The Crystal Chemistry of Gorceixite, Grandidierite, and Traskite with The
THE CRYSTAL CHEMISTRY
OF
GORCEIXITE, GRANDIDIERITE, AND TRASKITE
by
TASHIA JAYNE DZIKOWSKI
B.Sc, The University of Manitoba, 2004
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
in
THE FACULTY OF GRADUATE STUDIES
^Geological Sciences^
THE UNIVERSITY OF BRITISH COLUMBIA
August 2006
© Tashia Jayne Dzikowski, 2006 ABSTRACT
This thesis reinvestigates the crystal structures of gorceixite and traskite, and the geometric effects of vFe2+ for vMg substitution on the crystal structures of the grandidierite- ominelite series. All data was measured using using MoKa radiation on an automated Bruker X8 single-crystal diffractometer with a SMART APEX CCD (charge coupled device) detector.
The crystal structure of gorcexite (BaAl3(P030,OH)2(OH6), 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-
2+ 2+ 2+ ominelite (MgAl3BSi09-Fe Al3BSi09) series withX- (Fe + Mn + Zn)/(Fe + Mn + Zn +
Mg) ranging from 0.00 to 0.52 were studied to determine the geometric effects of Fe substitution
for Mg 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 )05 polyhedron, which
increases in volume by 0.36 A3 (5.0%), largely as a result of expansion of the MgFe-05, -02,
and -06 (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
2+ of the traskite (Ba9Fe 2Ti2(Si03)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.
ii TABLE OF CONTENTS
ABSTRACT ii
TABLE OF CONTENTS ; iii
LIST OF TABLES. v
LIST OF FIGURES vi
ACKNOWLEDGEMENTS vii
1.0 INTRODUCTION 1
2.0 GORCEIXITE 2
2.1 Introduction 2
2.2 Experimental 4
2.3 Results 7
2.4 Discussion 17
3.0 GRANDIDIERITE 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
iii 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 vFe2+ 58
3.5.6 Conclusion: vFe in minerals 58
4.0 TRASKITE 60
4.1 Introduction 60
4.2 Experimental 60
4.3 Results and Discussion 62
REFERENCES 72
APPENDIX A.l Commonly used symbols and terms 80
iv LIST OF TABLES
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 (Fe2+ + Mn + Zn)/(Fe2+ + Mn + Zn + Mg) vs. (a) a, (b) b, (c) c, (d) Ffor grandidierite and ominelite 41
3.4 (Fe2+ + Mn + Zn)/(Fe2+ + Mn + Zn + Mg) vs. (a) MgFe-05a, (b) MgFe-02, (c) MgFe-06 x 2 for grandidierite and ominelite 42
3.5 (Fe2+ + Mn + Zn)/(Fe2+ + Mn + Zn + Mg) vs. (a)All-06 x 2; (b) A12-04 x 2; (c) A12-07f x 2 (squares), -05c x 2 (triangles) for grandidierite and ominelite 43
3.6 (Fe2+ + Mn + Zn)/(Fe2+ + Mn + Zn + Mg) vs. (a) Ol-MgFe-02 (squares), 06-MgFe-06b (triangles); (b) Ol-MgFe-06 x 2; (c) 02-MgFe-06 x 2 (squares), 01-MgFe-05a (triangles); and (d) 02-MgFe-05a for grandidierite and ominelite 45
3.7 (Fe2+ + Mn + Zn)/(Fe2+ + Mn + Zn + Mg) vs. (a) 06-A11-02 x 2 (squares), -02d x 2 (triangles); (b) 01-A13-05a (squares), -02i (triangles) for grandidierite and ominelite 46
3.8 (Fe2+ + Mn + Zn)/(Fe2+ + Mn + Zn + Mg) vs. (a) 04-Si-06j x 2 (squares), -Ol (triangles); (b) 06j-Si-06f (squares), -Ol x 2 (triangles) for grandidierite and ominelite 47
2+ 2+ 2+ 3.9 (Fe + Mn + Zn)/(Fe + Mn + Zn + Mg) vs. (Mg,Fe )05 polyhedral edges: (a) 02-06 x 2 (squares), 01-05a (triangles); (b) 06-05a x 2 (squares), -6b (triangles); (c) 01-02 (squares), -06 x 2 (triangles) 49
3.10 (Fe2+ + Mn + Zn)/(Fe2+ + Mn + Zn + Mg) vs. polyhedral edges:
(a) A1106, 06-02d x 2; (b) A1206, 07f-04h x 2 (squares),
-04 x 2 (triangles); (c) A1305, 02i-01 50
2+ 2+ 3.11 (Fe + Mn + Zn)/(Fe + Mn + Zn + Mg) vs. Si04 tetrahedral edges, 04-06 x 2 51
3.12 (Fe2+ + Mn + Zn)/(Fe2+ + Mn + Zn + Mg) vs. (a) volume of the (Mg,Fe2+)05 (squares) and A130s (triangles) polyhedra, (b) volume of
the All06 (squares) and A1206 (triangles) octahedra, (c) tetrahedral angle variance for Si04 tetrahedron in grandidierite and ominelite 53
4.1 Structure of traskite projected down (001) 61
vi ACKNOWLEDGEMENTS
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 Colin Fyfe and Mati 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 of their help with interpreting my results. I would also like to thank Allison Brand for helping prepare and revise my manuscripts. My 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 NSERC operating grants to Lee A. Groat.
Personal financial support was provided by a Post-Graduate Masters and a Canada Graduate
Scholarship Masters NSERC as well as the University of British Columbia in the form of
scholarships and teaching assistantships.
vii 1.0 INTRODUCTION
Here I reinvestigate the crystal structures of gorceixite and traskite, and the geometric effects of vFe2+ for vMg substitution on the crystal structures of the grandidierite-ominelite series. For data collection I used a Bruker X8 single crystal X-ray diffractometer with a SMART
APEX CCD (charge coupled device) detector in the Center for Higher Order Structure
Elucidation (C-HORSE) 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 X8 single crystal X-ray diffractometer with a SMART APEX CCD detector primarily
because of the advancements of the SMART APEX CCD detector over the former area or serial
detectors (Bruker AXS 2000). The X8 diffractometer with the SMART APEX CCD detector has
higher sensitivity, greater precision, resolution, accuracy and shorter collection times than other
detectors for a number of reasons. First, the SMART APEX CCD 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 CCD 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,
BaAl3(P030,0H)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 Agrium 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,
BaAl3(As04)(As03-OH)(OH)6]. In natural gorceixite, partial substitution of Ba 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 V3+ and 0.18 mol Cr3+ (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
As5+ or P5+, and S6+ is <0.25 mol %, whereas minerals of the alunite group have (sensu stricto)
have the T site dominated (> 0.75 mol %) by S6+. The primary distinction between the alunite
supergroup and the jarosite supergroup rests on whether the proportion of Al is greater than that 2 of Fe or vice versa. Of the more than 25 CNMMN-approved members with Al > Fe, three have
Ba 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
3+ dussertite BaFe3(As04)2(OH)6, and springcreekite BaV3 [(OH,H20)6(P04)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 Alice, New 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 CaAl3(P03-(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
BaAl3(P04)(P03-OH)(OH)6 was therefore suggested. Blanchard (1989) collected powder X-ray diffraction data from a gorceixite sample from the Big 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, Kolitsch 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 XL30
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 CAMECA SX-50 electron microprobe operated in the wavelength-dispersion mode.
Operating conditions were as follows: accelerating voltage, 15 kV; 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 "PAP" <)>(pZ) method (Pouchou and Pichoir 1985). For the
elements considered, the following standards, X-ray lines, and crystals were used: grossular,
AlKa, TAP; apatite, ?Ka, CaKa, PET; SrTi03, SrZa, TAP; barite, Bala, 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 X8 APEX diffractometer with graphite monochromated
MoKa radiation. The data were obtained at room temperature to a maximum 29 value of 55.7°.
4 TABLE 2.1. ELECTRON-MICROPROBE COMPOSITION OF THE GORCEIXITE SINGLE- CRYSTAL USED IN THIS STUDY
Point 1 Point 2 Point 3
P205 (wt%) 27.02 27.03 28.79
Al203 28.74 28.94 29.09 CaO 0.05 0.02 0.12 FeO 0.12 0.12 0.12 SrO 0.25 0.28 0.26 BaO 29.50 29.43 29.51
Na20 0.17 0.17 0.17
H20* 11.97 11.98 12.78 F 0.07 0.05 0.01 0=F -0.03 -0.02 0.00 TOTAL 97.86 98.00 100.85
P5+ (apfu) 2.000 2.000 2.000 Al3+ 2.962 2.981 2.813 Ca2+ 0.005 0.002 0.011 Fe2+ 0.009 0.009 0.008 Si2* 0.013 0.014 0.012 Ba2+ 1.011 1.008 0.949 Na+ 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: Compositions were recalculated on the basis of 2 (P5+) atoms per formula unit. *Determined by stoichiometry, assuming 7 (OH + 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. Of the 14,812 reflections that were collected, 253
were unique (Rmt = 0.036). Data were collected and integrated using the Bruker SAINT software package. The linear absorption coefficient, p, for MoKa radiation was 4.21 mm-1. Data were corrected for absorption effects using the multi-scan technique (SADABS), with minimum and maximum transmission coefficients of 0.441 and 0.714, respectively. The data were corrected for
Lorentz and polarization effects.
All refinements were performed using the SHELXTL crystallographic software package of
Bruker AXS. 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 TWIN and BASF commands in SHELXTL. 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). All 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
2 2 2 2 minimized: XwCF0 - Fc ) on F ) 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 e7A3, 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 TABLE 2.2 GORCEIXITE: DATA COLLECTION AND STRUCTURE-REFINEMENT INFORMATION
a (A) 7.0538(3) F0 > 4a F0 253
c(A). 17.2746(6) RM 0.036(3)
V(A3) 744.36(5) L.s. parameters 29
R3M 166 Space Group 0^°- ) for F0 > 4o F0 0.0231
Z 3 F?i for all unique F0 0.0231
Crystal size (mm) 0.10 x 0.09 x 0.007 wR2 0.0633
Radiation MoKa a (see Note) 0.0235
Monochromator graphite b (see Note) 7.97
Total F0 14812 GooF (= S) 1.355
Unique F0 253
2 2 2 2 2 Note: w = 1/[a (F0 ) + (a x P) + b x P] where P = [Max (F0 , 0) + 2 x Fc )]/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-01a x 6 2.825(3) 01a-A-01f x 6 106.87(6)
-OHb x 6 2.859(3) -Olg x 6 73.13(6)
-OHh x 12 55.56(5)
G-01c x 2 1.914(3) -OHa x 6 79.19(9)
-OHd x 4 1.902(1) -OHi x 6 100.81(8)
-OHg x 2 124.1(1)
T-01e x 3 1.538(3) <0-A-0> 90.0 -02 1.563(6)
-G-OHi x 4 87.9(1)
OH-H 0.980(1) OHd-G-OHe x 2 89.6(2)
H-02e 1.904(5) -OHj x 2 90.4(2) 0H-02e 2.884(4) <0-G-0> 90.0
01e-T-01k x 3 109.8(1)
-02 x 3 109.1(1)
<0-T-0> 109.5
OH-H-02C 179(8)
Equivalent positions: a = x - y + VS, x - VS, -z + 2A\ b = -x + VS, -y + 2A, -z + 2A\ c = y, -x +
2 2 2 2 1 y, -z; d = x - y + A, x - A, -z + "A; e = -x + A, -y + "A, -z + VS; f = y - A, -x + y - /3, -z + 2 2 2 2 A\ g = -y + A, x - y + Vs, z + VS; h = x - VS, y - A, z + VS; i = -x + y + VS, -x + A, 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 OH molecules to form an icosahedron. TheA-0 and^l-OH 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 a2; Hawthorne et al. 1989) are 0.0004 and 729.53, respectively, and the polyhedral volume is 55.64 A3. Electron-microprobe results indicate that the site is completely occupied by Ba, but the site occupancy refines to 88%
Ba (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% Ba
(and 4% vacancy) in his Cm refinement. The bond-valence sum (Table 2.5) assuming complete occupancy by Ba is 2.70 valence units; this improves to 2.38 valence units if we assume partial occupancy, but it is important to note that Ba compounds in general commonly give poor bond- valence sums (Brown and Wu 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 OH molecules to form a distorted octahedron. The G-0 and
G-OH distances are 1.914 (x 2) and 1.902 A (x 4), respectively (mean 1.906 A), and the
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 02 site that together form a tetrahedron. The 7-01 and 7-02 distances are
1.538 (x 3) and 1.563 A respectively. The 01-7-01 angles are 109.8° and the
12 TABLE 2.5 BOND-VALENCE* ANALYSIS OF GORCEIXITE
Site A (BA2+) G(ALi+) H ^\
01 0.24 x6l 0.49x2^ 1.20x34 1.92
02 1.12 0.08 x 3 -> 1.34
OH 0.21x6^ 0.51x44x2^ 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 01-7-02 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 EDS spectra, electron-microprobe compositions, and refined site-occupancy indicate that the site is completely occupied by P5+. The mean P-01,02 distance of 1.544 A is slightly longer than the
(2002).
The H atom site (at special position 18/z, x, -x, z) was identified from a difference-Fourier map. Without constraints the OH-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 02 atom is involved in hydrogen bonding (as an acceptor) with three different OH groups; the H-02 distance is 1.904 A, the OH-02 distance is 2.884 A, and the
OH-H-02 angle is close to linear (179°).
The low bond-valence sum of 1.34 valence units for 02 suggests that 02 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 02 position, and one 02 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-02-01 angle of 35.1°, the hypothetical 02-H--01 angle would be expected to be relatively sharp. Although it is beyond the scope of this study, it would be
14 interesting to see if this hypothetical hydrogen-bonding scheme is detectable in spectrographic studies of gorceixite. The infrared spectrum for gorceixite from the Kovdor massif in Russia
1 shows a broad band at 1680 cm" that might indicate the presence of H20 (Liferovich et al.
1999).
The presence of OH groups at the 02 site would also help resolve the problem of charge balance. If the cation sites are fully occupied with Ba, Al, and P, the total charge is +21.
Assuming O at all 01 and 02 sites, and OH at the OH site, the total negative charge is -22. This may be resolved by assuming that the 02 site is half-occupied by O and half-occupied by OH, 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 Al3+02(OH)4 octahedra share corner OH atoms to form sheets perpendicular to the c axis (Figure 2.2). The OH groups form a plane roughly parallel to (001).
The 01 atoms lie on opposite sides of the OH 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 OH ions enclose a site wherein the 12-coordinated Ba ion is located (Figure 2.2). The apical 02 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 02 atom forms weak hydrogen bonds with the three closest hydroxyl groups. The smallest 02-02 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 3+ AI 02(OH)4 octahedra, P04 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-rich members the observed deviation was less than 1°. All synthesized samples of K-rich 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°. An 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 will require more work.
17 3.0 THE GEOMETRIC EFFECTS OF VFE2+ FOR VMG SUBSTITUTION ON THE
CRYSTAL STRUCTURES OF THE GRANDIDIERITE-OMINELITE SERIES
3.1 Introduction
2+ Grandidierite, (Mg,Fe )Al3BSi09, (Lacroix 1902; McKie 1965; Stephenson and Moore
2+ 2+ 1968) and its Fe -dominant analog ominelite, (Fe ,Mg)Al3BSi09 (Hiroi et al. 2002), form a continuous series in which Fe substitutes for Mg 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 = Mg 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 vMg or vFe2+, 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 vFe2+ for vMg substitution on the crystal structures of the grandidierite-ominelite series, and to investigate the reasons for the apparent rarity of vMg and vFe2+ 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 > Mg 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-Al-Si phases that includes boralsilite, synthetic Alg[(Al,B)i2B4]033, and werdingite, all of which have structures based on chains of edge-sharing Al 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 MgFe-02 and
MgFe-05 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 AI3O5 polyhedra and A106 octahedra all have some edges that are shared. Each (Mg,Fe )Os polyhedron shares two 02-06 edges with two different All06 octahedra and one 01-05 edge with an ABO5 polyhedron. All06 octahedra share two 02-03 edges with two adjacent All06 octahedra and two 02-06 edges with (Mg,Fe2+)Os polyhedra.
Every A1206 octahedron shares two 04-05 edges with other A1206 octahedra and two 05-07
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 ABO5 polyhedra share one 01-05 edge with an
(Mg,Fe2+)05 polyhedron and two 05-07 edges with A1206 octahedra. It is interesting to note that in this case all of the shared edges meet at the same 05 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,Fe2+)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
XAFS spectra from eight grandidierite samples from Madagascar and Zimbabwe. The pre-edge spectra were consistent with dominantly five-coordinated Fe2+. Analysis of the XANES and
EXAFS spectra confirmed that Fe2+ substitutes for Mg in grandidierite with a slight expansion
(~2%) of the local structure around Mg. In addition, Fe was detected in some samples (5-10 mol% of total Fe); based on theoretical calculations of the EXAFS region this was thought to be located at the five-coordinated MgFe sites or the most distorted six-coordinated Al 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 CAMECA SX-50
22 TABLE 3.1 SAMPLE INFORMATION FOR GRANDIDIERITE AND OMINELITE
G17 G8 G4 G12 G1 G2 G9
Long Lake, Sahakondra, Almgjotheii, Locality Karibe area, Andrahomana, Larsemann Hills, Ampamatoa, Zimbabwe Rogaland, Madagascar Zimbabwe Madagascar Antarctica Madagascar Norway Canadian Royal Ontario Mus. Nat. Hist. Source H.-M. Braun Harvard Museum of Smithsonian ESG Museum Naturelle Nature
Sample 32806 63 108118 80693 144869 102.149 Aim 8a number Color transparent turquoise light blue dark blue green-blue turquoise medium blue Stuwe et al. (1989), Carson et Grew et al. Grew et al. Grew et al. Grew et al. References al. (1995), Grew (1997) (1997) (1998a) (1998a) etal. (1998b) electron microprobe operated in the wavelength-dispersion mode. Operating conditions were as follows: accelerating voltage, 15 kV; 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 "PAP" (diopside, Ka, TAP), Al (kyanite, Ka, PET), Cr (MgCr204, Ka, LiF), Mn (MnSi03, Ka, LiF), Fe (Fe2Si04, Ka, LiF), and Zn (gahnite, Ka, LiF). Formulas were calculated on the basis of six cations and nine O atoms per formula unit (Table 3.2). Three of the samples (Gl, 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 kV and 40 mA, using a take-off angle of 6°. The X-ray diffraction pattern was analyzed using the ICDD (International Centre for Diffraction Data) database PDF-4 using search-match software supplied by Siemens (Bruker). Cell dimensions were determined using X-ray powder-diffraction data fitted with the LeBail method and the Rietveld program Topas 3.0 (Bruker AXS) 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 UBC following the description in Cordero-Borboa (1985). Data were collected at C-HORSE (the Centre for Higher Order Structure Elucidation, in the Department of Chemistry at UBC) using a Bruker X8 24 TABLE 3.2 AVERAGE ELECTRON-MICROPROBE COMPOSITIONS OF GRANDIDIERITE AND OMINELITE CRYSTALS USED IN THE SINGLE-CRYSTAL X-RAY DIFFRACTION STUDY G17 G8 G4 G12 G1 G2 G9 n 7 4 4 5 4 4 3 P205 bdl 0.24(5) bdl 0.07(5) 0.19(6) 0.08(3) bdl Si02 20.26(6) 19.88(4) 20.12(19) 19.77(9) 19.53(9) 19.49(10) 19.57(4) B203* 11.91(2) 11.78(3) 11.84(3) 11.64(2) 11.57(3) 11.41(2) 11.33(3) Al203 52.01(20) 50.74(15) 51.65(27) 50.68(10) 50.18(10) 49.63(11) 48.93(3) Cr203 bdl 0.34(5) bdl bdl bdl bdl bdl Fe203 1.03(5) 1.62(19) 1.35(41) 1.38(29) 1.62(11) 1.09(15) 1.21(45) MgO 13.71(5) 11.99(8) 11.35(5) 10.02(7) 9.06(8) 7.30(3) 6.22(6) MnO bdl bdl 0.06(3) 0.08(3) 0.08(2) bdl bdl FeO 0.01(2) 2.81(23) 3.73(33) 5.78(29) 7.39(7) 10.36(15) 11.95(19) ZnO bdl bdl bdl bdl bdl bdl 0.23(5) TOTAL 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) - Si4+ 0.99(0) 0.98(0) 0.98(1) 0.98(0) 0.98(0) 0.99(0) 1.00(0) B3+ 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Al3+ 2.98(1) 2.94(0) 2.98(1) 2.97(0) 2.96(1) 2.97(1) 2.95(2) Cr3+ - 0.01(0) - - - - - Fe3+ 0.04(0) 0.06(1) 0.05(2) 0.05(1) 0.06(0) 0.04(1) 0.05(2) Mg2+ 0.99(0) 0.88(0) 0.83(0) 0.74(1) 0.68(0) 0.55(0) 0.47(0) 2+ Mn - - 0.00(0) 0.00(0) 0.00(0) - - Fe2+ 0.00(0) 0.12(1) 0.15(1) 0.24(1) 0.31(0) 0.44(1) 0.51(1) Zn2+ ------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) ^SREF* 0.024(1) 0.126(2) 0.184(4) 0.273(2) 0.336(2) 0.450(2) 0.522(2) Note: The G8 crystal was lost subsequent to SREF data collection; the analyses were obtained from a crystal from the same sample. Compositions were recalculated on the basis of 6 cations and 9 O apfu. Ti, Ca, Na, and K were sought but not detected. bdl = below detection limit (assumed to be 0.05 oxide wt%). *Determined by stoichiometry. ^EMPA = (Fe2+ + Mn + Zn)/(Fe2+ + Mn + Zn + Mg). %REF = Fe/(Fe + Mg). 25 APEX diffractometer with graphite-monochromated MoKa radiation and a CCD 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 SAINT software package and were corrected for absorption effects using the multi-scan technique (SADABS) and for Lorentz and polarization effects. All refinements were performed using the SHELXTL crystallographic software package of Bruker AXS. Neutral-atom scattering factors were taken from Cromer and Waber (1974). Anomalous dispersion effects were included in Fcaic (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). An 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(.F0 -Fc) on F~. The weighting scheme was based on counting statistics. The total occupancy factors of the three Al sites were refined to test the possibility of (Al,Fe3+) solid solution, as suggested by the electron microprobe compositions. The results ranged from 0.487(2) to 0.494(2) for All, 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 Al sites, but were unsuccessful, likely because the amounts of Fe (as indicated by the electron microprobe compositions) are so small. Accordingly, the occupancies of all three Al sites were fixed (at 1.0 Al 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 "IUCr" 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 (EMPA) 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 Al 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 Mn that attain a maximum of 0.14 wt% MnO (-0.01 Mn apfu) in sample G12. Samples G8 and Gl 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 Al at one of the Al sites. Sample G9 27 TABLE 3.3 DATA MEASUREMENT AND REFINEMENT INFORMATION FOR GRANDIDIERITE AND OMINELITE G17 G8 G4 G12 G1 G2 G9 SSCXRD* (A) 10.3640(4) 10.3529(7) 10.3590(3) 10.3660(9) 10.3643(5) 10.3631(4) 10.3675(5) 11.0147(3) 11.0296(9) 11.0438(4) 11.0627(5) 11.0873(6) frsCXRD (A) 10.9995(5) 10.9971(7) CsCXRD (A) 5.7805(2) 5.7754(4) 5.7762(2) 5.7790(5) 5.7800(3) 5.7778(2) 5.7879(3) 665.30(8) VsCXRD (A ) 658.98(6) 657.5(1) 659.07(4) 660.7(1) 661.58(7) 662.39(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) Space group Pbnm Pbnm Pbnm Pbnm Pbnm Pbnm Pbnm Z 4 4 4 4 4 4 4 Crystal size (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 Radiation MoKoc MoKa MoKa MoKa MoKa MoKa MoKa Monochromator graphite graphite graphite Graphite graphite graphite graphite 13867 18782 17377 14875 Total F0 13314 16164 13534 908 901 906 898 Unique F0 902 900 901 854 833 894 882 873 F0 > 4o F0 869 870 0.021(9) 0.03(1) 0.02(1) 0.03(1) 0.023(8) 0.023(9) 0.022(9) L.s. parameters 87 87 87 87 87 87 87 0.0205 0.0164 0.0141 0.0168 for F0 > 4a F0 0.0163 0.0166 0.0211 0.0225 0.0166 0.0145 0.0173 Ri, all unique F0 0.0169 0.0172 0.0223 0.0502 0.0500 0.0584 0.0555 0.0485 0.0412 0.0466 W/R2 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 GooF (= S) 1.223 1.228 1.173 1.140 1.331 1.154 1.161 2 2 2 2 2 Note: w = 1/[a (F0 ) + (a x P) + b x P] where P = [Max (F0 , 0) + 2 x Fc )]/3 *Single-crystal X-ray diffraction data. fPowder X-ray diffraction data. TABLE 3.4 ATOMIC PARAMETERS FOR GRANDIDIERITE AND OMINELITE G17 G8 . G4 G12 G1 G2 G9 MgFe X 0.09183(6) 0.09262(5) 0.09293(6) 0.09348(5) 0.09387(4) 0.09438(3) 0.09462(3) 0.21894(3) 0.21896(3) y 0.21910(5) 0.21906(5) 0.21903(5) 0.21897(5) 0.21896(4) 1/ v v. V. VA VA % z /4 74 /4 74 /4 / 4 Occ. Mg 0.488(1) 0.437(1) 0.409(2) 0.363(2) 0.333(1) 0.275(1) 0.239(1) Fe 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 0 y 0 0 0 0 0 0 z 0 0 0 0 0 0 0 1 1 1 1 1 / /2 /2 AI2 X /2 72 % /2 2 0 0 y 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) 0.44810(4) 0.44811(4) y 0.44792(4) 0.44799(4) 0.44795(6) 0.44796(5) 0.44807(4) v 17 V. VA VA % y* z /4 74 /4 74 /4 Si X 0.43356(5) 0.43370(5) 0.43377(6) 0.43394(5) 0.43406(5) 0.43423(4) 0.43431(5) 0.26345(4) y 0.26330(4) 0.26325(4) 0.26334(5) 0.26340(5) 0.26340(4) 0.26343(3) 1/ v v. V. % 1/4 % z /4 /4 /4 74 B X 0.2512(2) 0.2512(2) 0.2512(2) 0.2511(2) 0.2512(2) 0.2512(2) 0.2510(2) 0.0002(1) 0.0003(2) y 0.0003(2) 0.0004(2) 0.0004(2) 0.0002(2) 0.0003(2) 3 3 3 3 /4 z 3/4 % % /4 /4 /4 01 X 0.2750(1) 0.2756(1) 0.2755(1) 0.2758(1) 0.2761(1) 0.2763(1) 0.2765(1) 0.28964(9) 0.2898(1) y 0.2882(1) 0.2883(1) 0.2888(1) 0.2892(1) 0.2891(1) v v. v. V. VA Vt Vi z /4 74 /4 74 /4 02 X 0.1186(1) 0.1183(1) 0.1184(1) . 0.1183(1) 0.11818(9) 0.1182(1) 0.1181(1) 0.0205(1) y 0.0224(1) 0.0222(1) 0.0216(1) 0.0214(1) 0.0214(1) 0.02087(9) 1/ v v. V. VA VA Vi z /4 /4 74 74 /4 / 4 03 X 0.1210(1) 0.1211(1) 0.1212(2) 0.1209(1) 0.1210(1) 0.1210(1) 0.1211(1) -0.0037(1) y -0.0035(1) -0.0033(1) -0.0036(1) -0.0037(1) -0.0036(1) -0.00373(8) 3 3 3 3 3 z 3/4 % /4 /4 /4 /4 /4 04 X 0.4738(1) 0.4738(1) 0.4739(2) 0.4738(1) 0.4739(1) 0.4738(1) 0.4740(1) y 0.1199(1) 0.1202(1) 0.1201(1) 0.1203(1) 0.1205(1) 0.12070(9) 0.1208(1) •7 VA VA 1 1 /4 /4 /4 /4 /4 % % 05 X 0.5465(1) 0.5465(1) 0.5463(1) 0.5464(1) 0.5465(1) 0.54644(9) 0.5464(1) y 0.1002(1) 0.0999(1) 0.0997(1) 0.0992(1) 0.0988(1) 0.09836(9) 0.0981(1) 3 3 3 3 3 3 /4 /4 /4 /4 /4 z /4 06 X -0.00731(8) -0.00755(8) -0.00720(9) -0.00728(9) -0.00724(8) -0.00717(6) -0.00700(8) y 0.17099(8) 0.17090(8) 0.1708(1) 0.1707(1) 0.17053(8) 0.17035(7) 0.17034(8) z -0.0227(2) -0.0227(2) -0.0225(2) -0.0228(2) -0.0228(2) -0.0231(1) -0.0231(1) 07 X 0.18068(9) 0.18059(9) 0.1807(1) 0.1807(1) 0.18054(9) 0.18067(7) 0.18070(8) y 0.50112(7) 0.50118(7) 0.50117(9) 0.50113(9) 0.50112(7) 0.50109(6) 0.50115(7) z -0.0452(2) -0.0452(2) -0.0453(2) -0.0455(2) -0.0452(2) -0.0454(1) -0.0453(2) o TABLE 3.5 ATOMIC DISPLACEMENT PARAMETERS FOR GRANDIDIERITE AND OMINELITE (FOR DEPOSIT) G17 G8 G4 G12 G1 G2 G9 MgFe 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) -0.0017(1) UM -0.0013(2) -0.0013(2) -0.0017(2) -0.0017(2) -0.0016(1) -0.0016(1) 0.00000 0.00000 Wis 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 U23 0.0082(2) 0.0067(2) 0.0072(1) 0.0081(1) ueq 0.0070(2) 0.0069(2) 0.0105(2) AI1 0.0057(3) 0.0056(3) 0.0087(3) 0.0065(3) 0.0051(3) 0.0054(2) 0.0060(3) 0.0057(3) 0.0084(3) 0.0066(3) 0.0056(3) 0.0058(2) 0.0071(2) u22 0.0052(3) 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) 0.0000(2) 0.0001(2) 0.0000(2) -0.0001(2) 0.0001(2) 0.0000(1) 0.0000(2) U23 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) 0.0048(3) 0.0041(3) 0.0049(2) 0.0050(3) u33 0.0053(3) 0.0049(3) 0.0066(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) 0.0005(2) 0.0006(2) 0.0006(1) 0.0006(2) u23 0.0005(2) 0.0005(2) 0.0005(2) 0.0054(1) 0.0054(1) 0.0081(2) 0.0061(2) 0.0051(1) 0.0056(1) 0.0063(1) Ue, 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 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 U23 0.0054(1) 0.0051(1) 0.0085(2) 0.0061(2) 0.0049(1) 0.0053(1) 0.0062(1) ueq Si1 Uu 0.0063(2) 0.0060(2) 0.0097(3) 0.0072(3) 0.0053(2) 0.0057(2) 0.0068(2) 0.0083(3) 0.0061(3) 0.0048(2) 0.0050(2) 0.0063(2) U22 0.0048(2) 0.0050(2) U33 0.0059(2) 0.0054(2) 0.0077(3) 0.0056(3) 0.0046(2) 0.0053(2) 0.0057(2) 0.0000(2) -0.0000(2) -0.0002(2) -0.0001(2) -0.0000(2) 0.0001(1) -0.0000(2) u» 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 0.0063(1) feq 0.0057(1) 0.0055(1) 0.0086(2) 0.0063(2) 0.0049(1) 0.0054(1) 0.0082(9) 0.0078(9) 0.011(1) 0.008(1) 0.0071(9) 0.0074(7) 0.0086(9) U22 0.0061(8) 0.008(1) 0.010(1) 0.009(1) 0.0068(8) 0.0069(8) 0.0081(9) 0.0075(9) 0.007(1) 0.009(1) 0.007(1) 0.0060(9) 0.0075(8) 0.0066(9) Un 0.0001(6) 0.0005(6) 0.0008(7) 0.0000(8) 0.0007(6) 0.0005(5) 0.0002(6) 0.00000 0.00000 0.00000 UM 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 U23 0.00000 0.00000 0.00000 u . 0.0073(4) 0.0079(4) 0.0100(5) 0.0081(5) 0.0066(4) 0.0073(3) 0.0078(4) e 0.0060(5) 0.0061(6) Uu 0.0069(6) 0.0066(6) 0.0101(7) 0.0076(7) 0.0058(6) 0.0078(5) 0.0079(5) 0.0086(5) U22 0.0062(5) 0.0079(6) 0.0096(7) 0.0076(7) 0.0130(8) 0.0117(6) 0.0126(6) 0.0133(6) U33 0.0126(6) 0.0123(6) 0.0144(7) -0.0001(4) UM -0.0000(4) 0.0000(4) -0.0001(5) -0.0001(5) -0.0001(4) -0.0003(4) 0.00000 UM' 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 U23 0.00000 0.00000 0.0088(2) u 0.0086(3) 0.0089(3) 0.0114(3) 0.0094(3) 0.0084(3) 0.0093(3) eq 0.0055(4) U 0.0058(5) 0.0063(5) 0.0087(6) 0.0073(6) 0.0053(5) 0.0061(5) u 0.0077(4) U22 0.0066(5) 0.0080(5) 0.0109(6) 0.0082(6) 0.0078(5) 0.0092(5) 0.0054(5) U33 0.0062(6) 0.0059(6) 0.0076(7) 0.0055(7) 0.0047(6) 0.0057(5) 0.0007(4) 0.0006(4) 0.0002(4) UM 0.0000(4) -0.0002(5) -0.0001(5) 0.0001(5) 0.00000 0.00000 0.00000 UM 0.00000 0.00000 0.00000 0.00000 0.0000 0.00000 0.00000 0.00000 0.00000 U23 0.00000 0.00000 0.0062(2) 0.0070(2) u 0.0062(2) 0.0067(2) 0.0091(3) 0.0070(3) 0.0059(2) eq 0.0045(6) 0.0055(5) 0.0065(6) Uu 0.0054(6) 0.0056(6) 0.0088(7) 0.0064(7) 0.0103(7) 0.0100(6) 0.0099(5) 0.0112(6) U22 0.0093(6) 0.0100(6) 0.0123(7) 0.0053(5) 0.0057(6) u 0.0059(6) 0.0058(6) 0.0076(7) 0.0062(7) 0.0050(6) 33 0.0005(5) 0.0002(3) 0.0001(4) UM 0.0002(4) 0.0002(4) 0.0004(5) -0.0001(4) 0.00000 0.00000 0.00000 UM 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 u23 0.0069(3) 0.0071(3) 0.0096(3) 0.0076(3) 0.0065(3) 0.0069(2) 0.0078(3) ueq Uu 0.0102(5) 0.0099(5) 0.0129(7) 0.0105(7) 0.0091(5) 0.0091(5) 0.0100(6) U22 0.0055(5) 0.0063(6) 0.0092(7) 0.0072(7) 0.0059(6) 0.0065(5) 0.0074(5) 0.0065(5) 0.0072(6) 0.0085(7) 0.0065(7) 0.0056(6) 0.0065(5) 0.0069(5) u33 UM 0.0010(4) 0.0010(5) 0.0010(5) 0.0009(5) 0.0011(5) 0.0008(4) 0.0009(4) UM 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 U23 0.00000 0.00000 0.00000 0.00000 0.0074(2) 0.0078(3) 0.0102(3) 0.0081(3) 0.0068(2) 0.0074(2) 0.0081(2) Uu 0.0064(5) 0.0067(5) 0.0096(6) 0.0074(7) 0.0060(6) 0.0065(5) 0.0074(6) U22 0.0061(5) 0.0069(6) 0.0093(7) 0.0074(7) 0.0067(5) 0.0063(5) 0.0076(5) 0.0062(5) 0.0061(6) 0.0081(7) 0.0062(7) 0.0054(6) 0.0059(5) 0.0060(5) u33 UM -0.0005(4) -0.0003(4) -0.0004(5) -0.0002(5) -0.0005(4) -0.0003(3) -0.0007(4) UM 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 U23 0.00000 0.00000 0.00000 0.00000 0.0062(2) 0.0066(2) 0.0090(3) 0.0070(3) 0.0060(2) 0.0062(2) 0.0070(2) ueq Uu 0.0100(4) 0.0100(4) 0.0130(5) 0.0109(5) 0.0098(4) 0.0100(4) 0.0105(4) U22 0.0057(4) 0.0065(5) 0.0085(5) 0.0069(5) 0.0064(4) 0.0065(4) 0.0074(4) u 0.0072(4) 0.0071(4) 0.0095(5) 0.0077(5) 0.0060(4) 0.0074(4) 0.0075(4) 33 -0.0001(3) UM 0.0002(3) 0.0002(3) 0.0003(3) 0.0004(4) 0.0002(2) 0.0000(3) -0.0018(3) UM -0.0016(3) -0.0015(3) -0.0018(4) -0.0015(4) -0.0018(3) -0.0017(3) 0.0002(4) 0.0003(3) 0.0003(3) 0.0004(3) U23 0.0004(3) 0.0004(3) 0.0003(4) 0.0074(2) feq 0.0076(2) 0.0079(2) 0.0103(2) 0.0085(2) 0.0080(2) 0.0085(2) 0.0054(4) Uu 0.0060(4) 0.0061(4) 0.0091(5) 0.0068(5) 0.0060(3) 0.0064(4) 0.0129(4) U22 0.0120(4) 0.0129(5) 0.0152(5) 0.0134(5) 0.0128(4) 0.0142(4) 0.0051(4) C33 0.0061(4) 0.0063(4) 0.0080(5) 0.0061(5) 0.0061(4) 0.0060(4) 0.0004(3) UM 0.0000(3) 0.0001(3) 0.0005(3) 0.0001(4) 0.0002(2) 0.0001(3) 0.0002(3) 0.0003(3) UM 0.0001(3) 0.0001(3) 0.0001(4) 0.0001(4) 0.0000(3) 0.0007(3) U 0.0008(3) 0.0008(3) 0.0010(4) 0.0010(4) 0.0006(2) 0.0008(3) 23 0.0078(2) 0.0080(2) 0.0084(2) 0.0108(2) 0.0088(2) 0.0083(2) 0.0088(2) ueq 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) 1 Note: a = x - y2, -y + /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 + 1 1 1 1 1 1 1 1 1 1 1 Yt, y -/2, z; h = -x + 1, -y, -z; i = -x +/2, y +/2, z; j = x +/2, -y +/2, z+/2, k = -x +/2, y -/2, -z +/2; I = -x +/2, y -/2, z + 1. TABLE 3.7 POLYHEDRAL EDGES (A) FOR GRANDIDIERITE AND OMINELITE Polyhedron Edge bnarea G17 G8 G4 G12 G1 G2 G9 with 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) 2.624(2) 2.626(2) 2.622(1) 2.627(2) Si04 06j-06f 2.628(2) 2.625(2) 2.628(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) 2.363(2) 2.368(2) 2.365(2) 2.370(2) B03 07-07 2.368(2) 2.365(2) 2.365(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) = x + !4, -y + y2, -z; g Note: a = x - Yt, -y- +z +Yt, 1; b= x, y, -z + yc2; = x, y, -1z-; d = -x,-y , -z; e = -x-y, , -z+ 1; f 1 1 1 = -x + y2, y - y2, z; h = -x + 1, -y, -x + y2, y -/2, -z +/2.; I = -z; i = -x + Yt, y +/2, z;x j + = Yt, -y + Yt, z+ Yt, k = -x + Yt, 1 y- /2, z + 1. TABLE 3.8 POLYHEDRAL VOLUMES AND DISTORTION PARAMETERS FOR GRANDIDIERITE AND OMINELITE G17 G8 G4 G12 G1 G2 G9 MgFe 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 OAV 30.712 31.037 30.402 30.456 30.903 30.455 30.780 MOQE 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 OAV 78.195 77.716 77.535 77.900 78.288 77.930 77.715 MOQE 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 Si V 2.235 2.219 2.234 2.229 2.231 2.228 2.237 TAV 6.491 6.969 7.264 7.642 7.789 8.538 8.819 MTQE 1.002 1.002 1.002 1.002 1.002 1.002 1.002 Note: V= polyhedral volume; OAV = octahedral angle variance; MOQE = mean octahedral quadratic elongation; TAV = tetrahedral angle variance; MTQE = mean tetrahedral quadratic elongation. Angle variance is a measure of the distortion of the intra-polyhedral bond angles from the ideal polyhedron; quadratic elongation is a measure of the distortion of bond lengths from the ideal polyhedron as defined by Robinson etal. (1971). 39 contains up to 0.29 wt% ZnO (0.01 Zn apfu). Overall, the samples show a very low degree of substitution, except for Fe2+ for Mg 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= (Fe2+ + Mn)/(Fe2+ + Mn + 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 MgFe-0 bond distances lengthen with increasing Fe content (Figure 3.4). For example, MgFe-05, -02, and -06 (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%) fromX= 0.0 ioX= 1.0 and Mg-Ol (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 5.79 666 • • 664 5.78 m 662 m m X 660 5:77 II m • CO ' 658 < < 5.76 :s> 656 654 5.75 652 Q . 650 5.74 .1 1 1 0.0 0.2 0.4 0,6 0:8 1.0 648 0.0 0.2 0.4 0.6 0.8 1.0 X= (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) X= (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) Figure 3.3 (Fe2+ + Mn + Zn)/(Fe^.2++ + 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. 41 2.12 2.24 MgFe-05a •= 0.0929X+ 2.040 MgFe-02 = 0.0625X + 2.179 ^ = 0.986 2.23 - ^ = 0.943 2.22 - 2.04 4 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 X = (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) X= (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) 1,990 1.980 4 X 1.970 -\ to Oi 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 (Fe2+ + 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 2.000 AI2-04 x 2 = 0.0297X + 1.973 t2 •= 0.950 1.896 1.995 1.894 1.990 < CM 1.892 CM x x 1.985 4 9 1.890 O < 11 < 1.980 1.888 .. 1.975 * 1.886 + I 1970 0.0 0.2 04 0.6 0.8 1.0 1,884 0.0 0.2 0.4 0.6 0.8 1.0 X = (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) 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 (Fe2+ + 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 All- and A12-0 bond distances show minor (< 1.5%) changes with increasingX (Figure 3.5). Once again the ominelite data points (especially for All-06) fall below the regression line based on our data. The A13-, Si-, 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 01-MgFe-02 angle expands the most (Figure 3.6a), followed by the two Ol-MgFe-06 angles (Figure 3.6b). The 06-MgFe-06b, 02-MgFe-06 (x2), and 01-MgFe-05a angles decrease (Figures 3.6a and c) and the two 05- MgFe-06 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 01- MgFe-02, -06 (x2), and 06-MgFe-06b, respectively], but the pattern of points suggests that a somewhat better fit could be obtained with a curve. The 02-MgFe-05a 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 06-A11-02 (x2) angles increase and the 06-All-02d (x2) angles decrease by an equal amount (Figure 3.7a). The other O-All-0 angles (not shown) display no significant changes, nor do any of the 0-A12-0 angles (also not shown). Considering the ABO5 polyhedron, with increasing Fe the 01-A13-05a angle increases and the 01-A13-02i angle decreases by about the same amount (Figure 3.7b). None of the other 0-A13-0 angles 44 108.0 127.0 107.5 X Q 126:8 CM X I I § 126.6 -| t (U Lien• 126.4 O 126.2 b 126.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 X= (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) X = (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) 82 174.5 CM O2-MgFe-O6x2 = -1.2590X + 78.37 p o ^ = 0.993 76 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 X= (Fe2'+Mn+Zn)/(Fe2'+Mn+Zn+Mg) X= (Fe2++Mn+ZnV(Fe2++Mn+Zn+Mg) Figure 3.6 (Fe2+ + 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, -06 (*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 10.1.0 92.75 100.5 92.50 92.25 100:0 -] 92.00 CM 99.5 06-AI1-02d x 2 =-1.0210X+ 92.86 Oi 01-AI3-02i 1.8255X+ 100.94 2 91.75 Vi = 0.986 CO 99.0 1/^ = 0:983 92.0 / V 01-AI3-05a = 1.8514X+ 90.19 O i2- 0.979 91.5 91.0 -| O 90.5 87.00 90.0 0.0 0.2 04 0.6 0.8 1.0 X =. (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) X= (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) Figure 3.7 (Fe2+ + Mn + Zn)/(Fe2+ + Mn + Zn + Mg) vs. (a) 06-AI1-02 x 2 (squares), 02d x 2 (triangles); (b) 01-AI3-05a (squares), -02i (triangles) for grandidierite and ominelite. 46 109.0 115.0 A 108.5 II I £ 108:0 • • 04-Si-01 = 0.7405X4- 114.29 ? - 0.930 / 04-S-06J x 2 = 1.1354X+ 109.54 i2 = 0.979 V? 107.0 110.5 H to O O 110.0 06j-Si-01 =-1.1686X+ 107.41 ^ t2 = 0.989 D 109.5 106.0 0.0 0.2 0.4 0.6 0.8 1.0 X= (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) X= (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) Figure 3.8 (Fe2+ + Mn + Zn)/(Fe2+ + Mn + Zn + Mg) vs. (a) 04-Si-06j 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-Si-0 angles show some changes with Fe substitution at the MgFe site. As shown in Figure 3.8, the 04-Si-06j (x2) and -01 angles increase and the 06j-Si-06f 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 01- 02 edge increases the most, followed by the 06-05a x 2 and 01-06 x 2 edges (Figure 3.9). The shared 01-05a and 02-06 x 2 edges also increase but the 06-06b edge shows only a very slight expansion. With respect to the All06 octahedron, the 02-06 x 2 edges, which are shared with the (Mg,Fe )0s polyhedron, increase the most (see above), and the 06-02d x 2 edges decrease slightly fromX = 0.0-1.0 (Figure 3.10a). The 06-03c x 2 and -03e x 2 edges show a very slight increase (not shown) and the 02-03e x 2 shared and 02-03c x 2 unshared edges (also not shown) remain constant with changing X. The edges of the A1206 octahedron show very minor changes; the 07f-04h x 2 and -04 x 2 edges increase (Figure 3.10b) but the other edges (not shown) show little change. With respect to the ABO5 polyhedron the 05a-01 edge 94- which is shared with the (Mg,Fe )0s polyhedron increases the most (see above), but the 02i-01 edge shows a noticeable decrease (Figure 3.10c). The other edges show little change withX The edges of the Si04 tetrahedra also show minor changes with X, with the 04-06 x 2 edge changing the most (Figure 3.11). The 04-01 edge also increases and the 01-06 x 2 and 06j-06f edges decrease with increasing X, but the amount of change is less than or equal to 0.02 48 2.72 3.18 01-05a = 0.0427X + 2.667 ^-0.978 3.16 H & 3.14 o 3.12 -| 8 3.10 o 06-05a x 2 = 0.0882X+ 3.018 3:08 -] r' = 0.975 p o 3.06 3.04 3.02 2.60 3.00 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 2+ 2+ (Fe +Mn+Zn)/(Fe +Mn+Zn+Mg) (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) 3.65 01-06 x 2 = 0.0517X+ 3.564 r2 = 0.986 A2 = 0:981 3.30 0.0 0.2 0.4 0.6 0.8 1.0 (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) 2+ 2+ 2+ Figure 3.9 (Fe + Mn + Zn)/(Fe + Mn + Zn + Mg) vs. (Mg,Fe )05 polyhedral edges: (a) 02-06 x 2 (squares), 01-05a (triangles); (b) 06-05a x 2 (squares), 6b (triangles); (c) 01-02 (squares), -06 x 2 (triangles). 49 2.755 2.80 2.750 - CM 2.745 - X << 2.78 A O7f-04 x 2 = 0.0222X + 2.785 CN O l2 = 0.943 X 2.740 - i. •CoM CM" 2.76 O 2.735 - X CO St • • ' O O A CD 2.730 - it 2.70 g O < 2.725 - CM 2.68 2.720 - 3 b 2.715 2.66 0.0 0.2 0.4 0.6 0.8 1.0 (Fe'!++Mn+Zn)/(Fe"++Mn+Zn+Mg) (Fe2++Mn+Zn)/(Fe2++Mn+Zn+Mg) 2.81 (Fe2'+Mn+Zn)/(Fe-"+Mn+Zn+Mg) 2+ Figure 3.10 (Fe + Mn + Zn)/(Fe + Mn + Zn + Mg) vs. polyhedral edges: (a) AI106, 06-02d x 2; (b) AI206, 07f-04h x 2 (squares), -04 x 2 (triangles); (c) AI305, 02i-01. 50 2.675 2:670 CM X 2.665 CD Oi o 2.660 -T •5- o CO 2.655 + 2.650 o.o 0.2 0.4 0.6 0.8 1.0 (Fe2'+Mn+Zn)/(Fe?'+Mn+Zn+Mg) 2+ 2+ Figure 3.11 (Fe + Mn + Zn)/(Fe + Mn + Zn + Mg) vs. Si04 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 As expected, the volume of the (Mg,Fe )Os polyhedron increases dramatically with 3 increasing X (Figure 3.12a), from 6.871 to 7.229 A fromX= 0-1. The volumes of the A106 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 (TAV; Figure 12c) and mean tetrahedral quadratic elongation (MTQE; Robinson et al. 1971; not shown in Figure 3.12 but follows exactly the trend for TAV 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 Mg substitution at the MgFe site are as follows: (1) increase in the volume of the 2+ (Mg,Fe )05 polyhedron (5.0% change); (2) expansion of the MgFe-05 bond distance (4.4%); (3) expansion of the 01-02 edge (3.6%); (4) opening of the Ol-MgFe-02 angle (3.2%); (5) increase in the length of the 06-05a (x2) edges (2.8%); (6) lengthening of the MgFe-02 bond distance (2.8%); (7) decrease in the 06-MgFe-06b angle (-2.1%); (8) increase in the MgFe- 06 (x2) bond distances (2.0%); and (9) opening of the 01-A13-05a 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) 2+ 2+ 2+ Figure 3.12 (Fe + Mn + Zn)/(Fe + Mn + Zn + Mg) vs. (a) volume of the (Mg,Fe )05 (squares) and AI305 (triangles) polyhedra, (b) volume of the AM 06 (squares) and AI206 (triangles) octahedra, (c) tetrahedral angle variance for Si04 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 Fe2+ for Mg 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 06 and 07 are at special positions (All at 0,0,0; A12 at '/2,0,0; MgFe, A13, l 01, 02, and 04 at x,y,A; B, 03, and 05 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 of the MgFe-02 and -05 bond lengths withX However, our results show that with substitution of Fe at the MgFe site the only MgFe-0 bond distance that doesn't increase is that to 01. The O atom at 01 is also bonded to an Al atom at A13 and an Si atom at the Si site. The A13-01 and Si-01 distances also remain constant (within error) with increasing X, perhaps because the 01 atom is prevented from moving by the relatively strong Si-0 bond. The two MgFe-0 distances that increase the most are the two (MgFe-05 and MgFe-02) that are approximately perpendicular to the Mg-01 bond. The two MgFe-06 bond lengths do not expand as much as the MgFe-05 and -02 distances, likely because the O atoms at the 06 sites also form bonds with Si atoms. The two short All-06 bond 55 distances increase only slightly withX, likely because the All site is constrained at the origin, but probably also because of the strong Si-06 bonds. The A12-05 distance shows the greatest decrease withX, probably in response to the increase in MgFe-05 (the O atom at the 05 site is bonded to Al 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 04 is bonded to Al 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 01-02 edge and Ol-MgFe-02 angle are primarily due to changes in the position of the 02 atom. As 01-02 and Ol-MgFe-02 increase the 02-MgFe-06 (x2) angles decrease. Together this amount is about the same as the increase in Ol-MgFe-02. Although the 02-MgFe-06 angles decrease, the shared 02-06 (x2) edges expand slightly because of the increasing MgFe-02 and -06 (x2) bond distances. Although the 05a-MgFe-06 (x2) angles show no significant trends with increasing X, the 06-05a (x2) edges increase because of the increasing MgFe-05 and -06 (x2) bond distances. The 06-MgFe-06b angle decreases significantly with X but the 06-06b edge shows only a very slight increase, likely because the position of the 06 atom is constrained by bonds to the Si atom at Sil and the Al atom at All. The opening of the 01-A13-05 angle with corresponding increase in the 01-05 edge is of course due mainly to the increase in the MgFe-05 bond distance. The final "significant" change, the decrease in the 01-A13-02i angle, is probably in response to the increasing 01- A13-05 angle. As suggested above, it is not surprising that the lengths of the relatively strong Si-0 bonds show no apparent change with X. Instead, the Si04 tetrahedra react to Fe for Mg substitution at 56 the MgFe site by changing O-Si-0 angles such that the tetrahedral angle variance and mean tetrahedral quadratic elongation increase. This is not surprising given that three of the four O atoms coordinating each Si atom (01 and 06 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 Fe2+ 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% MnO (-0.04 Mn apfu) in their ominelite sample, and according to Shannon (1976) the ionic radius of Mn2+ (high spin) is 0.75 A, so substitution of Mn2+ at the MgFe site would be expected to cause more distortion than an equivalent amount of Fe2+. On the other hand, the ionic radius of vZn, given by Shannon (1976) as 0.68 A, is only slightly larger than that of Mg and would likely have little effect. The ionic radii of VA1 and VIA1 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 VICr3+; Shannon 1976) at any of the Al sites would be expected to increase the size of the coordination sphere. On the other hand, the substitution of P5+ 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 vMg but no value was given for five-coordinated Fe2+. However, the average of the radii of IVFe2+ (0.63 A) and vlFe2+ (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; if the difference (0.047 A) is added to the ionic radius of vMg the result is 0.70 A. These ionic radii differ from that of vMg 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 VIMg versus VIFe2+ (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 vFe2+-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 Fe2+04(OH) and an average bond distance of 2.10 A. The Yl 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 As noted by Stephenson and Moore (1968), the degree of distortion of the (Mg,Fe )Os polyhedron can be estimated from the 02-MgFe-05a 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 vFe 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 Fe2+. 59 4.0 CRYSTAL STRUCTURE OF TRASKITE 4.1 Introduction z Traskite, (Ba9Fe 2Ti2)(Si03)i2(OH,Cl,F)6-6H20, 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 Malinovskii 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 SiC^ tetrahedra (Figure 4.1). The octahedra are occupied by transition metals (Ti, Fe, Mn 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 XL30 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 CAMECA SX-50 electron microprobe operated in the wavelength- dispersion mode. Operating conditions were as follows: accelerating voltage, 15 kV; 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 "PAP" <\>(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, SrLa, TAP; diopside, 60 Figure 4.1 Structure of traskite projected down (001) using positions from Malinovskii et al. (1976). Red octahedra are Fe2+, green octahedra are Ti2+, tetrahedra are Si4+, red spheres are O2", and light green spheres are Ba2+, dark green spheres are CI". 61 CsJCa, scapolite, CXKa, PET; rutile, TiKa, synthetic rhodonite, MnKa, synthetic fayalite, FeKa, barite, BaZa, LIF. 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 X8 APEX diffractometer with graphite- monochromated MoKa radiation and a CCD detector. Data were collected in a series of All refinements were performed using the SHELXTL crystallographic software package of Bruker AXS. 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 Af" were those of Creagh and McAuley (1992). The values for the mass attenuation coefficients were those of Creagh and Hubbell (1992). 4.3 Results and Discussion An average electron microprobe analysis (EMPA) of one crystal collected at UBC, 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 4+ the basis of 12 Si and assuming 18 H20 and that the (CI, OH, F) site is filled entirely with CI. 62 TABLE 4.1 Electron microprobe analyses of traskite TR-2* traskite4I Si02 23.86 27.77 Ti02 5.40 5.6 Al203 0.26 0.33 FeO 2.99 4.201 MnO 1.50 1.36 MgO 0.32 0.30 CaO 0.60 0.86 SrO 0.00 0.34 BaO 48.94 51.19 2 K20 - <0.05 3 H20 11.55 5.10 CI 12.56 3.502 F 0.06 0.404 0=F -0.03 0=CI -0.98 0 = CI + F -1.00 Total 98.83 100.00 apfu Si4+ 12.00 12.00 Ti4+ 2.04 1.820 Al3+ 0.15 0.168 Fe2+ 1.25 1.518 Mn2+ 0.64 0.498 Mg2+ 0.24 0.193 Ca2+ 0.32 0.398 Sr2* 0.00 0.085 Ba2+ 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 CATSUM 26.31 25.371 AN SUM 42.34 48.169 Note: Compositions were calculated on the basis 4+ of 12 Si atoms per formula unit, 18 H20, (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 K20 and CI determined by X-ray spectroscopy 3 H20 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?jnt = 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 09, C12, and C13 sites had to be split as well. The 09A and 09B 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 MISSYM was used to determine if 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 will 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 will 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 will need to be done to determine the correct formula. 65 TABLE 4.2 Attempted space groups and resulting Flack x parameters, and |E2-1| values of traskite in this study Flack x Space Group Centrosymmetric R-value (%) |£2-1| parameter 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 TABLE 4.3 TRASKITE: DATA COLLECTION AND STRUCTURE-REFINEMENT INFORMATION a (A) 17.863(3) F0 > 4a F0 3087 c(A) 12.298(3) Pint 0.05(2) L.s. parameters 189 P3im(No. 162) Space Group Ri for F0 > 4a F0 0.0537 Z 3 Pi for all unique F0 0.0618 Crystal size (mm) 0.1 x 0.1 x 0.1 wR2 0.1516 Radiation MoKa a (see Note) 0.0725 Monochromator graphite b (see Note) 118.80 Total F0 86343 GooF (= S) 0.989 Unique F0 3547 2 2 2 2 Note: w= 1/[a (F0 ) + (a x Pf + b x P] where P = [Max (F0 , 0) + 2 x Fc )]/3 66 TABLE 4.4 ATOM PARAMETERS FOR TRASKITE U13 U2z UE, Site sof X y z Uu* U22 I/33 UM 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) 02 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) 03 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) 04 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) 05 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) 06 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) 0.017(2) 0.014(2) 0.008(2) 0.003(2) -0.003(1) 0.017(1) 08 1.0 0.4130(4) 0.0968(4) 0.1067(4) 0.020(2) 0.017(2) 0.013(2) 0.009(2) -0.006(2) -0.002(2) 0.016(1) 09A 0.53(4) 0.5665(9) 0.2829(9) 0.161(1) 0.026(7) 0.039(7) 0.020(1) 0.014(6) -0.006(6) -0.004(5) 0.029(5) 09B 0.55(4) 0.5859(9) 0.2930(8) 0.100(2) 0.035(7) 0.029(6) 0.021(9) 0.016(5) -0.002(5) -0.002(5) 0.028(5) 010 1.0 0.6169(5) 0.2340(4) 0.3535(8) 0.031(4) 0.009(3) 0.091(7) 0.004(3) -0.003(4) -0.007(3) 0.046(2) 011 0.33333 2/3 1/3 0.371(1) 0.031(4) 0.031(4) 0.041(7) 0.016(2) 0 0 0.034(3) CM 0.5 0.3980(5) 0.19990(2) 1/2 0.166(6) 0.056(2) 0.012(1) 0.083(3) 0 0.0003(9) 0.066(2) 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) 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) 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) 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-Si1-02 105.1(4) <0-Si1-0> 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 107.4(3) O3-Si2-O10 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 REFERENCES Alfors, J.T. and Putman, G.W. 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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 Miller index V Volume Z number of empirical formula units in the unit cell p Linear absorption coefficient R R = S|F0-FC|/ZF0 ; indicates how closely your model matches the true model F0 observed structure factor Fc calculated structure factor Rw Weighted R Rjnt Integrated R |E2-1| 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 dcaic Calculated distance between planes 80