 ^ 1 . 2 0 x 3 4 1.92 0 2 1.12 0.08 x 3 -> 1.34 OH 0 . 2 1 x 6 ^ 0 . 5 1 x 4 4 x 2 ^ 0.92 2.15 Total 2.70 3.01 4.70 1.00 Calculated from the bond-valence parameters of Brese and O'Keeffe (1991). 13 0 1 - 7 - 0 2 angles are 109.1° (each x 3; mean 109.5°). The bond-length and bond-angle distortion parameters are 0.0002 and 0.125, respectively. The variance in the tetrahedron angle is 0.1448, the mean tetrahedral quadratic elongation is 1.0001, and the polyhedron volume is 1.89 A3. Although the bond-valence sum of 4.70 valence units is somewhat low, the E D S spectra, electron-microprobe compositions, and refined site-occupancy indicate that the site is completely occupied by P 5 + . The mean P - 0 1 , 0 2 distance of 1.544 A is slightly longer than the <P-<j)> (<j> = unspecified anion) distance of 1.537 A reported by Baur (1974) and Huminicki and Hawthorne (2002). The H atom site (at special position 18/z, x, -x, z) was identified from a difference-Fourier map. Without constraints the O H - H distance refined to a distance of -0.85 A; this was considered unrealistically short and subsequently the distance was constrained to 0.98 A. The high standard deviations associated with the positional and isotopic displacement parameters are most likely an artefact of the absorption correction. The interatomic distances and bond-valence analysis suggests that each 0 2 atom is involved in hydrogen bonding (as an acceptor) with three different O H groups; the H - 0 2 distance is 1.904 A, the O H - 0 2 distance is 2.884 A, and the O H - H - 0 2 angle is close to linear (179°). The low bond-valence sum of 1.34 valence units for 0 2 suggests that 0 2 acts not only as an acceptor, but also as a donor. However, no hydrogen-atom sites could be identified from the difference-Fourier map. In terms of possible acceptors, there are three 01 sites at distances of 2.527 A from each 0 2 position, and one 0 2 site at the same distance from each 01 position, so presumably an oxygen atom at 01 could act as an acceptor (this would also help improve the somewhat low bond-valence sum to 01 of 1.92 valence units). Given the relatively short donor-acceptor distance and the r - 0 2 - 0 1 angle of 35.1°, the hypothetical 0 2 - H - - 0 1 angle would be expected to be relatively sharp. Although it is beyond the scope of this study, it would be 14 interesting to see i f this hypothetical hydrogen-bonding scheme is detectable in spectrographic studies of gorceixite. The infrared spectrum for gorceixite from the Kovdor massif in Russia shows a broad band at 1680 cm"1 that might indicate the presence of H 2 0 (Liferovich et al. 1999). The presence of O H groups at the 0 2 site would also help resolve the problem of charge balance. If the cation sites are fully occupied with Ba, A l , and P, the total charge is +21. Assuming O at all 01 and 0 2 sites, and O H at the O H site, the total negative charge is -22. This may be resolved by assuming that the 0 2 site is half-occupied by O and half-occupied by O H , which would lead to a general formula for gorceixite of BaAl3(P030,OH)2(OH)6. The topology of the gorceixite structure is the same as that of other members of the plumbogummite group. The Al 3 +02(OH)4 octahedra share corner O H atoms to form sheets perpendicular to the c axis (Figure 2.2). The O H groups form a plane roughly parallel to (001). The 01 atoms lie on opposite sides of the O H layers. The octahedra form six- and three-membered rings, and the three apical 01 atoms from each triad of octahedra form the base of a PO4 tetrahedron. Additional octahedral sheets are located in such a way that two triads of O H ions enclose a site wherein the 12-coordinated B a ion is located (Figure 2.2). The apical 0 2 atoms on each of the PO4 tetrahedra point alternately up and down the c axis, and project into the six-membered rings of octahedral hydroxyl groups. Each 0 2 atom forms weak hydrogen bonds with the three closest hydroxyl groups. The smallest 0 2 - 0 2 distance of 3.74 A is not only contrary to Blount's (1974) structure for crandallite, but also precludes hydrogen bonding between atoms at these sites in members of the plumbogummite group. 15 Figure 2.2 The gorceixite structure projected onto (a) (100) and (b) (001), showing AI 3 +0 2(OH) 4 octahedra, P 0 4 tetrahedra, H atoms (large spheres), and Ba atoms (ellipsoids). The atomic displacement ellipsoids represent 50% probability. 16 2.4 Discussion Although R 3m is the most appropriate space group for the gorceixite studied here I do not claim that all gorceixite samples or all minerals of the alunite supergroup crystallize in this space group. Several exceptions are known, and a recent example is that Gottlicher and Gasharova (1999) observed split reflections (except 00/) in X-ray powder patterns of synthetic jarosite crystals, indicating deviation from trigonal symmetry. Reflections and intensities indicated monoclinic C2/m when an ortho-hexagonal cell was chosen, and P deviated slightly from 90°. A dependance of P on composition was thought likely because the K-free end-member of the solid-solution series (K,H30)Fe3(S04)2(OH)6 showed no splitting. For the K- r i ch members the observed deviation was less than 1°. A l l synthesized samples of K- r i ch jarosite were deficient in Fe, and in none did K fully occupy the A site. Increasing synthesis temperature was said to reduce the deviation of P from 90°. A n explanation for the non-stoichiometry, which is common in synthetic jarosite-type compounds, and for the deviation from trigonal symmetry was not given. Gottlicher et al. (2000) refined the crystal structure of synthetic jarosite in both R 3m (to R\ = 0.025) and C2/m (to R\ = 0.028) and concluded that there was a significantly better agreement of symmetrically equivalent reflections for the latter. It was suggested that additional protons in the structure, perhaps to charge-balance the Fe deficiency, might be responsible for the reduction in symmetry. The gorceixite sample studied by Radoslovich and Slade (1980) and Radoslovich (1982) is from a different locality than the one studied here. The composition is also different, with 96% Ba at the A site (as opposed to 88% in our sample) and 2.3 wt. % F. Different parageneses and compositions might be responsible for the lowered symmetry, although the mechanism remains unclear. The question of the symmetry of minerals of the alunite supergroup has yet to be answered and w i l l require more work. 17 3.0 THE GEOMETRIC EFFECTS OF V F E 2 + FOR V M G SUBSTITUTION ON THE CRYSTAL STRUCTURES OF THE GRANDIDIERITE-OMINELITE SERIES 3.1 Introduction Grandidierite, ( M g , F e 2 + ) A l 3 B S i 0 9 , (Lacroix 1902; M c K i e 1965; Stephenson and Moore 1968) and its Fe 2 +-dominant analog ominelite, ( F e 2 + , M g ) A l 3 B S i 0 9 (Hiroi et al. 2002), form a continuous series in which Fe substitutes for M g at a five-fold coordinated site. This relatively simple solid solution series offers an unusual opportunity to study the changes in bond lengths and angles in a structure in which Fe = M g substitution is restricted to a single site and other compositional variations are much subordinate. Few other minerals (e.g., farringtonite, graftonite, joaquinite, vesuvianite, werdingite, yoderite) are known to contain v M g or v F e 2 + , but in some of these the substitution is complicated by the presence of other constituents. We undertook this study to characterize the geometric effects of of v F e 2 + for v M g substitution on the crystal structures of the grandidierite-ominelite series, and to investigate the reasons for the apparent rarity of v M g and v F e 2 + in minerals. 3.2 Background Grandidierite and ominelite are relatively high-temperature, low-pressure minerals (mostly 500-800 °C, 0.3-7 kbar). These P-T estimates are consistent with preliminary experimental data on the stability range for end-member grandidierite: Werding and Schreyer (1996) reported that its upper pressure stability limit is roughly coincident with that of sillimanite under nearly anhydrous conditions, but that this limit is shifted to lower pressures under excess-FLO 18 conditions. Grandidierite is found in granulite-facies pegmatites, migmatites, and regionally and contact metamorphosed pelitic and calcareous rocks at approximately 40 localities worldwide (e.g., Grew 1996; Grew et al. 1998a). The type locality for ominelite is a porphyritic granite in Japan, but compositions with Fe > M g have also been reported from a pegmatite at Almgjotheii, Norway [X= Fe/(Fe + Mg) = 0.50-0.81, Huijsmans et al. 1982; Grew et al. 1998a], hornfels at Morton Pass, Wyoming (X = 0.58, Grant and Frost 1990) and at Bellerberg, Eifel , Germany (X~ 0.5, Blass and Graf 1994), and in a regional aureole at Mt . Stafford, Australia (X = 0.50-0.55, calculated from Greenfield et al. 1998). Grandidierite and ominelite belong to the family of B - A l - S i phases that includes boralsilite, synthetic Alg[(Al,B)i2B4]033, and werdingite, all o f which have structures based on chains of edge-sharing A l octahedra parallel to a lattice translation of ca. 5.6 A (c in grandidierite and ominelite). According to Peacor et al. (1999), the phases in this family differ from one another in the nature of the polyhedral units that cross-link the chains of A1G*6 octahedra. Fivefold coordination polyhedra are a common building block in the cross-linking units. In grandidierite 2+ and ominelite these units are (Mg,Fe )Os and AIO5 polyhedra, Si04 tetrahedra, and BO3 2"F triangles (Figures 3.1 and 3.2). The (Mg,Fe )Os polyhedron is a distorted trigonal bipyramid about the MgFe site, in which the long axis, which is defined by nearly parallel M g F e - 0 2 and M g F e - 0 5 bonds, is approximately parallel to b. The other polyhedron of the dimer is an approximately trigonal bipyramid about the A13 site. The (Mg,Fe )Os and A I 3 O 5 polyhedra and A106 octahedra all have some edges that are shared. Each (Mg,Fe )Os polyhedron shares two 0 2 - 0 6 edges with two different A l l 0 6 octahedra and one 0 1 - 0 5 edge with an A B O 5 polyhedron. A l l 0 6 octahedra share two 0 2 - 0 3 edges with two adjacent A l l 0 6 octahedra and two 0 2 - 0 6 edges with (Mg,Fe 2 + )Os polyhedra. Every A1206 octahedron shares two 0 4 - 0 5 edges with other A1206 octahedra and two 0 5 - 0 7 19 re 3.1 Projection of the crystal structure of grandidierite and ominelite onto (001). The atomic displacement ellipses represent 99% probability. The z coordinates * 100 are given for each cation. 20 Figure 3.2 Coordination polyhedra for the cations in the grandidierite-ominelite structure. Orientations were chosen to give the best view of the atoms and bonds. The diagrams are in perspective with a view distance of 50 cm. The atomic displacement ellipsoids represent 90% probability. edges with A130s polyhedra. Finally, all A B O 5 polyhedra share one 0 1 - 0 5 edge with an (Mg,Fe 2 +)05 polyhedron and two 0 5 - 0 7 edges with A1206 octahedra. It is interesting to note that in this case all of the shared edges meet at the same 0 5 atom at one end of the trigonal bipyramid. Olesch and Seifert (1976) were the first to study the effects of increasing X on the crystallographic properties of grandidierite, including both synthetic and natural samples. They reported that b shows a strong positive correlation with X, whereas a and c remain essentially constant; therefore the expansion of the unit cell is anisotropic, and leads to increasing distortion of the (Mg,Fe 2 +)05 polyhedron. Seifert and Olesch (1977) studied the Mossbauer spectrum of grandidierite and reported that the degree of distortion of the coordination polyhedron around the MgFe site can also be inferred from the hyperfine parameters. Farges (2001) collected Fe-Kedge X A F S spectra from eight grandidierite samples from Madagascar and Zimbabwe. The pre-edge spectra were consistent with dominantly five-coordinated F e 2 + . Analysis of the X A N E S and E X A F S spectra confirmed that F e 2 + substitutes for M g in grandidierite with a slight expansion (~2%) of the local structure around M g . In addition, Fe was detected in some samples (5-10 mol% of total Fe); based on theoretical calculations of the E X A F S region this was thought to be located at the five-coordinated MgFe sites or the most distorted six-coordinated A l positions (depending on the sample studied). 3.3 Experimental Seven samples covering a range of compositions (Table 3.1) were investigated in this study. Compositional data were obtained from the same crystals used for the crystal structure study (except for G8, which was lost during the preparation stage) with a C A M E C A SX-50 22 T A B L E 3.1 S A M P L E I N F O R M A T I O N F O R G R A N D I D I E R I T E A N D O M I N E L I T E G 1 7 G 8 G 4 G 1 2 G1 G 2 G 9 Local i ty S o u r c e S a m p l e number C o l o r R e f e r e n c e s M a d a g a s c a r R o y a l Ontar io M u s e u m 3 2 8 0 6 t ransparent Long L a k e , L a r s e m a n n Hil ls, An ta rc t i ca H . -M . B r a u n 6 3 tu rquo ise S t u w e et a l . (1989), C a r s o n et a l . (1995), G r e w e t a l . (1998b) S a h a k o n d r a , A m p a m a t o a , M a d a g a s c a r Harvard 108118 light b lue Z i m b a b w e C a n a d i a n M u s e u m of Nature 80693 dark blue G r e w et a l . (1997) Kar ibe a rea , Z i m b a b w e Smi thson ian 144869 green-b lue G r e w et a l . (1997) A n d r a h o m a n a , M a d a g a s c a r M u s . Nat. Hist. Naturel le 102.149 turquoise G r e w et a l . (1998a) Almgjothei i , R o g a l a n d , Norway E S G A i m 8a med ium blue G r e w et a l . (1998a) electron microprobe operated in the wavelength-dispersion mode. Operating conditions were as follows: accelerating voltage, 15 k V ; beam current, 10 nA; peak count time, 20 s; background count-time, 10 s; spot diameter (standards and specimen), 10 pm. Data reduction was done using the " P A P " <KpZ) method (Pouchou and Pichoir 1985). For the elements considered, the following standards, X-ray lines, and crystals were used: P (apatite, Ka, PET) , S i and M g (diopside, Ka, T A P ) , A l (kyanite, Ka, PET) , Cr ( M g C r 2 0 4 , Ka, L i F ) , M n ( M n S i 0 3 , Ka, L i F ) , Fe (Fe2Si0 4 , Ka, L i F ) , and Z n (gahnite, Ka, L iF ) . Formulas were calculated on the basis of six cations and nine O atoms per formula unit (Table 3.2). Three of the samples ( G l , G2, G4, and G8) were large enough to provide sufficient material for study by powder X-ray diffraction. Each sample was first ground into fine powder using an alumina mortar and smeared onto a glass slide. Data were collected over the range 10-80° 20 with CoKa radiation on a standard Siemens (Bruker) D5000 Bragg-Brentano diffractometer equipped with a Vantec-1 strip detector, 0.6 mm (0.3°) divergence and antiscatter slits, and incident- and diffracted-beam Soller slits. The long fine-focus Co X-ray tube was operated at 35 k V and 40 m A , using a take-off angle of 6°. The X-ray diffraction pattern was analyzed using the I C D D (International Centre for Diffraction Data) database PDF-4 using search-match software supplied by Siemens (Bruker). Ce l l dimensions were determined using X-ray powder-diffraction data fitted with the LeBa i l method and the Rietveld program Topas 3.0 (Bruker A X S ) in space group Pbmn. Starting values for cell dimensions were taken from Stephenson and Moore (1968), and the results are listed in Table 3.3. For single-crystal X-ray diffraction measurements, the crystals were ground to approximate spheres using both an Enraf Nonius FR512 sphere grinder and a grinder made at U B C following the description in Cordero-Borboa (1985). Data were collected at C - H O R S E (the Centre for Higher Order Structure Elucidation, in the Department of Chemistry at U B C ) using a Bruker X 8 24 T A B L E 3.2 A V E R A G E E L E C T R O N - M I C R O P R O B E C O M P O S I T I O N S O F G R A N D I D I E R I T E A N D O M I N E L I T E C R Y S T A L S U S E D IN T H E S I N G L E - C R Y S T A L X - R A Y D I F F R A C T I O N S T U D Y G17 G8 G4 G12 G1 G2 G9 n 7 4 4 5 4 4 3 P 2 0 5 bdl 0.24(5) bdl 0.07(5) 0.19(6) 0.08(3) bdl S i 0 2 20.26(6) 19.88(4) 20.12(19) 19.77(9) 19.53(9) 19.49(10) 19.57(4) B 2 0 3 * 11.91(2) 11.78(3) 11.84(3) 11.64(2) 11.57(3) 11.41(2) 11.33(3) A l 2 0 3 52.01(20) 50.74(15) 51.65(27) 50.68(10) 50.18(10) 49.63(11) 48.93(3) C r 2 0 3 bdl 0.34(5) bdl bdl bdl bdl bdl F e 2 0 3 1.03(5) 1.62(19) 1.35(41) 1.38(29) 1.62(11) 1.09(15) 1.21(45) M g O 13.71(5) 11.99(8) 11.35(5) 10.02(7) 9.06(8) 7.30(3) 6.22(6) M n O bdl bdl 0.06(3) 0.08(3) 0.08(2) bdl bdl F e O 0.01(2) 2.81(23) 3.73(33) 5.78(29) 7.39(7) 10.36(15) 11.95(19) Z n O bdl bdl bdl bdl bdl bdl 0.23(5) T O T A L 99.00(18) 99.46(27) 100.17(24) 99.45(18) 99.70(27) 99.48(22) 99.60(33) p5+ - 0.01(0) - 0.00(0) 0.01(0). 0.00(0) -S i 4 + 0.99(0) 0.98(0) 0.98(1) 0.98(0) 0.98(0) 0.99(0) 1.00(0) B 3 + 1.00 1.00 1.00 1.00 1.00 1.00 1.00 A l 3 + 2.98(1) 2.94(0) 2.98(1) 2.97(0) 2.96(1) 2.97(1) 2.95(2) C r 3 + - 0.01(0) - - - - -F e 3 + 0.04(0) 0.06(1) 0.05(2) 0.05(1) 0.06(0) 0.04(1) 0.05(2) M g 2 + 0.99(0) 0.88(0) 0.83(0) 0.74(1) 0.68(0) 0.55(0) 0.47(0) M n 2 + - - 0.00(0) 0.00(0) 0.00(0) - -F e 2 + 0.00(0) 0.12(1) 0.15(1) 0.24(1) 0.31(0) 0.44(1) 0.51(1) Z n 2 + - - - - - - 0.01(0) XEMPA* 0.00(0) 0.12(1) 0.16(1) 0.25(1) 0.32(0) 0.45(0) 0.52(1) S^REF* 0.024(1) 0.126(2) 0.184(4) 0.273(2) 0.336(2) 0.450(2) 0.522(2) Note: T h e G8 crysta l w a s lost s u b s e q u e n t to S R E F data co l lect ion; the a n a l y s e s we re obta ined from a crystal f rom the s a m e samp le . C o m p o s i t i o n s were reca lcu la ted on the b a s i s of 6 ca t ions and 9 O apfu. T i , C a , N a , and K w e r e sough t but not de tec ted . bdl = be low detect ion limit ( a s s u m e d to be 0.05 ox ide wt%). *Determined by sto ich iometry. ^EMPA = ( F e 2 + + M n + Z n ) / ( F e 2 + + M n + Z n + Mg) . %REF = F e / ( F e + Mg) . 25 A P E X diffractometer with graphite-monochromated MoKa radiation and a C C D detector. Data were collected in a series of § and co scans in 0.50° oscillations with exposure times of 15.0 s. The crystal-to-detector distance was 40 mm. Data were collected and integrated using the Bruker S A I N T software package and were corrected for absorption effects using the multi-scan technique ( S A D A B S ) and for Lorentz and polarization effects. A l l refinements were performed using the S H E L X T L crystallographic software package of Bruker A X S . Neutral-atom scattering factors were taken from Cromer and Waber (1974). Anomalous dispersion effects were included in F c a i c (Ibers and Hamilton 1964); the values for Af and Af" were those of Creagh and McAuley (1992). The values for the mass attenuation coefficients were those of Creagh and Hubbell(1992). The structures were refined in space group Pbnm (a non-standard setting of Prima, verified by the presence or absence of reflections in the full set of intensities) using the atom positions for grandidierite in Stephenson and Moore (1968). A n extinction parameter was refined, and all atoms were refined anisotropically. Refinement was done using full-matrix least-squares in 9 9 9 9 which the minimized function was Xw(.F 0 -Fc) on F~. The weighting scheme was based on counting statistics. The total occupancy factors of the three A l sites were refined to test the possibility of (Al ,Fe 3 + ) solid solution, as suggested by the electron microprobe compositions. The results ranged from 0.487(2) to 0.494(2) for A l l , 0.490(2) to 0.499(2) for A12, and 0.488(2) to 0.498(2) for A13, which would normally be indicative of a small degree of substitution. We then attempted to refine for Fe at the A l sites, but were unsuccessful, l ikely because the amounts of Fe (as indicated by the electron microprobe compositions) are so small. Accordingly, the occupancies of all three A l sites were fixed (at 1.0 A l atom each) in the final cycles of refinement. 26 In order to estimate the accuracy of unit-cell parameters obtained with our single-crystal diffractometer we also collected a data set from a single-crystal of " I U C r " ruby, for which Wong-Ng et al. (2001) give unit-cell dimensions of a = 4.7608(3) and c = 12.9957(9) A. Data collection and refinement parameters are summarized in Table 3.3, observed and, positional parameters in Table 3.4, displacement parameters in Table 3.5, bond lengths and angles in Table 3.6, polyhedral edges in Table 3.7, and polyhedral volumes and distortion parameters in Table 3.8. 3.4 Results 3.4.1. Electron microprobe analyses Average electron microprobe analyses ( E M P A ) of the crystals used in the structure refinement (SREF) study are given in Table 3.2. The calculated average Fe compositions (0.04-0.06 apfu) are very low and the Fe atoms are presumably randomly distributed between all three A l sites, which is most likely why we were unable to refine for Fe at these sites in the SREF study. The electron microprobe compositions show low concentrations of M n that attain a maximum of 0.14 wt% M n O (-0.01 M n apfu) in sample G12. Samples G8 and G l contain up to 0.31 and 0.24 wt% P2O5, respectively, corresponding to -0.01 P apfu; G8 also shows up to 0.42 wt% Cr203 (0.02 Cr apfu). The significance of P and Cr is unknown; presumably the former would substitute for Si at the Si position, and the latter for A l at one of the A l sites. Sample G9 27 T A B L E 3.3 D A T A M E A S U R E M E N T A N D R E F I N E M E N T I N F O R M A T I O N F O R G R A N D I D I E R I T E A N D O M I N E L I T E G 1 7 G 8 G 4 G 1 2 G1 G 2 G 9 S S C X R D * (A) 10.3640(4) 10.3529(7) 10.3590(3) 10.3660(9) 10.3643(5) 10.3631(4) 10.3675(5) frsCXRD (A) 10.9995(5) 10.9971(7) 11.0147(3) 11.0296(9) 11.0438(4) 11.0627(5) 11.0873(6) CsCXRD (A) 5.7805(2) 5.7754(4) 5.7762(2) 5.7790(5) 5.7800(3) 5.7778(2) 5.7879(3) VsCXRD (A ) 658.98(6) 657.5(1) 659.07(4) 660.7(1) 661.58(7) 662.39(8) 665.30(8) SpXRDt (A) 10.3330(2) 10.3317(2) 10.3360(2) 10.3403(2) fcpXRD (A) 10.9858(4) 10.9904(3) 11.0148(4) 11.0332(3) CpXRD (A) 5.7667(3) 5.7634(2) 5.7657(2) 5.7655(2) VPXRD (A3) 654.62(4) 654.44(3) 656.41(3) 657.77(3) S p a c e g roup Pbnm Pbnm Pbnm Pbnm Pbnm Pbnm Pbnm Z 4 4 4 4 4 4 4 Crys ta l s i z e (mm) 0.28 x 0.27 x 0.26 x 0.26 x 0.25 x 0.20 x 0.14 x 0.14 x 0.32 x 0.26 x 0.24 x 0.24 x 0.32 x 0.25 x 0.24 0.24 0.20 0.20 0.20 0.18 0.25 Rad ia t ion MoKoc MoKa MoKa MoKa MoKa MoKa MoKa M o n o c h r o m a t o r graphi te graphi te graphite Graph i te graphite graphite graphi te Tota l F0 13314 16164 13534 13867 18782 17377 14875 Un ique F0 902 900 901 908 901 906 898 F0 > 4 o F 0 869 870 854 833 894 882 873 0.021(9) 0.03(1) 0.02(1) 0.03(1) 0.023(8) 0.023(9) 0.022(9) L.s. pa ramete rs 87 87 87 87 87 87 87 for F0 > 4 a F0 0.0163 0 .0166 0.0211 0 .0205 0.0164 0.0141 0.0168 Ri, al l un ique F 0 0.0169 0.0172 0.0223 0 .0225 0.0166 0.0145 0.0173 W/R2 0.0502 0 .0500 0.0584 0.0555 0.0485 0.0412 0.0466 a 0 .0236 0 .0237 0 .0285 0.0276 0.0218 0.0233 0.0267 b 0.45 0.44 0.65 0.58 0.38 0.23 0.32 G o o F (= S) 1.223 1.228 1.173 1.140 1.331 1.154 1.161 Note: w = 1 / [a 2 (F 0 2 ) + (a x P ) 2 + b x P] whe re P = [Max (F 0 2 , 0) + 2 x F c 2 ) ] /3 *S ing le -c rys ta l X - ray diffraction da ta . f P o w d e r X - ray diffraction da ta . T A B L E 3.4 A T O M I C P A R A M E T E R S F O R G R A N D I D I E R I T E A N D O M I N E L I T E G 1 7 G 8 . G 4 G 1 2 G1 G 2 G 9 M g F e X 0.09183(6) 0.09262(5) 0.09293(6) 0.09348(5) 0.09387(4) 0.09438(3) 0.09462(3) y 0.21910(5) 1/ 0.21906(5) v 0.21903(5) v. 0.21897(5) V. 0.21896(4) VA 0.21894(3) VA 0.21896(3) % O c c . z M g / 4 0.488(1) 74 0.437(1) / 4 0.409(2) 74 0.363(2) / 4 0.333(1) / 4 0.275(1) 0.239(1) F e 0.012(1) 0.063(1) 0.091(2) 0.137(2) 0.167(1) 0.225(1) 0.261(1) AI1 X 0 0 0 0 0 0 0 y 0 0 0 0 0 0 0 z 0 0 0 0 0 0 0 AI2 X 1/2 72 % 1/2 1/2 1/2 1/2 y 0 0 0 0 0 0 0 z 0 0 0 0 0 0 0 AI3 X 0.22634(5) 0.22643(5) 0.22643(6) 0.22641(6) 0.22643(5) 0.22648(4) 0.22649(5) y 0.44792(4) v 0.44799(4) 17 0.44795(6) V. 0.44796(5) VA 0.44807(4) VA 0.44810(4) % 0.44811(4) y* Si z X / 4 0.43356(5) 74 0.43370(5) / 4 0.43377(6) 74 0.43394(5) / 4 0.43406(5) 0.43423(4) 0.43431(5) y 0.26330(4) v 0.26325(4) 1/ 0.26334(5) v. 0.26340(5) V. 0.26340(4) % 0.26343(3) 1/4 0.26345(4) % B z X / 4 0.2512(2) / 4 0.2512(2) / 4 0.2512(2) 74 0.2511(2) 0.2512(2) 0.2512(2) 0.2510(2) y 0.0003(2) 0.0004(2) 0.0004(2) 0.0002(2) 0.0003(2) 0.0002(1) 0.0003(2) z 3 /4 % % 3/4 3/4 3/4 3/4 0 1 X 0.2750(1) 0.2756(1) 0.2755(1) 0.2758(1) 0.2761(1) 0.2763(1) 0.2765(1) y 0.2882(1) v 0.2883(1) v. 0.2888(1) v. 0.2892(1) V. 0.2891(1) VA 0.28964(9) Vt 0.2898(1) Vi 0 2 z X / 4 0.1186(1) 74 0.1183(1) / 4 0.1184(1) . 74 0.1183(1) / 4 0.11818(9) 0.1182(1) 0.1181(1) y 0.0224(1) 1/ 0.0222(1) v 0.0216(1) v. 0.0214(1) V. 0.0214(1) VA 0.02087(9) VA 0.0205(1) Vi 0 3 z X / 4 0.1210(1) / 4 0.1211(1) 74 0.1212(2) 74 0.1209(1) / 4 0.1210(1) / 4 0.1210(1) 0.1211(1) y -0.0035(1) -0.0033(1) -0.0036(1) -0.0037(1) -0.0036(1) -0.00373(8) -0.0037(1) z 3/4 % 3/4 3/4 3/4 3/4 3/4 0 4 X 0.4738(1) 0.4738(1) 0.4739(2) y •7 0.1199(1) 0.1202(1) VA 0.1201(1) VA 0 5 X / 4 0.5465(1) / 4 0.5465(1) / 4 0.5463(1) y 0.1002(1) 0.0999(1) 0.0997(1) z 3/4 3 / 4 3 /4 0 6 X -0 .00731(8) -0.00755(8) -0.00720(9) y 0.17099(8) 0.17090(8) 0.1708(1) z -0.0227(2) -0.0227(2) -0.0225(2) 0 7 X 0.18068(9) 0.18059(9) 0.1807(1) y 0.50112(7) 0.50118(7) 0.50117(9) z -0 .0452(2) -0.0452(2) -0.0453(2) o 0.4738(1) 0.1203(1) 1 /4 0.5464(1) 0.0992(1) 3 / 4 -0.00728(9) 0.1707(1) -0.0228(2) 0.1807(1) 0.50113(9) -0.0455(2) 0.4739(1) 0.1205(1) 1 /4 0.5465(1) 0.0988(1) -0.00724(8) 0.17053(8) -0.0228(2) 0.18054(9) 0.50112(7) -0.0452(2) 0.4738(1) 0.12070(9) % 0.54644(9) 0.09836(9) 3 / 4 -0.00717(6) 0.17035(7) -0.0231(1) 0.18067(7) 0.50109(6) -0.0454(1) 0.4740(1) 0.1208(1) % 0.5464(1) 0.0981(1) 3 /4 -0.00700(8) 0.17034(8) -0.0231(1) 0.18070(8) 0.50115(7) -0.0453(2) T A B L E 3.5 A T O M I C D I S P L A C E M E N T P A R A M E T E R S F O R G R A N D I D I E R I T E A N D O M I N E L I T E ( F O R D E P O S I T ) G 1 7 G 8 G 4 G 1 2 G1 G 2 G 9 M g F e Uu 0.0083(3) 0.0080(3) 0.0125(3) 0.0098(3) 0.0079(2) 0.0084(2) 0.0094(2) U22 0.0063(3) 0.0065(3) 0.0102(3) 0.0078(3) 0.0063(2) 0.0066(2) 0.0079(2) Uzz 0.0064(3) 0.0062(3) 0.0086(3) 0.0070(3) 0.0060(2) 0.0067(2) 0.0071(2) UM -0 .0013(2) -0.0013(2) -0.0017(2) -0.0017(2) -0.0016(1) -0.0016(1) -0.0017(1) Wis 0 .00000 0 .00000 0 .00000 0.00000 0.00000 0 .00000 0 .00000 U23 0.00000 0 .00000 0 .00000 0.00000 0.00000 0 .00000 0 .00000 ueq 0.0070(2) 0.0069(2) 0.0105(2) 0.0082(2) 0.0067(2) 0.0072(1) 0.0081(1) AI1 0.0057(3) 0.0056(3) 0.0087(3) 0.0065(3) 0.0051(3) 0.0054(2) 0.0060(3) u22 0.0052(3) 0.0057(3) 0.0084(3) 0.0066(3) 0.0056(3) 0.0058(2) 0.0071(2) 0.0051(3) 0.0048(3) 0.0064(3) 0.0050(3) 0.0040(3) 0.0047(2) 0.0051(3) UM 0.0001(2) 0.0001(2) 0.0002(2) 0.0002(2) 0.0001(1) 0.0002(1) 0.0002(2) UM -0 .0002(2) -0.0002(2) 0.0000(2) -0.0000(2) -0.0002(2) -0.0001(2) -0.0002(2) U23 0.0000(2) 0.0001(2) 0.0000(2) -0.0001(2) 0.0001(2) 0.0000(1) 0.0000(2) 0.0053(1) 0.0054(1) 0.0078(2) 0.0060(2) 0.0049(1) 0.0053(1) 0.0061(1) AI2 Uu 0.0048(3) 0.0047(3) 0.0079(3) 0.0057(3) 0.0042(3) 0.0045(2) 0.0053(3) U22 0.0066(3) 0.0068(3) 0.0097(3) 0.0077(3) 0.0070(3) 0.0073(2) 0.0084(3) u33 0.0053(3) 0.0049(3) 0.0066(3) 0.0048(3) 0.0041(3) 0.0049(2) 0.0050(3) UM -0 .0001(2) -0.0002(2) -0.0001(2) -0.0000(2) -0.0001(2) -0.0002(1) -0.0002(2) U^ 0.0002(1) 0.0003(2) 0.0002(2) 0.0002(2) 0.0003(2) 0.0001(2) 0.0002(2) u23 0.0005(2) 0.0005(2) 0.0005(2) 0.0005(2) 0.0006(2) 0.0006(1) 0.0006(2) Ue, 0.0054(1) 0.0054(1) 0.0081(2) 0.0061(2) 0.0051(1) 0.0056(1) 0.0063(1) AI3 Uu 0.0049(2) 0.0044(2) 0.0082(3) 0.0058(3) 0.0041(2) 0.0043(2) 0.0053(2) U22 0.0057(2) 0.0060(3) 0.0098(3) 0.0072(3) 0.0062(2) 0.0065(2) 0.0079(2) Un 0.0056(2) 0.0049(2) 0.0074(3) 0.0054(3) 0.0043(2) 0.0051(2) 0.0053(2) UM -0 .0003(2) -0.0004(2) -0.0002(2) 0.0000(2) -0.0003(2) -0.0003(1) -0.0003(2) Un 0.00000 0 .00000 0.00000 0.00000 0.00000 0.00000 0 .00000 U23 0.00000 0 .00000 0 .00000 0.00000 0.00000 0.00000 0 .00000 ueq 0.0054(1) 0.0051(1) 0.0085(2) 0.0061(2) 0.0049(1) 0.0053(1) 0.0062(1) Si1 Uu 0.0063(2) 0.0060(2) 0.0097(3) 0.0072(3) 0.0053(2) 0.0057(2) 0.0068(2) U22 0.0048(2) 0.0050(2) 0.0083(3) U33 0.0059(2) 0.0054(2) 0.0077(3) 0.0000(2) -0.0000(2) -0.0002(2) u» 0.00000 0.00000 0.00000 U23 0.00000 0.00000 0.00000 feq 0.0057(1) 0.0055(1) 0.0086(2) 0.0082(9) 0.0078(9) 0.011(1) U22 0.0061(8) 0.008(1) 0.010(1) 0.0075(9) 0.007(1) 0.009(1) Un 0.0001(6) 0.0005(6) 0.0008(7) UM 0.00000 0.00000 0.00000 U23 0.00000 0.00000 0.00000 ue. 0.0073(4) 0.0079(4) 0.0100(5) Uu 0.0069(6) 0.0066(6) 0.0101(7) U22 0.0062(5) 0.0079(6) 0.0096(7) U33 0.0126(6) 0.0123(6) 0.0144(7) UM -0.0000(4) 0.0000(4) -0.0001(5) UM' 0.00000 0.00000 0.00000 U23 0.00000 0.00000 0.00000 ueq 0.0086(3) 0.0089(3) 0.0114(3) Uu 0.0058(5) 0.0063(5) 0.0087(6) U22 0.0066(5) 0.0080(5) 0.0109(6) U33 0.0062(6) 0.0059(6) 0.0076(7) UM 0.0000(4) -0.0002(5) -0.0001(5) UM 0.00000 0.00000 0.00000 U23 0.00000 0.00000 0.00000 ueq 0.0062(2) 0.0067(2) 0.0091(3) Uu 0.0054(6) 0.0056(6) 0.0088(7) U22 0.0093(6) 0.0100(6) 0.0123(7) u33 0.0059(6) 0.0058(6) 0.0076(7) UM 0.0002(4) 0.0002(4) 0.0004(5) UM 0.00000 0.00000 0.00000 0.0061(3) 0.0056(3) -0.0001(2) 0.00000 0.00000 0.0063(2) 0.008(1) 0.009(1) 0.007(1) 0.0000(8) 0.00000 0.00000 0.0081(5) 0.0076(7) 0.0076(7) 0.0130(8) -0.0001(5) 0.00000 0.00000 0.0094(3) 0.0073(6) 0.0082(6) 0.0055(7) 0.0001(5) 0.00000 0.00000 0.0070(3) 0.0064(7) 0.0103(7) 0.0062(7) 0.0005(5) 0.00000 0.0048(2) 0.0046(2) -0.0000(2) 0.00000 0.00000 0.0049(1) 0.0071(9) 0.0068(8) 0.0060(9) 0.0007(6) 0.00000 0.00000 0.0066(4) 0.0058(6) 0.0078(5) 0.0117(6) -0.0001(4) 0.00000 0.00000 0.0084(3) 0.0053(5) 0.0078(5) 0.0047(6) 0.0007(4) 0.00000 0.00000 0.0059(2) 0.0045(6) 0.0100(6) 0.0050(6) -0.0001(4) 0.00000 0.0050(2) 0.0053(2) 0.0001(1) 0.00000 0.00000 0.0054(1) 0.0074(7) 0.0069(8) 0.0075(8) 0.0005(5) 0.00000 0.00000 0.0073(3) 0.0060(5) 0.0079(5) 0.0126(6) -0.0001(4) 0.00000 0.00000 0.0088(2) 0.0055(4) 0.0077(4) 0.0054(5) 0.0006(4) 0.00000 0.0000 0.0062(2) 0.0055(5) 0.0099(5) 0.0053(5) 0.0002(3) 0.00000 0.0063(2) 0.0057(2) -0.0000(2) 0.00000 0.00000 0.0063(1) 0.0086(9) 0.0081(9) 0.0066(9) 0.0002(6) 0.00000 0.00000 0.0078(4) 0.0061(6) 0.0086(5) 0.0133(6) -0.0003(4) 0.00000 0.00000 0.0093(3) 0.0061(5) 0.0092(5) 0.0057(5) 0.0002(4) 0.00000 0.00000 0.0070(2) 0.0065(6) 0.0112(6) 0.0057(6) 0.0001(4) 0.00000 u23 0.00000 0.00000 0.00000 ueq 0.0069(3) 0.0071(3) 0.0096(3) Uu 0.0102(5) 0.0099(5) 0.0129(7) U22 0.0055(5) 0.0063(6) 0.0092(7) u33 0.0065(5) 0.0072(6) 0.0085(7) UM 0.0010(4) 0.0010(5) 0.0010(5) UM 0.00000 0.00000 0.00000 U23 0.00000 0.00000 0.00000 0.0074(2) 0.0078(3) 0.0102(3) Uu 0.0064(5) 0.0067(5) 0.0096(6) U22 0.0061(5) 0.0069(6) 0.0093(7) u33 0.0062(5) 0.0061(6) 0.0081(7) UM -0.0005(4) -0.0003(4) -0.0004(5) UM 0.00000 0.00000 0.00000 U23 0.00000 0.00000 0.00000 ueq 0.0062(2) 0.0066(2) 0.0090(3) Uu 0.0100(4) 0.0100(4) 0.0130(5) U22 0.0057(4) 0.0065(5) 0.0085(5) u33 0.0072(4) 0.0071(4) 0.0095(5) UM 0.0002(3) 0.0002(3) 0.0003(3) UM -0.0016(3) -0.0015(3) -0.0018(4) U23 0.0004(3) 0.0004(3) 0.0003(4) feq 0.0076(2) 0.0079(2) 0.0103(2) Uu 0.0060(4) 0.0061(4) 0.0091(5) U22 0.0120(4) 0.0129(5) 0.0152(5) C33 0.0061(4) 0.0063(4) 0.0080(5) UM 0.0000(3) 0.0001(3) 0.0005(3) UM 0.0001(3) 0.0001(3) 0.0001(4) U23 0.0008(3) 0.0008(3) 0.0010(4) ueq 0.0080(2) 0.0084(2) 0.0108(2) 0.00000 0.0076(3) 0.0105(7) 0.0072(7) 0.0065(7) 0.0009(5) 0.00000 0.00000 0.0081(3) 0.0074(7) 0.0074(7) 0.0062(7) -0.0002(5) 0.00000 0.00000 0.0070(3) 0.0109(5) 0.0069(5) 0.0077(5) 0.0004(4) -0.0015(4) 0.0002(4) 0.0085(2) 0.0068(5) 0.0134(5) 0.0061(5) 0.0001(4) 0.0001(4) 0.0010(4) 0.0088(2) 0.00000 0.0065(3) 0.0091(5) 0.0059(6) 0.0056(6) 0.0011(5) 0.00000 0.00000 0.0068(2) 0.0060(6) 0.0067(5) 0.0054(6) -0.0005(4) 0.00000 0.00000 0.0060(2) 0.0098(4) 0.0064(4) 0.0060(4) -0.0001(3) -0.0018(3) 0.0003(3) 0.0074(2) 0.0054(4) 0.0129(4) 0.0051(4) 0.0004(3) 0.0002(3) 0.0007(3) 0.0078(2) 0.00000 0.0069(2) 0.0091(5) 0.0065(5) 0.0065(5) 0.0008(4) 0.00000 0.00000 0.0074(2) 0.0065(5) 0.0063(5) 0.0059(5) -0.0003(3) 0.00000 0.00000 0.0062(2) 0.0100(4) 0.0065(4) 0.0074(4) 0.0002(2) -0.0018(3) 0.0003(3) 0.0080(2) 0.0060(3) 0.0128(4) 0.0061(4) 0.0002(2) 0.0000(3) 0.0006(2) 0.0083(2) 0.00000 0.0078(3) 0.0100(6) 0.0074(5) 0.0069(5) 0.0009(4) 0.00000 0.00000 0.0081(2) 0.0074(6) 0.0076(5) 0.0060(5) -0.0007(4) 0.00000 0.00000 0.0070(2) 0.0105(4) 0.0074(4) 0.0075(4) 0.0000(3) -0.0017(3) 0.0004(3) 0.0085(2) 0.0064(4) 0.0142(4) 0.0060(4) 0.0001(3) 0.0003(3) 0.0008(3) 0.0088(2) TABLE 3.6 INTERATOMIC DISTANCES (A) AND ANGLES (°) FOR GRANDIDIERITE AND OMINELITE G17 G8 G4 G12 G1 G2 G9 MgFe-06 x 2 1.9545(9) 1.9588(9) 1.959(1) 1.964(1) 1.9675(9) 1.9715(7) 1.9745(8) -05a 2.0426(1) 2.048(1) 2.054(2) 2.064(2) 2.072(1) 2.081(1) 2.089(1) -01 2.045(1) 2.042(1) 2.041(1) 2.043(2) 2.041(1) 2.041(1) 2.043(1) -02 2.182(1) 2.182(1) 2.191(2) 2.194(2) 2.197(1) 2.205(1) 2.214(1) <MgFe-0> 2.036 2.038 2.041 2.046 2.049 2.054 2.059 06-MgFe-06b 107.50(6) 107.05(5) 106.97(6) 106.71(6) 106.55(5) 106.35(4) 106.35(5) -01 x2 126.06(3) 126.31(3) 126.36(3) 126.50(3) 126.58(3) 126.69(2) 126.69(2) -05a x2 98.19(4) 98.01(4) 98.01(4) 97.90(4) 97.91(4) 97.90(3) 97.90(3) -02 x2 78.37(4) 78.23(4) 78.14(4) 78.08(4) 77.94(3) 77.80(3) 77.72(3) 05a-MgFe-01 81.49(5) 81.60(5) 81.46(6) 81.40(6) 81.41(5) 81.28(4) 81.22(5) 01-MgFe-02 104.51(5) 104.92(5) 105.21(6) 105.55(6) 105.73(5) 106.10(4) 106.30(5) <0-MgFe-0> 99.86 99.85 99.85 99.85 99.84 99.83 99.83 AM-06 x2 1.8869(9) 1.8855(9) 1.887(1) 1.889(1) 1.8894(9) 1.8906(7) 1.8947(9) -02 x2 1.9132(8) 1.9086(8) 1.910(1) 1.909(1) 1.9089(8) 1.9078(6) 1.9091(8) -03c x2 1.9141(8) 1.9123(8) 1.914(1) 1.913(1) 1.9136(8) 1.9134(7) 1.9162(8) <AI1-0> 1.905 1.902 1.904 1.904 1.904 1.904 1.907 06-AI1-02 x2 87.14(4) 87.25(5) 87.32(5) 87.43(5) 87.43(5) 87.60(4) 87.68(4) -02d x2 92.86(4) 92.75(5) 92.68(5) 92.57(5) 92.57(5) 92.40(4) 92.32(4) -03c x2 89.66(4) 89.65(4) 89.69(5) 89.71(5) 89.67(4) 89.65(3) 89.62(4) -03e x2 90.34(4) 90.36(4) 90.31(5) 90.29(5) 90.33(4) 90.35(3) 90.38(4) 02-AI1-03C x2 98.73(4) 98.81(4) 98.73(5) 98.78(5) 98.85(4) 98.82(3) 98.89(4) -03e x2 81.27(4) 81.19(4) 81.27(5) 81.22(5) 81.15(4) 81.18(3) 81.11(4) <0-AI1-0> 90.00 90.00 90.00 90.00 90.00 90.00 90.00 AI2-05C x 2 1.8801(7) 1.8768(8) 1.8767(9) 1.8744(9) 1.8736(8) 1.8714(6) 1.8732(7) -07f x 2 1.8907(9) 1.8878(9) 1.890(1) 1.891(1) 1.8893(9) 1.8906(8) 1.8916(9) -04 x 2 1.9750(8) 1.9765(8) 1.977(1) 1.980(1) 1.9831(8) 1.9857(7) 1.9903(8) <AI2-0> 1.915 1.914 1.915 1.915 1.915 1.916 1.918 05c-AI2-07f x 2 81.74(4) 81.77(4) 81.79(5) 81.76(5) 81.72(4) 81.72(4) 81.74(4) - 0 7 g - 0 4 - 0 4 h 0 7 f - A I 2 - 0 4 - 0 4 h <0 -A I2 -0> A I 3 - 0 2 i - 0 1 - 0 7 b - 0 5 a <AI3-0> 0 2 i - A I 3 - 0 1 - 0 7 0 1 - A I 3 - 0 7 b - 0 5 a 0 7 b - A I 3 - 0 7 - 0 5 a < 0 - A I 3 - 0 > S i - 0 6 j - 0 4 - 0 1 <S i -0> 0 6 j - S i - 0 6 f - 0 4 - 0 1 0 4 - S i - O I < 0 - S i - 0 > B - 0 3 - 0 7 k < B - 0 > 0 3 - B - 0 7 k x 2 x 2 x 2 x 2 x 2 x2 x 2 x2 x2 x2 x2 x2 98. 101. 78. 92. 87. 90. 100. 94. 111. 90. 132. 80. 99. 1. 1. 1. 1. 108. 109. 107. 114. 109. 1. 1. 1. 120. 27(4) 90(4) 10(4) 25(4) 75(4) 00 804(1) 828(1) 8649(9) 938(1) 860 99(6) 79(4) 82(3) 17(6) 40(6) 89(3) 84 6202(9) 632(1) 666(1) 635 41(7) 55(4) 44(4) 28(7) 45 350(2) 379(1) 369 80(8) 98.23(4) 101.86(4) 78.13(4) 92.26(5) 87.74(5) 90.00 1.803(1) 1.828(1) 1.864(1) 1.936(1) 1.859 100.73(6) 94.88(4) 111.86(3) 90.39(6) 132.33(6) 80.81(3) 99.84 1.6178(9) 1.627(1) 1.660(1) 1.631 108.46(7) 109.68(4) 107.24(4) 114.35(7) 109.44 1.348(2) 1.377(1) 1.367 120.83(8) 98.21(5) 101.86(5) 78.14(5) 92.24(5) 87.76(5) 90.00 1.801(2) 1.825(2) 1.865(1) 1.938(2) 1.859 100.62(7) 94.88(4) 111.88(4) 90.44(7) 132.31(7) 80.83(4) 9.84 1.621(1) 1.632(2) 1.664(2) 1.635 108.33(8) 109.69(5) 107.23(5) 114.47(8) 109.44 1.348(3) 1.377(2) 1.367 120.8(1) 98.24(5) 101.89(5) 78.11(5) 92.24(5) 87.76(5) 90.00 1.802(2) 1.825(2) 1.866(1) 1.937(2) 1.859 100.40(7) 94.92(4) 111.90(4) 90.74(7) 132.31(7) 80.77(4) 99.85 1.619(1) 1.632(2) 1.663(2) 1.633 108.30(8) 109.81(5) 107.10(5) 114.51(8) 109.44 1.350(3) 1.377(2) 1.368 120.92(9) 98.28(4) 101.90(4) 78.10(4) 92.24(5) 87.76(5) 90.00 1.803(1) 1.829(1) 1.866(1) 1.936(1) 1.860 100.35(6) 94.98(3) 111.90(3) 90.82(6) 132.28(6) 80.70(3) 99.85 1.6206(9) 1.631(1) 1.662(1) 1.634 108.23(7) 109.92(4) 107.03(4) 114.49(7) 109.44 1.350(2) 1.379(1) 1.369 120.87(8) 98.28(4) 101.87(3) 78.13(3) 92.23(4) 87.77(4) 90.00 1.800(1) 1.828(1) 1.8658(8) 1.935(1) 1.859 100.15(5) 95.00(3) 111.92(2) 91.02(5) 132.31(5) 80.69(3) 99.86 1.6197(7) 1.631(1) 1.662(1) 1.633 108.04(6) 110.10(4) 106.87(3) 114.60(5) 109.43 1.350(2) 1.377(1) 1.368 120.85(7) 98.26(4) 101.86(4) 78.14(4) 92.19(4) 87.81(4) 90.00 1.800(1) 1.830(1) 1.8686(9) 1.936(1) 1.861 100.01(6) 95.00(3) 111.95(3) 91.10(5) 132.29(6) 80.70(3) 99.86 1.6260(9) 1.634(1) 1.662(1) 1.637 108.05(6) 110.09(4) 106.83(4) 114.70(6) 109.43 1.348(2) 1.381(1) 1.370 120.86(8) 07k-B-07l 118.4(2) 118.3(2) 118.4(2) 118.2(2) 118.3(2) 118.3(1) 118.3(2) <0-B-0> 120.0 120.0 120.0 120.0 120.0 120.0 120.0 Note: a = x - y2, -y + 1/2, -z + 1; b = x, y, -z + y2; c = x, y, z - 1; d = -x, -y, -z; e = -x, -y, -z + 1; f = x + y2, -y + y2, -z; g = -x + Yt, y - 1/2, z; h = -x + 1, -y, -z; i = -x + 1/2, y + 1/2, z; j = x + 1/2, -y + 1/2, z+ 1/2, k = -x + 1/2, y - 1/2, -z + 1/2; I = -x + 1/2, y - 1/2, z + 1. TABLE 3.7 POLYHEDRAL EDGES (A) FOR GRANDIDIERITE AND OMINELITE Polyhedron Edge bnarea with G17 G8 G4 G12 G1 G2 G9 MgFe05 02-06 AI106 x 2 2.619(1) 2.618(1) 2.621(2) 2.625(2) 2.625(1) 2.629(1) 2.635(1) 01-05a AI305 2.668(2) 2.672(2) 2.672(2) 2.678(2) 2.682(2) 2.685(1) 2.690(2) 06-05a x 2 3.022(1) 3.025(1) 3.029(2) 3.039(2) 3.047(1) 3.057(1) 3.065(1) 06-06b 3.152(2) 3.150(2) 3.148(2) 3.152(2) 3.154(2) 3.156(1) 3.161(2) 01-02 3.343(2) 3.350(2) 3.363(2) 3.375(2) 3.380(2) 3.395(1) 3.408(2) 01-06 x 2 3.565(1) 3.570(1) 3.570(2) 3.578(2) 3.581(1) 3.587(1) 3.591(1) AI106 02-03e AI106 x 2 2.493(2) 2.486(2) 2.490(2) 2.488(2) 2.486(2) 2.486(2) 2.487(2) 02-06 MgFe05 x2 2.619(1) 2.618(1) 2.621(2) 2.625(2) 2.625(1) 2.629(1) 2.635(1) 06-03c x2 2.680(1) 2.677(1) 2.680(2) 2.682(2) 2.681(1) 2.682(1) 2.686(1) 06-03e x2 2.696(1) 2.694(1) 2.695(2) 2.695(2) 2.697(1) 2.698(1) 2.704(1) 06-02d x2 2.753(1) 2.747(1) 2.747(2) 2.745(2) 2.745(1) 2.742(1) 2.744(1) 02-03c x2 2.9043(2) 2.9014(3) 2.9015(2) 2.9014(3) 2.9033(2) 2.9018(2) 2.9065(2) AI206 05c-04h A!206 x2 2.430(2) 2.430(2) 2.430(2) 2.430(2) 2.431(1) 2.432(2) 2.437(2) 05c-07f AI305 x2 2.467(1) 2.464(1) 2.466(2) 2.465(2) 2.462(1) 2.461(1) 2.464(1) 07f-04h x 2 2.680(1) 2.679(1) 2.681(2) 2.684(2) 2.685(1) 2.688(1) 2.693(1) 07f-04 x2 2.787(1) 2.787(2) 2.788(2) 2.791(2) 2.792(2) 2.795(1) 2.798(1) 05c-07g x 2 2.852(1) 2.846(1) 2.847(2) 2.847(2) 2.846(1) 2.845(1) 2.847(1) 05c-04 x2 2.9945(5) 2.9924(5) 2.9924(6) 2.9935(6) 2.9959(5) 2.9956(4) 3.0005(5) AI305 05a-07b AI206 x2 2.467(1) 2.464(1) 2.466(2) 2.465(2) 2.462(1) 2.461(1) 2.464(1) 05a-01 MgFe05 2.668(2) 2.672(2) 2.672(2) 2.678(2) 2.682(2) 2.685(1) 2.690(2) 02i-07 x2 2.701(1) 2.701(1) 2.700(2) 2.703(2) 2.704(1) 2.703(1) 2.705(1) 02i-01 2.802(2) 2.796(2) 2.790(2) 2.786(2) 2.789(2) 2.782(1) 2.781(2) 01-07b x2 3.058(1) 3.059(1) 3.057(2) 3.058(2) 3.061(1) 3.061(1) 3.066(1) 07-07b 3.413(2) 3.410(2) 3.411(2) 3.413(2) 3.412(2) 3.413(2) 3.418(2) Si0 4 06j-06f 2.628(2) 2.625(2) 2.628(2) 2.624(2) 2.626(2) 2.622(1) 2.627(2) 06J-01 x 2 2.649(1) 2.639(1) 2.645(2) 2.640(2) 2.640(1) 2.636(1) 2.638(1) 04-06J x 2 2.657(1) 2.653(1) 2.660(2) 2.660(2) 2.662(1) 2.665(1) 2.669(1) 04-01 2.770(2) 2.762(2) 2.772(2) 2.772(2) 2.770(2) 2.771(1) 2.775(2) B0 3 07-07 2.368(2) 2.365(2) 2.365(2) 2.363(2) 2.368(2) 2.365(2) 2.370(2) 07-03 x 2 2.372(1) 2.370(1) 2.369(2) 2.372(2) 2.374(1) 2.372(1) 2.373(1) Note: a = x - Yt, -y + Yt, -z + 1; b = x, y, -z + y2; c = x, y, z--1; d = -x, -y, -z; e = -x, -y, -z+ 1; f = x + !4, -y + y2, -z; g = -x + y2, y - y2, z; h = -x + 1, -y, -z; i = -x + Yt, y + 1/2, z; j = x + Yt, -y + Yt, z+ Yt, k = -x + y2, y -1/2, -z + 1/2.; I = -x + Yt, y-1/2, z + 1. T A B L E 3.8 P O L Y H E D R A L V O L U M E S A N D D I S T O R T I O N P A R A M E T E R S F O R G R A N D I D I E R I T E A N D O M I N E L I T E G 1 7 G 8 G 4 G 1 2 G 1 G 2 G 9 M g F e V 6 .888 6.901 6.917 6 .963 6 .985 7.027 7.067 AI1 V 9.094 9.057 9.078 9.081 9 .083 9.084 9.123 O A V 30 .712 31 .037 30 .402 30 .456 30 .903 30 .455 30 .780 M O Q E 1.009 1.009 1.009 1.009 1.009 1.009 1.009 AI2 V 9.064 9 .043 9.055 9.060 9 .063 9.071 9.107 O A V 78 .195 77 .716 77 .535 77 .900 78 .288 77 .930 77 .715 M O Q E 1.023 1.023 1.023 1.023 1.023 1.023 1.023 AI3 V 5 .373 5.369 5.363 5.368 5 .375 5.369 5.386 S i V 2 .235 2 .219 2.234 2 .229 2.231 2 .228 2 .237 T A V 6.491 6 .969 7.264 7.642 7 .789 8.538 8.819 M T Q E 1.002 1.002 1.002 1.002 1.002 1.002 1.002 Note: V= po lyhedra l vo lume ; O A V = oc tahedra l ang le var iance ; M O Q E = m e a n oc tahedra l quadrat ic e longat ion; T A V = te t rahedra l ang le var iance ; M T Q E = m e a n tet rahedral quadra t i c e longat ion. A n g l e var iance is a m e a s u r e of the distort ion of the intra-polyhedral bond a n g l e s f rom the ideal po lyhedron; quadrat ic e longat ion is a m e a s u r e of the distort ion of bond lengths f rom the ideal po lyhedron a s def ined by Rob inson e t a l . (1971). 39 contains up to 0.29 wt% ZnO (0.01 Z n apfu). Overall, the samples show a very low degree of substitution, except for F e 2 + for M g substitution. 3.4.2 Unit-cell parameters Olesch and Seifert (1976) and Hiroi et al. (2002) showed that the unit-cell parameters of grandidierite and ominelite increase with X= (Fe 2 + + Mn) / (Fe 2 + + M n + Mg) , with b expanding the most. The unit-cell parameters from this and previous studies are plotted against XEMPA in Figure 3.3; the graphs show that b increases dramatically with increasingX(note that in this and subsequent Figures the value of X used for ominelite is that of Yokoyama, 0.908, as listed in Hiroi et al. 2002). The amounts of expansion from X= 0 to X= 1, obtained from the regression equation calculated from our single-crystal data, is 0.18 A (corresponding to a percentage increase of 1.6%). In contrast to b the a and c parameters show considerable scatter from X= 0-1. The unit-cell volume increases by approximately 13 A3 (1.9%) over the same range. 3.4.3. Bond distances Most of the M g F e - 0 bond distances lengthen with increasing Fe content (Figure 3.4). For example, M g F e - 0 5 , - 0 2 , and - 0 6 (x2) all increase (by approximately 0.09, 0.06, and 0.04 A, corresponding to percentage increases of 4.4, 2.8, and 2.0%) f r o m X = 0.0 ioX= 1.0 and M g - O l (not shown) remains relatively constant at approximately 2.04 A. The ominelite data points (from Hiroi et al. 2002) fall slightly below the regression line established by our data. 40 < 5.79 5.78 5:77 5.76 5.75 5.74 0.0 0.2 0.4 0,6 0:8 1.0 X= (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) 666 664 662 660 CO ' 658 < :s> 656 654 652 650 648 • • m m m I I m • X .1 1 1 Q. 0.0 0.2 0.4 0.6 0.8 1.0 X= (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) Figure 3.3 (Fe 2 + + Mn + Zn)/(Fe^+ + Mn + Zn + Mg) vs. (a) a, (b) b, (c) c, (d) Vfor grandidierite and ominelite. Filled squares, this study, single-crystal X-ray diffraction; open squares, this study, powder X-ray diffraction; filled upward-pointing triangles, Hiroi et al. (2002); unfilled upward-pointing triangles, Heide (1992); filled downward-pointing triangles, Qiu et al. (1990) forX, Tan and Lee (1988) for cell parameters; unfilled downward-pointing triangles, Olesch and Seifert (1976); filled diamond, von Knorring (1969); unfilled diamond, McKie (1965). The Hiede (1992) and Olesch and Seifert (1976) X= 0 data is from synthetic samples. The lowest point on each graph corresponding to Hiroi et al. (2001) and Qiu et al. (1990)/Tan and Lee (1988) are from single-crystal X-ray diffraction experiments; the rest of the points from the literature are from powder data. .2+ 41 2.12 MgFe-05a •= 0.0929X+ 2.040 ^ = 0.986 2.04 4 0.0 0.2 0.4 0.6 0.8 1.0 X = (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) 2.24 2.23 -2.22 -MgFe-02 = 0.0625X + 2.179 ^ = 0.943 0.0 0.2 0.4 0.6 0.8 1.0 X= (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) 1,990 1.980 4 X to O i <D Li. O) 2 1.970 -\ 1.960 4 1.950 4 Mg Fe-06 x 2 = 0.0398X + 1.954 « ^ = 0.987 0.0 0.2 0.4 0.6 0.8 1.0 X= (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) Figure 3.4 (Fe 2 + + Mn + Zn)/(Fe2 + + Mn + Zn + Mg) vs. (a) MgFe-05a, (b) MgFe-02, (c) MgFe-06 * 2 for grandidierite and ominelite. In this and succeeding graphs (except Figures. 6a and b) linear regression lines are shown when r2 > 0.90. 42 1.898 1.896 1.894 < CM 1.892 x 9 1.890 < 1.888 . . 1.886 + 1,884 I 11 0.0 0.2 0.4 0.6 0.8 1.0 X = (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) 2.000 1.995 1.990 1.985 4 CM x O < 1.980 1.975 * 1970 AI2-04 x 2 = 0.0297X + 1.973 t2 •= 0.950 0.0 0.2 04 0.6 0.8 1.0 X= (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) 1.88 0.0 0.2 0.4 0.6 0.8 1.0 X= (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) Figure 3.5 (Fe 2 + + Mn + Zn)/(Fe2 + + Mn + Zn + Mg) vs. (a)AI1-06 x 2; (b) AI2-04 x 2 (c) AI2-07f x 2 (squares), - 05c x 2 (triangles) for grandidierite and ominelite. 43 The A l l - and A 1 2 - 0 bond distances show minor (< 1.5%) changes with increasingX (Figure 3.5). Once again the ominelite data points (especially for A l l - 0 6 ) fall below the regression line based on our data. The A13-, S i - , and B - 0 bond lengths and atomic displacement parameters for all atoms evidence very minor to no consistent trends with increasing X and are not shown. 3.4.4 Bond angles Many of the interatomic angles change with increasing X. We begin by considering our data for the MgFeOs polyhedron, which shows that the 0 1 - M g F e - 0 2 angle expands the most (Figure 3.6a), followed by the two O l - M g F e - 0 6 angles (Figure 3.6b). The 0 6 - M g F e - 0 6 b , 0 2 - M g F e - 0 6 (x2) , and 0 1 - M g F e - 0 5 a angles decrease (Figures 3.6a and c) and the two 0 5 -M g F e - 0 6 angles (not shown) show no significant trends with increasing X. The trends in Figures 3.6a and b could be modeled by linear regression [with r2 = 0.99, 0.94, and 0.94 for 0 1 -M g F e - 0 2 , - 0 6 (x2) , and 0 6 - M g F e - 0 6 b , respectively], but the pattern of points suggests that a somewhat better fit could be obtained with a curve. The 0 2 - M g F e - 0 5 a angle may be used to estimate the degree of distortion in the MgFeOs polyhedron (see Discussion) and as shown in Figure 3.6d the angle decreases with increasing X. Once again the trend could be modeled by linear regression (with r = 0.98) but the pattern of points described a curve. With increasing Fe content the 0 6 - A 1 1 - 0 2 (x2) angles increase and the 0 6 - A l l - 0 2 d (x2) angles decrease by an equal amount (Figure 3.7a). The other O - A l l - 0 angles (not shown) display no significant changes, nor do any of the 0 - A 1 2 - 0 angles (also not shown). Considering the A B O 5 polyhedron, with increasing Fe the 0 1 - A 1 3 - 0 5 a angle increases and the 0 1 - A 1 3 - 0 2 i angle decreases by about the same amount (Figure 3.7b). None of the other 0 - A 1 3 - 0 angles 44 108.0 107.5 X 0.0 0.2 0.4 0.6 0.8 1.0 X= (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) 127.0 Q 126:8 CM X § 126.6 -| t (U L i -en O 126.4 126.2 126.0 I I b 0.0 0.2 0.4 0.6 0.8 1.0 X = (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) 82 CM o 76 O2-MgFe-O6x2 = -1.2590X + 78.37 p ^ = 0.993 0.0 0.2 0.4 0.6 0.8 1.0 X= (Fe2'+Mn+Zn)/(Fe2'+Mn+Zn+Mg) 174.5 0.0 0.2 0.4 0.6 0.8 1.0 X= (Fe2 ++Mn+ZnV(Fe2 ++Mn+Zn+Mg) Figure 3.6 (Fe 2 + + Mn + Zn)/(Fe2 + + Mn + Zn + Mg) vs. (a) 01 -MgFe-02 (squares), 06-MgFe-06b (triangles); (b) 01-MgFe-06 x 2; (c) 02-MgFe-06 * 2 (squares), 01-MgFe-05a (triangles); and (d) 02-MgFe-05a for grandidierite and ominelite. We note that the trends in Figures 6a, b, and d could be modeled by linear regression [with r2 = 0.99, 0.94, 0.94, and 0.98 for 01-MgFe-02, - 0 6 (*2), 06-MgFe-06b, and 02-MgFe-05a, respectively], but the pattern of points suggests that a somewhat better fit could be obtained with a curve. 45 93:00 92.75 92.50 92.25 92.00 91.75 06-AI1-02d x 2 =-1.0210X+ 92.86 Vi2 = 0.986 87.00 X =. (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) C M O i CO O O 10.1.0 100.5 100:0 -] 99.5 99.0 V 91.5 91.0 -| 90.5 90.0 92.0 / 01-AI3-02i 1/^ = 0:983 1.8255X+ 100.94 01-AI3-05a = 1.8514X+ 90.19 i2- 0.979 0.0 0.2 04 0.6 0.8 1.0 X = (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) Figure 3.7 (Fe 2 + + Mn + Zn)/(Fe2 + + Mn + Zn + Mg) vs. (a) 06-AI1-02 x 2 (squares), 02d x 2 (triangles); (b) 01-AI3-05a (squares), -02 i (triangles) for grandidierite and ominelite. 46 115.0 A O 110.5 H 110.0 109.5 04-Si-01 = 0.7405X4- 114.29 ? - 0.930 / 04-S-06J x 2 = 1.1354X+ 109.54 i2 = 0.979 X= (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) 109.0 108.5 £ 108:0 V? 107.0 to O 106.0 I I I • • 06j-Si-01 =-1.1686X+ 107.41 ^ t2 = 0.989 D 0.0 0.2 0.4 0.6 0.8 1.0 X = (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) Figure 3.8 (Fe 2 + + Mn + Zn)/(Fe2 + + Mn + Zn + Mg) vs. (a) 04-S i -06 j x 2 (squares), 01 (triangles); (b) 06j-Si-06f (squares), -01 x 2 (triangles) for grandidierite and ominelite. 47 show any significant changes and are not shown. In the graphs shown the ominelite data points lie on or close to the regression line established from our data. Surprisingly, the O - S i - 0 angles show some changes with Fe substitution at the MgFe site. As shown in Figure 3.8, the 0 4 - S i - 0 6 j (x2) and - 0 1 angles increase and the 0 6 j - S i - 0 6 f and -01 (x2) angles decrease with increasing X On the other hand, the O - B - 0 angles show little discernable change with increasing X and therefore are not shown in the Figures. 3.4.5 Polyhedral edges Many of the polyhedral edges (Table 3.8) change with increasing X. Not surprisingly, the greatest changes are associated with the edges of the (Mg,Fe )0s polyhedron, for which the 0 1 -0 2 edge increases the most, followed by the 0 6 - 0 5 a x 2 and 0 1 - 0 6 x 2 edges (Figure 3.9). The shared 0 1 - 0 5 a and 0 2 - 0 6 x 2 edges also increase but the 0 6 - 0 6 b edge shows only a very slight expansion. With respect to the A l l 0 6 octahedron, the 0 2 - 0 6 x 2 edges, which are shared with the (Mg,Fe )0s polyhedron, increase the most (see above), and the 0 6 - 0 2 d x 2 edges decrease slightly fromX = 0.0-1.0 (Figure 3.10a). The 0 6 - 0 3 c x 2 and - 0 3 e x 2 edges show a very slight increase (not shown) and the 0 2 - 0 3 e x 2 shared and 0 2 - 0 3 c x 2 unshared edges (also not shown) remain constant with changing X. The edges of the A1206 octahedron show very minor changes; the 0 7 f - 0 4 h x 2 and - 0 4 x 2 edges increase (Figure 3.10b) but the other edges (not shown) show little change. With respect to the A B O 5 polyhedron the 05a -01 edge 94-which is shared with the (Mg,Fe )0s polyhedron increases the most (see above), but the 0 2 i - 0 1 edge shows a noticeable decrease (Figure 3.10c). The other edges show little change w i t h X The edges of the Si04 tetrahedra also show minor changes with X, with the 0 4 - 0 6 x 2 edge changing the most (Figure 3.11). The 0 4 - 0 1 edge also increases and the 0 1 - 0 6 x 2 and 0 6 j - 0 6 f edges decrease with increasing X, but the amount of change is less than or equal to 0.02 48 2.72 2.60 01-05a = 0.0427X + 2.667 ^-0.978 0.0 0.2 0.4 0.6 0.8 1.0 (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) & o 8 o p o 3.18 3.16 H 3.14 3.12 -| 3.10 3:08 -] 3.06 3.04 3.02 3.00 06-05a x 2 = 0.0882X+ 3.018 r' = 0.975 0.0 0.2 0.4 0.6 0.8 1.0 (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) 3.65 3.30 01-06 x 2 = 0.0517X+ 3.564 r2 = 0.986 A2 = 0:981 0.0 0.2 0.4 0.6 0.8 1.0 (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) Figure 3.9 (Fe 2 + + Mn + Zn)/(Fe2 + + Mn + Zn + Mg) vs. (Mg,Fe 2 +)0 5 polyhedral edges: (a) 02 -06 x 2 (squares), 01-05a (triangles); (b) 06 -05a x 2 (squares), 6b (triangles); (c) 01 -02 (squares), - 0 6 x 2 (triangles). 49 2.755 2.750 -<< 2.745 -CN X 2.740 -•o CM O CO 2.735 -O CD 2.730 -g < 2.725 -2.720 -2.715 2.80 2.78 A 2.76 CM X O i. CM" X St • • ' O it 2.70 O CM 2.68 3 2.66 O7f-04 x 2 = 0.0222X + 2.785 l2 = 0.943 A b (Fe' !++Mn+Zn)/(Fe"++Mn+Zn+Mg) 0.0 0.2 0.4 0.6 0.8 1.0 (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) 2.81 (Fe2'+Mn+Zn)/(Fe-"+Mn+Zn+Mg) Figure 3.10 (Fe 2 + + Mn + Zn)/(Fe + Mn + Zn + Mg) vs. polyhedral edges: (a) AI10 6, 06-02d x 2; (b) AI20 6, 07f-04h x 2 (squares), - 0 4 x 2 (triangles); (c) AI30 5, 02 i -01 . 50 2.675 2:670 CM X CD O i o •5-o CO 2.665 2.660 -T 2.655 + 2.650 o.o 0.2 0.4 0.6 0.8 1.0 (Fe2'+Mn+Zn)/(Fe?'+Mn+Zn+Mg) Figure 3.11 (Fe 2 + + Mn + Zn)/(Fe2 + + Mn + Zn + Mg) vs. S i 0 4 tetrahedral edges, 04 -06 x 2. 51 A (or 0.6%) and they are not shown in the Figures. The sides of the BO3 triangles show no significant variations with increasing X (and are not shown either). 3.4.6. Polyhedral volumes and distortion parameters A s expected, the volume of the (Mg,Fe )Os polyhedron increases dramatically with increasing X (Figure 3.12a), from 6.871 to 7.229 A3 f r o m X = 0-1. The volumes of the A 1 0 6 octahedra show no real trends (Figure 3.12b), but those of the A130s polyhedron and SiC^ tetrahedron appear to remain constant. Distortion indices (Table 3.9) for the A106 octahedra reveal no trends, but the tetrahedral angle variance ( T A V ; Figure 12c) and mean tetrahedral quadratic elongation ( M T Q E ; Robinson et al. 1971; not shown in Figure 3.12 but follows exactly the trend for T A V shown in Figure 3.12c) values for the Si04 tetrahedra increase with Fe substitution. 3.4.7 Summary In summary, the most "significant" changes (arbitrarily chosen to be those >2%) resulting from Fe for M g substitution at the MgFe site are as follows: (1) increase in the volume of the ( M g , F e 2 + ) 0 5 polyhedron (5.0% change); (2) expansion of the M g F e - 0 5 bond distance (4.4%); (3) expansion of the 0 1 - 0 2 edge (3.6%); (4) opening of the O l - M g F e - 0 2 angle (3.2%); (5) increase in the length of the 0 6 - 0 5 a (x2) edges (2.8%); (6) lengthening of the M g F e - 0 2 bond distance (2.8%); (7) decrease in the 0 6 - M g F e - 0 6 b angle (-2.1%); (8) increase in the M g F e -0 6 (x2) bond distances (2.0%); and (9) opening of the 0 1 - A 1 3 - 0 5 a angle (2.0%). 52 0) H 6.0 -I , , • , --, — ' 0.0 0.2 0.4 0.6 0.8 1.0 X= (Fe2 ++Mn+Zn)/(Fe2 ++Mn+Zn+Mg) Figure 3.12 (Fe 2 + + Mn + Zn)/(Fe2 + + Mn + Zn + Mg) vs. (a) volume of the (Mg,Fe 2 +)0 5 (squares) and AI30 5 (triangles) polyhedra, (b) volume of the AM 06 (squares) and AI206 (triangles) octahedra, (c) tetrahedral angle variance for S i 0 4 tetrahedron in grandidierite and ominelite. 53 3.5 Discussion 3.5.1 Unit-cell parameters Figure 3 also shows that the unit-cell parameters from the single-crystal studies are displaced above (our data) and below (previous studies) the trends established by parameters from powder experiments (both our study and previous studies). It is possible that the unit-cell parameters derived from powder diffraction data (especially when obtained using the Rietveld method and an internal.standard) are more accurate than those obtained from single-crystal data. However, the unit-cell dimensions obtained from the "IUCr" ruby [a = 4.7642(6) and c = 13.010(2) A], although somewhat higher than the published values (by 0.07 and 0.11%, respectively), are not displaced to the same degree as the grandidierite and ominelite cell parameters. Figure 3.3 also shows that, as previously noted by Hiroi et al. (2002), the a dimension for the synthetic samples (from powder data) is much longer than expected (and similar to our single-crystal results), and b and c are noticeably shorter. We do not know the reason for this, but suggest that it might be due to Mg-Al disorder in the synthetic samples. Mg-Al disorder might also be invoked to explain the overall scattering of the a and c values, as might the presence of structural vacancies (perhaps balanced by Fe /Fe ) and substitutions (Be, B, etc.) at the tetrahedral site. Figure 3.3 also shows that the unit-cell parameters of ominelite from the single-crystal study of Hiroi et al. (2002) are considerably offset from the trends established by the single-crystal data from this study. Given that bond distances and angles and other geometrical parameters strongly depend on the unit-cell dimensions it is not surprising that in many cases the correlation between our parameters and those reported in Hiroi et al. (2002) is less than ideal. 54 This might be due to some unknown characteristic of their crystal but is more likely due to the fact that the data was collected with different instruments. It is unfortunate that we were unable to obtain the sample studied by Hiroi et al. (2002) or any other crystals with X> 0.52. 3.5.2 Geometric effects Given the difference in diameter of almost 0.1 A it is not surprising that F e 2 + for M g substitution at the MgFe site in members of the grandidierite-ominelite series leads to noticeable changes in the crystal structure. However, these are influenced by the following factors: (1) all of the atoms except 0 6 and 0 7 are at special positions ( A l l at 0,0,0; A12 at '/2,0,0; MgFe, A13, 0 1 , 0 2 , and 0 4 at x,y,lA; B , 0 3 , and 0 5 at 0,0,3/4) where z (at least) is constrained. Therefore, changes to atom positions are mostly limited to the ab plane. (2) B and Si are small, relatively highly charged cations, and thus would be expected to make strong bonds to O atoms that would resist change in length. Olesch and Seifert (1976) and Hiroi et al. (2002) suggested that the increase in unit-cell dimensions with increasing X is due to expansion o f the M g F e - 0 2 and - 0 5 bond lengths w i t h X However, our results show that with substitution of Fe at the MgFe site the only M g F e - 0 bond distance that doesn't increase is that to 0 1 . The O atom at 01 is also bonded to an A l atom at A13 and an Si atom at the Si site. The A13-01 and S i - 0 1 distances also remain constant (within error) with increasing X, perhaps because the 01 atom is prevented from moving by the relatively strong S i - 0 bond. The two M g F e - 0 distances that increase the most are the two (MgFe-05 and M g F e - 0 2 ) that are approximately perpendicular to the M g - 0 1 bond. The two M g F e - 0 6 bond lengths do not expand as much as the M g F e - 0 5 and - 0 2 distances, likely because the O atoms at the 0 6 sites also form bonds with Si atoms. The two short A l l - 0 6 bond 55 distances increase only slightly withX, likely because the A l l site is constrained at the origin, but probably also because of the strong S i - 0 6 bonds. The A12-05 distance shows the greatest decrease withX, probably in response to the increase in M g F e - 0 5 (the O atom at the 0 5 site is bonded to A l atoms at two A12 and one A13 sites, and to the atom at one MgFe position). The A13-05 distance shows only a minor decrease. It is a bit of a mystery as to why the A12-04 distance increases so much with X (the atom at 0 4 is bonded to A l atoms at two A12 sites and an Si atom at the Si position), but this might be in response to the contraction of the two A12-05 distances. Since the position of the 01 atom changes only slightly with X the expansion of the 0 1 - 0 2 edge and O l - M g F e - 0 2 angle are primarily due to changes in the position of the 0 2 atom. A s 0 1 - 0 2 and O l - M g F e - 0 2 increase the 0 2 - M g F e - 0 6 (x2) angles decrease. Together this amount is about the same as the increase in O l - M g F e - 0 2 . Although the 0 2 - M g F e - 0 6 angles decrease, the shared 0 2 - 0 6 (x2) edges expand slightly because of the increasing M g F e - 0 2 and - 0 6 (x2) bond distances. Although the 0 5 a - M g F e - 0 6 (x2) angles show no significant trends with increasing X, the 0 6 - 0 5 a (x2) edges increase because of the increasing M g F e - 0 5 and - 0 6 (x2) bond distances. The 0 6 - M g F e - 0 6 b angle decreases significantly with X but the 0 6 - 0 6 b edge shows only a very slight increase, likely because the position of the 0 6 atom is constrained by bonds to the Si atom at S i l and the A l atom at A l l . The opening of the 0 1 - A 1 3 - 0 5 angle with corresponding increase in the 0 1 - 0 5 edge is of course due mainly to the increase in the M g F e - 0 5 bond distance. The final "significant" change, the decrease in the 0 1 - A 1 3 - 0 2 i angle, is probably in response to the increasing 0 1 -A13-05 angle. As suggested above, it is not surprising that the lengths of the relatively strong S i - 0 bonds show no apparent change with X. Instead, the Si04 tetrahedra react to Fe for M g substitution at 56 the MgFe site by changing O - S i - 0 angles such that the tetrahedral angle variance and mean tetrahedral quadratic elongation increase. This is not surprising given that three o f the four O atoms coordinating each Si atom (01 and 0 6 x 2) also form bonds to atoms at three different MgFe sites. The BO3 triangles appear to behave as relatively invariant units in the crystal structure; this is also not surprising given that none of the O atoms coordinating each B atom form bonds to atoms at MgFe sites. 3.5.3 Effect of other substituents Although the concentrations of substituents other than F e 2 + in our samples is very low, it is interesting to speculate on the effects of other reported substitutions on the structures of grandidierite and ominelite. For example, Hiroi et al. (2002) reported up to 0.77 wt% M n O (-0.04 M n apfu) in their ominelite sample, and according to Shannon (1976) the ionic radius of M n 2 + (high spin) is 0.75 A, so substitution of M n 2 + at the MgFe site would be expected to cause more distortion than an equivalent amount of F e 2 + . On the other hand, the ionic radius of v Z n , given by Shannon (1976) as 0.68 A, is only slightly larger than that of M g and would likely have little effect. The ionic radii of V A 1 and V I A 1 were given by Shannon (1976) as 0.48 and 0.535 A, respectively, hence the presence of Cr (with an ionic radius of 0.615 A for V I C r 3 + ; Shannon 1976) at any of the A l sites would be expected to increase the size of the coordination sphere. On the other hand, the substitution of P 5 + for Si at the Si sites, with the respective ionic radii of 0.17 and 0.26 A (Shannon 1976), would be expected to decrease the bond distances, and of course there would be a charge imbalance to deal with. 57 3.5.4 Ionic radius of vFe2Jr Shannon (1976) reported an "ionic radius" of 0.66 A for v M g but no value was given for five-coordinated Fe 2 + . However, the average of the radii of I V F e 2 + (0.63 A) and v l F e 2 + (0.78 A) (both high spin) is 0.71 A. In addition, the average MgFe-0 distances determined from the regression equations (with MgFe-Ol = 2.04 A) in Figure 4 are 2.033 A foxX= 0 and 2.080 A for X= 1; i f the difference (0.047 A) is added to the ionic radius of v M g the result is 0.70 A. These ionic radii differ from that of v M g by - 7 % which is much lower than the generally accepted upper limit for solid solution of 15%, but similar to the difference of ~8% reported for V I M g versus V I F e 2 + (Oberti 2001). 3.5.6 Conclusion: vFe in minerals Ominelite is one of the few minerals in which Fe is the dominant cation in the fivefold coordinated site; other examples are graftonite, joaquinite, and vesuvianite. Kostiner and Rea (1974) studied the crystal structure of synthetic end-member graftonite and showed that there is one octahedron and two five-coordinated polyhedra that lie somewhere between a trigonal bipyramid and a tetragonal pyramid. They obtained average v F e 2 + - 0 bond distances of 2.134 and 2.101 A. Dowty (1975) showed that the structure of monoclinic joaquinite, ideal formula NaFe2+Ba2REE2Ti2Si80280H-H20, contains a trigonal dipyramid with composition Fe 2 +04(OH) and an average bond distance of 2.10 A. The Y l site in vesuvianite is coordinated by five anions that form a tetragonal pyramid (Groat et al. 1992). However, the site generally contains more than one element, and the substitutions and order/disorder in the vesuvianite structure make it difficult to say anything conclusive about Fe in this coordination. 58 A s noted by Stephenson and Moore (1968), the degree of distortion of the (Mg,Fe )Os polyhedron can be estimated from the 0 2 - M g F e - 0 5 a angle (which is 180° for a perfect trigonal bipyramid). A linear regression fit to the points in Figure 6d shows that this angle increases from 173.9° for X= 0 to 176.7° for X= 1. The apparent rarity of v F e in minerals is likely a function of the polyhedral distortion that is required to maintain this coordination as opposed to an octahedral coordination, especially for F e 2 + . 59 4.0 CRYSTAL STRUCTURE OF TRASKITE 4.1 Introduction Traskite, (Ba 9 Fe z 2Ti 2)(Si03)i2(OH,Cl,F)6-6H 20, was first described from Fresno County, California by Alfors et al. (1965). It occurs in sanbornite-bearing metamorphic rocks near a granodiorite contact. The presently accepted formula was determined by Alfors and Putman (1965) and was confirmed by Malinovski i et al. (1976). The crystal structure of traskite was solved in space group P6m2 by Malinovskii et al. (1976) to R = 0.12. The model proposed by Malinovskii et al. (1976) contains five Ba(0,OH,Cl)io polyhedra, three octahedra, one trigonal prism, and four S iC^ tetrahedra (Figure 4.1). The octahedra are occupied by transition metals (Ti, Fe, M n etc.) and the trigonal prism by Ca and Sr. The Si04 tetrahedra form SM2O36 rings. We chose to re-examine this mineral because of the high 7?-value and because the positions of the water molecules and the hydrogen bonding scheme were not determined. 4.2 Experimental Qualitative chemical data was collected from the samples in this study using a Philips X L 3 0 scanning electron microscope equipped with a Princeton Gamma-Tech energy-dispersion X-ray spectrometer. Compositional data were obtained from the same crystals used for the crystal structure study with a C A M E C A SX-50 electron microprobe operated in the wavelength-dispersion mode. Operating conditions were as follows: accelerating voltage, 15 k V ; beam current, 20 nA; peak count time, 20 s; background count-time, 10 s; spot diameter (standards and specimen), 5 um. Data reduction was done using the " P A P " <\>(pZ) method (Pouchou and Pichoir 1985). For the elements considered, the following standards, X-ray lines, and crystals were used: topaz , FKa, diopside, MgKa, kyanite, AlKa, diopside, SiKa, SrTi03, S r L a , T A P ; diopside, 60 Figure 4.1 Structure of traskite projected down (001) using positions from Malinovskii et al. (1976). Red octahedra are Fe 2 + , green octahedra are Ti 2 + , tetrahedra are S i 4 + , red spheres are O2", and light green spheres are Ba 2 + , dark green spheres are CI". 61 CsJCa, scapolite, CXKa, P E T ; rutile, TiKa, synthetic rhodonite, MnKa, synthetic fayalite, FeKa, barite, BaZa, L IF . The formula was calculated on the basis of 12 Si atoms. For single-crystal X-ray diffraction measurements, the crystals were ground to approximate spheres using a Nonius grinder. We used a Bruker X 8 A P E X diffractometer with graphite-monochromated MoKa radiation and a C C D detector. Data were collected in a series of <j) and co scans in 0.50° oscillations with exposure times of 15.0 s. The crystal-to-detector distance was 40 mm. Data were collected and integrated using the Bruker S A I N T software package. Data were corrected for absorption effects using the multi-scan technique ( S A D A B S ) . The data were corrected for Lorentz and polarization effects. A l l refinements were performed using the S H E L X T L crystallographic software package of Bruker A X S . Neutral-atom scattering factors were taken from Cromer and Waber (1974). Anomalous dispersion effects were included in F c a | C (Ibers and Hamilton 1964); the values for Af and Af" were those of Creagh and M c A u l e y (1992). The values for the mass attenuation coefficients were those of Creagh and Hubbell (1992). 4.3 Results and Discussion A n average electron microprobe analysis ( E M P A ) of one crystal collected at U B C , which was used in the structure refinement (SREF) study, is presented along with the only other known analysis of traskite by Alfors and Putman (1965) in Table 4.1. Our analyses were calculated on the basis of 12 S i 4 + and assuming 18 H 2 0 and that the (CI, O H , F) site is filled entirely with CI. 62 TABLE 4.1 Electron microprobe analyses of traskite TR-2* traskite4 I Si02 23.86 27.77 Ti0 2 5.40 5.6 A l 2 0 3 0.26 0.33 F e O 2.99 4.201 M n O 1.50 1.36 M g O 0.32 0.30 C a O 0.60 0.86 S r O 0.00 0.34 B a O 48.94 51.19 K 20 - <0.052 H 2 0 11.55 5.103 CI 12.56 3.502 F 0.06 0.404 0=F -0.03 0=CI -0.98 0 = CI + F -1.00 Tota l 98.83 100.00 S i 4 + apfu 12.00 12.00 T i 4 + 2.04 1.820 A l 3 + 0.15 0.168 F e 2 + 1.25 1.518 M n 2 + 0.64 0.498 M g 2 + 0.24 0.193 C a 2 + 0.32 0.398 S r 2 * 0.00 0.085 B a 2 + 9.64 8.668 K + n/a 0.022 cr 3.71 2.563 F" 0.09 0.547 H + 18.00f 14.700 o2- 38.53 45.059 C A T S U M 26.31 25.371 A N S U M 42.34 48.169 Note: Compositions were calculated on the basis of 12 S i 4 + atoms per formula unit, 18 H 2 0, (OH.CI.F). *average wt% oxides based on 5 analyses determined by stoichiometry * (Alfors and Putman 1965) Analyses determined by d-arc emission spectroscopy except 1 Iron was determined as Fe°, but is reported as FeO 2 K 2 0 and CI determined by X-ray spectroscopy 3 H 2 0 was determined by ignition loss 4 F was determined by BaF band spectra 63 There are some discrepancies between our data and the previously published data, but this could be due to inaccurate measurements in the older data. Some additional problems are that density for the crystal with Z = 2 is 2.86 and Z = 3 is 4.30, however the published density is 3.71. This could mean that the published density is wrong and that re-determination of the density needs to be done. I attempted to solve and refine the crystal structure of traskite in many different space groups (see Table 4.2). I initially tried replicating the experiment done by Malinovskii et al. (1976) in P6m2, but was unsuccessful. The most successful model was P 31 m. It had i?j n t = 5.3% as well as R\ = 5.3% indicating that our data is good and that our model is close to being correct. Data collection and refinement parameters are summarized in Table 4.3, positional and displacement parameters in Table 4.4, and bond lengths and angles in Table 4.5. However, there are some problems with this model. To begin with many sites had to be split. The Ba4 and Ba5 atoms are only 0.7 A apart, and when allowed to refine the sum of their occupancies adds up to 1. The 0 9 , C12, and C13 sites had to be split as well . The 0 9 A and 0 9 B sites are only 0.8 A apart and their occupancy adds up to ~1.1. The C12A and C12B sites are only 0.98 A and their occupancies adds up to ~0.5. Similarly, the C13A and C13B sites are only 0.99 A and their occupancies add up to -0.5 as well . These split CI sites and C14 could not be modeled anisotropically. This could mean that some symmetry elements in the structure are unaccounted for. The program M I S S Y M was used to determine i f any symmetry was missing. It indicated that there was a 6-fold axis with parallel mirror planes, suggesting that the correct space group was P6/mmm, but we were unable to refine the structure in this space group. Some options for future work include recollecting X-ray diffraction data from another crystal. There was no indication of twinning with the first crystal, however having a second data set may help rule out the possibility. In addition, data w i l l be collected on the new neutron 64 single-crystal diffractometer at the Spallation Neutron Source (SNS) at Oakridge in Tennessee. This is the first facility that allows neutron data collection from crystals of the same size as those used by X-ray single crystal diffractometers. Using neutrons w i l l obviate the source of absorption problems associated with studying traskite with X-ray data given the mixture of heavy and light atoms. We plan to attempt this when the SNS opens later this year. Furthermore, additional work w i l l need to be done to determine the correct formula. 65 TABLE 4.2 Attempted space groups and resulting Flack x parameters, and |E 2-1| values of traskite in this study Space Group Centrosymmetric R-value (%) Flack x parameter |£ 2 -1 | P-1 y 24.99 0.975 Film y 7.42 - 0.971 C2/m y 15.47 - 0.978 P3 n 6.15 0.4417 0.975 P3 y 6.78 - 0.975 P3m1 y 29.44 - 0.975 P31m y 5.37 - 0.975 P622 n 7.26 0.4212 0.975 PSmm n 7.14 0.3947 0.975 P6/mmm y 37.26 - 0.975 PQm2 n 18.23 0.2569 0.975 P62m n 47.96 0.3258 0.975 y = yes n = no T A B L E 4.3 T R A S K I T E : D A T A C O L L E C T I O N A N D S T R U C T U R E - R E F I N E M E N T I N F O R M A T I O N a (A) 17.863(3) F 0 > 4a F 0 3087 c(A) 12.298(3) Pint 0.05(2) L.s. parameters 189 S p a c e G r o u p P3im(No. 162) Ri for F0 > 4a F 0 0.0537 Z 3 P i for all un ique F 0 0.0618 Crysta l s i ze (mm) 0.1 x 0.1 x 0.1 wR2 0.1516 Radiat ion M o K a a (see Note) 0.0725 Monochromator graphite b (see Note) 118.80 Total F 0 86343 G o o F (= S) 0.989 Unique F0 3547 Note: w= 1/[a2(F02) + (a x Pf + b x P] where P = [Max ( F 0 2 , 0) + 2 x Fc2)]/3 66 T A B L E 4.4 A T O M P A R A M E T E R S FOR TRASKITE Site sof X y z Uu* U22 I/33 UM U13 U2z UE, Ba1 0.5 0.64407(4) 0 0.50002(4) 0.0203(3) 0.0155(3) 0.0103(3) 0.0078(1) -0.0000(1) 0 0.0159(2) Ba2 0.5 0.57427(2) 0.14854(5) 0 0.0140(3) 0.0164(3) 0.0623(6) 0.0082(2) 0.0000(3) 0 0.0307(2) Ba3 0.166(2) 1/3 0.23166(8) 0.166(2) 0.0090(4) 0.0090(4) 0.0074(5) 0.0045(2) 0 0 0.0085(3) Ca3 0.168(2) 2/3 1/3 0.23166(8) 0.0090(4) 0.0090(4) 0.074(5) 0.0045(2) 0 0 0.0085(3) Ba4 0.446(9) 0.7709(2) 0.2291(2) 0.2540(1) 0.026(1) 0.026(1) 0.0163(6) -0.0108(9) -0.0066(5) 0.0067(5) 0.034(1) Ba5 0.554(9) 0.4126(3) 0.2063(1) 0.2578(1) 0.042(1) 0.0189(6) 0.0110(4) 0.0213(8) 0.0012(5) 0.0007(3) 0.0214(6) Ti1 0.5 0.5981(1) 0 0.7929(1) 0.0153(6) 0.0066(7) 0.0062(6) 0.0033(3) -0.0034(5) 0 0.0104(3) Ti2 0.5 0.5981(1) 0 0.2072(1) 0.0154(6) 0.0064(7) 0.0064(6) 0.0032(3) 0.0033(5) 0 0.0104(3) Ti3 0.16667 2/3 1/3 1/2 0.0093(7) 0.0093(7) 0.004(1) 0.0046(4) 0 0 0.0077(5) Si1 1.0 0.7328(1) 0.0912(1) 0.9999(1) 0.0090(7) 0.0066(7) 0.0093(7) 0.0023(6) 0.0000(6) -0.0002(6) 0.0090(3) Si2 1.0 0.5654(1) 0.1310(1) 0.3701(2) 0.0134(8) 0.0109(8) 0.0079(8) 0.0056(7) -0.0009(6) -0.0022(6) 0.011(4) 01 0.5 0.7345(4) 0 0.0002(6) 0.009(3) 0.010(3) 0.019(3) 0.005(1) -0.001(2) 0 0.013(1) 0 2 0.5 0.8335(3) 0.1665(3) 1.0 0.008(2) 0.008(2) 0.051(5) -0.002(3) 0.001(3) 0.001(3) 0.025(2) 0 3 0.5 0.5553(5) 0.111(1) 1/2 0.047(4) 0.095(9) 0.002(3) 0.047(5) 0.000(3) 0 0.043(3) 0 4 1.0 0.5304(3) -0.0913(3) 0.6796(4) 0.014(2) 0.015(2) 0.018(2) 0.006(2) -0.005(2) -0.000(2) 0.0161(9) 0 5 0.5 0.5002(5) 0 0.1404(6) 0.27(3) 0.016(3) 0.017(3) 0.008(2) 0.001(3) 0 0.021(2) 0 6 1.0 0.6216(3) 0.0914(3) 0.3205(4) 0.016(2) 0.014(2) 0.018(2) 0.008(2) 0.004(2) -0.000(2) 0.016(1) 07 1.0 0.6837(4) 0.0965(4) 0.1066(4) 0.018(2) 08 1.0 0.4130(4) 0.0968(4) 0.1067(4) 0.020(2) 09A 0.53(4) 0.5665(9) 0.2829(9) 0.161(1) 0.026(7) 09B 0.55(4) 0.5859(9) 0.2930(8) 0.100(2) 0.035(7) 010 1.0 0.6169(5) 0.2340(4) 0.3535(8) 0.031(4) 011 0.33333 2/3 1/3 0.371(1) 0.031(4) CM 0.5 0.3980(5) 0.19990(2) 1/2 0.166(6) CI2A 0.20(1) .0.773(1) -0.0298(9) 0.288(1) 0.045(5) CI2B 0.31(1) 0.7319(9) -0.009(1) 0.2911(8) 0.061(4) CI3A 0.20(1) 0.774(1) -0.0298(9) 0.712(1) 0.043(5) CI3B 0.32(1) 0.733(1) -0.008(2) 0.7089(8) 0.066(4) CI4 0.28(1) 0.9257(4) 0.0743(4) 1.0 0.069(4) 0.017(2) 0.017(2) 0.039(7) 0.029(6) 0.009(3) 0.031(4) 0.056(2) 0.014(2) 0.013(2) 0.020(1) 0.021(9) 0.091(7) 0.041(7) 0.012(1) 0.008(2) 0.009(2) 0.014(6) 0.016(5) 0.004(3) 0.016(2) 0.083(3) 0.003(2) -0.006(2) -0.006(6) -0.002(5) -0.003(4) 0 0 -0.003(1) -0.002(2) -0.004(5) -0.002(5) -0.007(3) 0 0.0003(9) 0.017(1) 0.016(1) 0.029(5) 0.028(5) 0.046(2) 0.034(3) 0.066(2) TABLE 4.5 SELECTED INTERATOMIC DISTANCES (A) (°) FOR TRASKITE Ba1-04a x 2 2.889(5) Ti1-05b 1.937(9) -06a x 2 2.891(5) -04a x 2 2.023(5) -CI2Ba x 2 3.06(1) -08i x 2 2.052(5) -CI3Ba x 2 3.06(1) <Ti1-0> 2.052 -03b x 2 3.090(8). <Ba1-0> 2.998 TJ2-05 1.932(9) -06 x 2 2.024(5) Ba2-09Bc x 4 2.77(1) -07 x 2 2.051(5) -08c x 2 2.865(6) <Ti2-0> 2.016 -07c x 2 2.868(6) -05d x 2 2.874(5) Ti3-011 x 2 1.59(1) <Ba2-0> 2.829 -O10j x 6 2.368(8) <Ti3-0> 2.174 Ba3-011 1.71(1) -09Ae x 3 1.78(1) Si1-07k 1.606(5) -09Be x 3 2.04(1) -08i 1.607(5) -01 o- x 3 2.147(9) -02 1.621(3) <Ba3-0> 1.961 -01k 1.645(4) <Si1-0> 1.620 Ba4-Ba5f 0.708(4) -09Af 2.03(2) Si2-06 1.609(5) -04g 2.695(5) -04b 1.610(5) -06 2.697(5) -010 1.607(7) -09Bf 2.74(2) -03 1.629(3) -08f 2.759(6) <Si2-0> 1.614 07 2.763(6) 01 Of x 2 3.05(1) <Ba4-0> 2.499 Ba5-Ba4 0.708(4) -09A 2.66(2) -08 2.701(5) -07e 2.704(5) -04b 2.818(5) -06e 2.819(5) 69 CM 2.987(2) CI2Bh 3.18(2) CI3Bb 3.20(3) CI2Ah 3.26(1) CI3Ab 3.27(1) -09B 3.31(2) <Ba5-0> 2.801 Equivalent positions: a = x - y, - y , z ; b = -x + 1, -y, -z + 1; c = -x + y + 1, y, -z; d = -x + 1, x - y , -z; e = -x + y +1, -x + 1, z; f = -y + 1, x - y, z; g = y + 1, -x + y + 1, -z + 1; h -x + 1, -x + y + 1, z; i = -x + y + 1, y, -z + 1; j = x, x - y, -z + 1; k = x, y, z + 1. 70 TABLE 4.6 SELECTED INTERATOMIC ANGLES (°) FOR TRASKITE 04ab-Ti1-05b x 2 96.7(2) 08i-Si1-07k 109.4(3) -08i x 2 92.3(2) 02-Si1-07k 111.3(3) 04-Ti1-04a 88.6(3) 01k-Si1-07k 109.7(3) 08i-Ti1-04a x 2 88.2(2) 02-Si1-08i 111.2(3) 08b-Ti1-08i 93.7(3) 01k-Si1-08i 110.1(3) <0-Ti1-0> 92.1 01k-Si1-02 <0-Si1-0> 105.1(4) 109.5 06-TJ2-05 x 2 96.7(2) 07-Ti2-05 x 2 92.2(2) 04b-Si2-06 115.0(3) 06a-Ti2-06 88.6(3) O10-Si2-O6 109.3(4) 07-TJ2-07 x 2 88.3(2) 03-Si2-06 107.3(3) 07a-Ti2-07 93.4(3) O10-Si2-O4b 109.2(4) <0-Ti2-0> 92.1 03-Si2-04b O3-Si2-O10 107.4(3) 108.5(6) O10j-Ti3-O11 139.5(2) <0-Si2-0> 109.5 O10e-Ti3-O11 x6 40.5(2) O10i-Ti3-O11 x 6 139.5(2) O10e-Ti3-O10j x 3 99.1(4) O10-Ti3-O10j x 3 142.0(4) O10f-Ti3-O10j x 3 142.2(4) O10f-Ti3-O10e x 4 68.4(3) <0-Ti3-0> 101.7 Equivalent positions: a = x - y, -y, z ; b = -x + 1, -y, -z + 1; c = -x + y + 1, y, -z; d = -x + 1, x - y , -z; e = -x + y +1, -x + 1, z; f = -y + 1, x - y, z; g = y + 1, -x + y + 1, -z + 1; h = -x + 1, -x + y + 1, z; i = -x + y + 1, y, -z + 1; j = x, x - y, -z + 1; k = x, y, z + 1. 71 R E F E R E N C E S Alfors, J.T. and Putman, G . W . (1965) Revised chemical analyses of traskite, verplanckite and murite from Fresno County, California. American Mineralogist, 50, 1500-1503 Alfors, J.T., Stinson, M . C . , Matthews, R . A . (1965) Seven new barium minerals from eastern Fresno County, California, 50, 314-339 Baldwin, J.R., H i l l , P .G . , von Knorring, O. and Oliver, G J . H . (2000): Exotic aluminium phosphates, natromontebrasite, brazilianite, goyazite, gorceixite and crandallite from rare-element pegmatites in Namibia. Mineralogical Magazine, 64, 1147-1164. Baron, D . and Palmer, C D . (1996): Solubility of K F e 3 ( C r 0 4 ) 2 ( O H ) 6 at 4 to 35 °C. Geochimica et Cosmochimica Acta, 60, 3815-3824. Baur, W . H . (1974): The geometry of polyhedral distortions. Predictive relationships for the phosphate group Acta Crystallographica, B30, 1195-1215. Blanchard, F . N . (1989): N e w X-ray powder data for gorceixite, B a A l 3 ( P 0 4 ) 2 ( O H ) 5 H 2 0 , an evaluation of d-spacings and intensities, pseudosymmetry and its influence on the figure of merit. Powder Diffraction, 4, 227-230. Blass, G. and Graf, H . - W . (1994) Uber neue Mineralien vom Bellerberg, Eifel . Mineralien Welt, 5, 53-55. Blount, A . M . (1974): The crystal structure of crandallite. American Mineralogist, 59, 41-47 Brese, N . E . and O'Keefe, M . (1991): Bond-valence parameters for solids. Acta Crystallographica, B47, 192-197. Brown, I.D. and Wu, K . K . (1976): Empirical parameters for calculating cation-oxygen bond valences. Acta Crystallographica, B32, 1957-1959. Bruker A X S (2000) Promotional pamphlet 72 Carson, C.J. , Dirks, P . H . G . M . and Hand, M . (1995) Stable coexistence of grandidierite and kornerupine during medium pressure granulite facies metamorphism. Mineralogical Magazine, 59, 327-339. Cordero-Borboa, A . E . (1985) A n improved grinder for single crystal X-ray diffraction work. Journal of Physics E : Scientific Instruments, 18, 393-395. Coutinho, J . M . V . , Atencio, D . , Coimbra, A . M . and Fernandes, L . A . (1999): Gorceixite, a singular product of replacement in fossil bones from the Bauru Basin, Brazi l . Canadian Mineralogist, 37, 945-950. Creagh, D . C . and Hubbell, J .H. (1992) International Tables for Crystallography, V o l . C , (A.J .C. Wilson, ed.). Kluwer Academic Publishers, Boston, 200-206. Creagh, D . C . and McAuley , W . J (1992) International Tables for Crystallography, V o l . C, (A.J .C. Wilson, ed.). Kluwer Academic Publishers, Boston, 219-222. Cromer, D.T. and Waber, J.T. (1974) International Tables for X-ray Crystallography, V o l . IV. The Kynoch Press, Birmingham, U K . Dowty, E . (1975) Crystal structure of joaquinite. American Mineralogist, 60, 872-878. Farges, F. (2001) Crystal chemistry of iron in natural grandidierite: an X-ray absorption fine-structure spectroscopy study. Physics and Chemistry of Minerals, 28, 619-629. Fleet, S.G. and Megaw, H . D . (1962) The crystal structure of yoderite. Acta Crystallographica, 15,721. Gottlicher, J. and Gasharova, B . (1999): Can jarosites be monoclinic? Beihefte zum European Journal of Mineralogy 11, 86. 73 Gottlicher, J., Gasharova, B . and Bernotat-Wulf, H . (2000): Pseudotrigonal jarosites (K,H30)Fe3(S04)2(OH)6. Geological Society of America, Program with Abstracts, 32(7), A180. Grant, J .A. and Frost, B . R . (1990) Contact metamorphism and partial melting of pelitic rocks in the aureole of the Laramie anorthosite complex, Morton Pass, Wyoming. American Journal of Science, 290, 425-472. Greenfield, J.E., Clarke, G . L . , and White, R . W . (1998) A sequence of partial melting reactions at Mt . Stafford, central Australia. Journal of Metamorphic Geology, 16, 363-378. Grew, E.S. (1996) Borosilicates (exclusive of tourmaline) and boron in rock-forming minerals in metamorphic environments. In L . M . Anovitz and E.S. Grew, Eds., Boron: Mineralogy, Petrology and Geochemistry, 33, 387-502. Reviews in Mineralogy, Mineralogical Society of America, Washington, D . C . Grew, E.S., McGee, J.J., Yates, M . G . , Peacor, D.R. , Rouse, R . C . , Huijsmanns, J.P.P., Shearer, C . K . , Wiedenbeck, M . , Thost, D . E . and Su, S.-C. (1998b) Boralsilite ( A l i 6 B 6 S i 2 0 3 7 ) : a new mineral related to sillimanite in pegmatites from granulite-facies rocks. American Mineralogist, 83, 638-651. Grew, E.S. , Yates, M . G . , Huijsmans, J.P.P., McGee, J.J., Shearer, C . K . , Wiedenbeck, M . , and Rouse, R . C . (1998a) Werdingite, a borosilicate new to granitic pegmatites. Canadian Mineralogist, 36, 399-414. Grew, E.S., Yates, M . G . , Shearer, C . K . and Wiedenback, M . (1997) Werdingite from the Urungwe district, Zimbabwe. Mineralogical Magazine, 61, 713-718. Groat, L . A . , Hawthorne, F . C , and Ercit, T.S. (1992) The chemistry of vesuvianite. Canadian Mineralogist, 30, 19-48. Hawthorne, F . C , Groat, L . A . and Eby, R . K . (1989): Antlerite, C u 3 S 0 4 ( O H ) 4 , a heteropolyhedral wallpaper structure. Canadian Mineralogist, 27, 205-209. 74 Heide, M . (1992) Synthese und Stabilitat von Grandidierit, M g A l 3 B S i 0 9 . Diplomarbeit, Ruhr-Universitat Bochum, 90 p. Hiroi , Y . Grew, E.S. , Motoyoshi, Y . , Peacor, D.R. , Rouse, R . C . , Matsubara, S., Yokoyama, K . , Miyawaki , R., McGee, J.J., Su, S.C., Hokada, T., Furukawa, N . , and Shibasaki, H . (2002) Ominelite, (Fe,Mg)Al3BSi09 (Fe 2 + analogue of grandidierite), a new mineral from porphyritic granite in Japan. American Mineralogist, 87, 160-170. Huijsmans, J.P.P., Barton, M . , and van Bergen, M . J . (1982) A pegmatite containing Fe-rcih grandidierite, Ti-r ich dumortierite and tourmaline from the Precambrian, high-grade metamorphic complex of Rogaland, S.W. Norway. Neues Jahrbuch fur Mineralogie Abhandlungen, 143, 249-261. Huminicki, D . M . C . and Hawthorne, F .C . (2002): The crystal chemistry of the phosphate minerals. In Phosphates: Geochemical, Geobiological, and Materials Importance ( M . L . Kohn, J. Rakovan and J . M . Hughes, eds.). Reviews in Mineralogy and Geochemistry, 48, 123-253. Ibers, J .A. and Hamilton, W . C . (1964) Dispersion corrections and crystal structure refinements. Acta Crystallographica, 17, 781-782. Jambor, J.L. (1999): Nomenclature of the alunite supergroup. Canadian Mineralogist, 37, 1323-1341. Johan, Z . , Johan, V . , Scharm, H . and Pouba, Z . (1995): Mineralogy and geochemistry of R E E and Cr in Proterozoic cherts of Koksin , Czech Republic. C.R. Acad. Sci. Paris 321, Ser. Ha, 1127-1138. Kato, T. (1971): The crystal structures of goyazite and woodhouesite. Neues Jahrbuch fiir Mineralogie Monatshefte, 241-247. Kato, T. (1987): Further refinement of the goyazite structure. Mineralogy Journal, 13, 390-396. 75 Kato, T. (1990): The crystal structure of florencite. Neues Jahrbuch fur Mineralogie Monatshefte, 227-231. Kharisun, Taylor, M . R . , Bevan, D . J . M . and Pring, A . (1997): The crystal structure of kintoreite, PbFe 3 (P04)2(OH,H 2 0)6. Mineralogical Magazine, 61, 123-129. Kolitsch, U . and Pring, A . (2001): Crystal chemistry of the crandallite, beudantite and alunite groups: a review and evaluation of the suitability as storage materials for toxic metals. Journal of Mineralogy and Petrology, 96, 67-78. Kolitsch, U . , Slade, P .G. , Tiekink, E .R. and Pring, A . (1999b): The structure o f antimonian dussertite and the role of antimony in oxysalt minerals. Mineralogical Magazine, 63, 17-26. Kolitsch, U . , Taylor, M . R . , Fallon, G .D . and Pring, A . (1999a): Springcreekite, B a V 3 + 3 ( P 0 4 ) 2 ( O H , H 2 0 ) 6 , a new member of the crandallite group, from the Spring Creek mine, South Australia: the first natural V 3 + -member of the alunite family and its crystal structure. Neues Jahrbuch fur Mineralogie Monatshefte, 529-544. Kolitsch, U . , Tiekink, E .R .T . , Slade, P .G. , Taylor, M . R . and Pring, A . (1999c): Hinsdalite and plumbogummite, their atomic arrangements and disordered lead sites. European Journal of Mineralogy. 11, 513-520. Kostiner, E . and Rea, J.R. (1974) Crystal structure of ferrous phosphate, Fe3(P04)2. Inorganic Chemistry, 13,2876-2880. Lacroix, A . (1902) Note preliminaire sur une nouvelle espece minerale. Bulletin de la Societe francaise de Mineralogie, 25, 85-86. Liferovich, R.P. , Yakovenchuk, V . N . , Pakhomovsky, Y . A . , Bogdanova, A . N . and Stumpel, G . (1999): Crandallite, goyazite and gorceixite from the Kovdor massif, Russia. Neues Jahrbuch fur Mineralogie Monatshefte, 145-166. 76 Malinovskii , Y . A . , Pobedimskaya, E . A . , and Belov, N . V . (1976) Crystal structure of traskite. Doklady Akademii Nauk SSSR, 229, 1101-1104 M c K i e , D . (1965) The magnesium aluminum borosilicates: kornerupine and grandidierite. Mineralogical Magazine, 34, 346-357. Menchetti, S. and Sabelli, C . (1976): Crystal structure of the alunite series: crystal structure refinement of alunite and synthetic jarosite. Neues Jahrbuch fur Mineralogie Monatshefte, 406-417. Oberti, R. (2001) The diffraction experiment in the study of solid solutions: Long-range properties. E M U Notes in Mineralogy, 3, 179-205. Olesch, M . and Seifert, F. (1976) Synthesis, powder data and lattice constants of grandidierite, ( M g , F e ) A l 3 S i B 0 9 . Neues Jahrbuch fur Mineralogie Monatshefte, 11,513-518. Peacor, D.R. , Rouse, R . C . , and Grew, E.S. (1999) Crystal structure of boralsilite and its relation to a family of boroaluminosilicates, sillimanite, and andalusite. American Mineralogist, 84, 1152-1161. Pouchou, J .L. and Pichoir, F. (1985) P A P cj)(pZ) procedure for improved quantitative microanalysis. Microbeam Analysis, 1985, 104-106. Qiu, Z . - M . , Rang, M . , Chang, J.-T., and Tan, M . - J . (1990) Mossbauer spectroscopy of grandidierite. Chinese Science Bulletin, 35, 43-47. Radoslovich, E . W . (1982): Refinement of gorceixite structure in Cm. Neues Jahrbuch fur Mineralogie Monatshefte, 446-464. Radoslovich, E . W . and Slade, P .G . (1980): Pseudo-trigonal symmetry and the structure of gorceixite. Neues Jahrbuch fur Mineralogie Monatshefte, 157-170. 77 Rasmussen, B . , Buick, R. and Taylor, W.R. (2000): Removal of oceanic R E E by authigenie precipitation of phosphatic minerals. Earth and Planetary Science Letters, 164, 135-149. Robinson, K . , Gibbs, G . V . , and Ribbe, P . H . (1971) Quadratic elongation: a quantitative measure of distortion in coordination polyhedra. Science, 172, 567-570. Schwab, R . G . , Gotz, C , Herold, H . and De Oliveira, N . P . (1991): Compounds of the crandallite type; synthesis and properties of pure (Ca, Sr, Ba, Pb, La , Ce to Eu) - arsenocrandallites. Neues Jahrbuch fur Mineralogie Monatshefte, 97-112. Schwab, R . G . , Herold, H . , Gotz, C. and De Oliveira, N . P . (1990): Compounds of the crandallite type: Synthesis and properties of pure goyazite, gorceixite and plumbogummite. Neues Jahrbuch fur Mineralogie Monatshefte, 113-126. Scott, K . M . (1987): Solid solution in, and classification of, gossan-derived members of the alunite-jarosite family, northwest Queensland, Australia. American Mineralogist, 72, 178-187. Seifert, F. and Olesch, M . (1977) Mossbauer spectroscopy of grandidierite, (Mg,Fe)Al3BSi09. American Mineralogist, 62, 547-553. Shannon, R . D . (1976) Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica, A32 , 751-767. Stephenson, D . A . and Moore, P .B . (1968) The crystal structure of grandidierite, ( M g , F e ) A l 3 S i B 0 9 . Acta Crystallographica, B24, 1518-1522. Stuwe, K . , Braun, H - M . and Peer, H . (1989) Geology and structure of the Larsemann Hil ls Area. Australian Journal of Earth Science, 36, 219-241. 78 Tan, M . - J . and Lee, H . - C . (1988) Discovery of grandidierite in China. Geological Science and Technology Information, 7, 30 (in Chinese). Taylor, M . , Smith, R . W . and Ahler, B . A . (1984): Gorceixite in topaz greisen assemblages, Silvermine area, Missouri . American Mineralogist, 69, 984-986. van Hees, E . H . , Sirbescu, M . - L . C , Shelton, K . L . and Pressacco, R. (2002): Supergene phosphate enrichment in carbonate-derived eluvial sediments: Agr ium phosphate mine, Kapuskasing, Ontario, Canada. Geological Society of America, Program with Abstracts, 34(6), A312. von Knorring, O., Sahama, T .G . , and Lehtinen, M . (1969) A note on grandidierite from Fort Dauphin, Madagascar. Bulletin of the Geological Society of Finland, 41, 71-74. Werding, G . and Schreyer, W . (1996) Experimental studies on borosilicates and selected borates. In L . M . Anovitz and E.S. Grew, Eds., Boron: Mineralogy, Petrology and Geochemistry, 33, 117-163. Reviews in Mineralogy, Mineralogical Society of America, Washington, D . C . Wong-Ng, W. , Siegrist, T., DeTitta, G.T., Finger, L . W . , Evans, H.T. , Jr., Gabe, E.J . , Enright, G.D. , Armstrong, J.T., Levenson, M . , Cook, L .P . , and Hubbard, C R . (2001) Standard reference material ( S R M 1990) for single crystal diffractometer alignment. Journal of Research of the National Institute of Standards and Technology, 106, 1071-1094. 79 A. l Commonly used symbols and terms. a, b, c Unit cell axes a, P, y Unit cell angles x, y, z Used to indicate atomic positions on cartesian axes hkl Mi l l e r index V Volume Z number of empirical formula units in the unit cell p Linear absorption coefficient R R = S | F 0 - F C | / Z F 0 ; indicates how closely your model matches the true model F 0 observed structure factor F c calculated structure factor R w Weighted R Rj n t Integrated R |E 2 -1 | Value of 0.968 indicates centrosymmetric, 0.736 indicates non-centrosymmetric I Intensity U Displacement factor < > Indicates average values on the tables of bond lengths and interatomic angles dmeas Measured distance between planes d c a i c Calculated distance between planes 80 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0052713/manifest

Comment

Related Items