Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

An x-ray crystallographic study of the crystal structures of four tellurium oxysalt minerals : dugganite,.. Lam, Anita Eva 1998-05-26

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata


831-ubc_1998-0508.pdf [ 8.54MB ]
JSON: 831-1.0088533.json
JSON-LD: 831-1.0088533-ld.json
RDF/XML (Pretty): 831-1.0088533-rdf.xml
RDF/JSON: 831-1.0088533-rdf.json
Turtle: 831-1.0088533-turtle.txt
N-Triples: 831-1.0088533-rdf-ntriples.txt
Original Record: 831-1.0088533-source.json
Full Text

Full Text

AN X-RAY CRYSTALLOGRAPHIC STUDY OF THE CRYSTAL STRUCTURES OF FOUR TELLURIUM OXYSALT MINERALS: DUGGANITE, CHOLOALITE, RODALQUILARITE, AND GRAEMITE by ANITA EVA LAM B.Sc. Honours (Chemistry and Geological Sciences), The University of British Columbia, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Earth and Ocean Sciences) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 1998 © Anita Eva Lam, 1998 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of &.Q/\Ik CUrJj Gcefrrt ScMti02S The University of British Columbia Vancouver, Canada Date Auy/af Sl}liU DE-6 (2/88) ABSTRACT The crystal structures of four tellurium oxysalt minerals, dugganite, choloalite, rodalquilarite, and graemite, were investigated with the use of single crystal X-ray crystallography. The crystal structure of dugganite, ideally Pb3Zn3Te6+As20i4, a 8.460(2), c 5.206(2) A, V 322.6(2) A3, space group P321, Z 1, has been solved by direct methods and Patterson techniques, and refined to an R index of'2.7% based on 636 unique reflections measured using MoAxx radiation on an automated four-circle diffractometer. The structure consists of heteropolyhedral sheets of edge-sharing TeC>6 octahedra and PbOs snub disphenoids, oriented parallel to (001). The sheets are cross-linked by ASO4 and ZnC>4 tetrahedra, which share corners to form an interlinked, two- and three-connected two-dimensional net parallel to (001). Cheremnykhite and kuksite are considered to be isostructural with dugganite, but with V and P respectively dominant at the As site. The crystal structure of choloalite, ideally Cu3Pb3Te4+60i8-(Cl,H20), a 12.520(4) A, V 1963(2) A3, space group P4j32, Z4, has been solved by direct methods and Patterson techniques, and refined to an R index of 5.2% based on 956 unique reflections measured using MoKa radiation on an automated four-circle diffractometer. The structure consists of distorted TeC>6 octahedra, Cufo square pyramids (where (j) = CI and H2O), Pb(l)09 triaugmented trigonal prisms, and Pb(2)Oi2 icosahedra. The Pb(l)09 polyhedra polymerize to form a three-dimensional network, as do the Cufc and Pb(2)Oi2 polyhedra. The two networks fit together in three-dimensional space, leaving voids which are filled by the Te06 octahedra. The crystal structure of rodalquilarite was originally solved, using photographic methods, to an R index of 9.2%by Dusausoy and Protas (1969). Rodalquilarite, ideally H3Fe2(Te03)4Cl, a ii 9.021(1) b 5.1170(7), c 6.6539(8) A, a 103.23(1)°, P 106.66(1)°, y 78.07(1)°, V 283.15(6) A3, space group P1, Z lwas redetermined and refined to an R index of 4.1% based on 1672 unique reflections measured using MoKa radiation on an automated four-circle diffractometer. The structure consists of chains of Fe06 octahedra parallel to the 6-axis connected with tellurium polyhedra to form planes parallel to be. These planes are held together by hydrogen and long (>3.0 A) Te-<j) (where (j) = O or CI) bonds. A four-circle diffractometer equipped with synchrotron radiation was used to collect a data set for graemite, CuTe06H20. Data yielded a 6.816, b 25.627, c 5.784, with all angles 90°. Structural models were refined to an R index of 6.9% in Pmc2\ and to 7.7% in a reduced cell QA a) using Pnal\ . Neither of the models gave a satisfactory result although a substructure in Pna2\ is proposed. Precession photographs show the presence of disorder in the structure. Further study, including upper level precession work and electron microprobe analysis, is required. iii TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iv LIST OF TABLES viLIST OF FIGURES x PREFACE xiv ACKNOWLEDGEMENTS xDEDICATION xvi 1.0 INTRODUCTION 1 1.1 General Overview of Tellurium 1 1.1.1 Discovery of tellurium1.1.2 General chemistry of tellurium 2 1.1.3 Geochemistry and occurrence of tellurium 3 1.1.4 Uses of tellurium 5 1.2 Tellurium Coordination and Structure in Minerals 5 1.2.1 Tellurium (IV) coordination 5 1.2.2 Coordination of tellurium (VI) 15 1.3 Known Tellurium Oxysalts and Structures2.0 EXPERIMENTAL PROCEDURES 20 2.1 Crystal Selection and Preparation2.2 Data Collection 21 2.2.1 Single crystal X-ray diffraction using molybdenum X-radiation 22 2.2.2 Single crystal X-ray diffraction using synchrotron radiation 23 2.3 Structure Solution and Refinement 24 2.3.1 MISSYM 25 2.3.2 STRUCTURE TIDY.2.4 Electron Microprobe Analysis 6 2.5 Infrared Analyses 7 2.6 Introduction to Bond Valence 23.0 DUGGANITE: CRYSTAL STRUCTURE AND REVISED FORMULA 29 3.1 Introduction 23.2 Experimental 31 3.3 Structure Solution and Refinement 33 3.4 Description of the Structure 9 3.4.1 Tellurium coordination3.4.2 Arsenic coordination3.4.3 Lead coordination 40 iv 3.4.4 Zinc coordination 40 3.4.5 Structure connectivity 1 3.5 Discussion 53.6 Conclusions 2 4.0 CHOLOALITE: CRYSTAL STRUCTURE AND REVISED FORMULA 55 4.1 Introduction4.2 Experimental 57 4.3 Structure Solution and Refinement 61 4.4 Description of the Structure 8 4.4.1 Te coordination 64.4.2 Copper coordination 9 4.4.3 Lead(I) coordination 71 4.4.4 Lead(2) coordination4.4.5 Structure connectivity 3 4.5 Discussion 84 4.6 Conclusions 5 5.0 RODALQUILARITE, A REFINEMENT OF THE STRUCTURE 86 5.1 Introduction5.2 Experimental 87 5.3 Structure Solution and Refinement 85.4 Description of the Structure Based on Earlier Work 95.4.1 Original structure description by Dusausoy and Protas (1969) 97 5.4.2 Previous work done by Back (1990) 100 5.5 Description of the Refined Structure 102 5.5.1 Coordination of tellurium5.5.2 Coordination of iron 103 5.5.2 Coordination of chlorine .... 105.5.3 Hydrogen-bonding5.5.4 Structure connectivy 4 5.6 Conclusions About the Refinement of Rodalquilarite 116 6.0 GRAEMITE 117 6.1 Introduction6.2 Experimental 8 6.3 Structure Solution and Refinement 119 6.3.1 Determination of possible space groups 116.3.2 Structure solution 126 6.4 Description of the Proposed Structure of Graemite 127 6.4.1 Description of the proposed substructure in Pna2i 127 6.4.2 The proposed structure in Pmc2j 128 6.5 Discussion 136.6 ConclusionsV 7.0 CONCLUSIONS 139 7.1 Dugganite, Choloalite, Rodalquilarite, and Graemite 137.2 A Comment on Experimental Procedures 141 7.3 Crystal Structure Analysis as a Means For Chemical Analysis of Crystals 144 8.0 CONSIDERATIONS FOR FUTURE RESEARCH 146 9.0 REFERENCES 149 APPENDIX A. COMMONLY USED SYMBOLS AND TERMS 155 APPENDIX B. CATEGORIZED TELLURIUM OXYSALT MINERALS 157 APPENDIX C. STRUCTURE FACTOR TABLES FOR DUGGANITE 162 APPENDIX D. STRUCTURE FACTOR TABLES FOR CHOLOALITE 167 APPENDIX E. STRUCTURE FACTOR TABLES FOR RODALQUILARITE 173 APPENDIX F. STRUCTURE FACTOR TABLES FOR GRAEMITE 183 vi LIST OF TABLES Page 1.1 Atomic radii of tellurium, selenium, and sulfur (Kudryavtsev, 1974). 4 1.2 Tellurium oxysalt minerals. 17-19 3.1 Chemical composition of dugganite. 32 3.2 Miscellaneous information: dugganite. 35 3.3 Atomic parameters for dugganite. 36 3.4 Selected interatomic distances (A) and angles (°) for dugganite. 37 3.5 Bond-valence arrangement in dugganite. 38 3.6 Indexed powder diffraction patterns for dugganite. 53-54 4.1 Chemical composition of choloalite. 59 4.2 Miscellaneous information: choloalite. 63 4.3 Atomic parameters for choloalite. 64 4.4 Selected interatomic distances (A) and angles (°) for choloalite. 65-66 4.5 Bond-valence arrangement in choloalite. 67 4.6 Bond lengths of twelve-coordinated lead icosahedra in different minerals. 72 5.1 Miscellaneous information: rodalquilarite. 89 5.2 Redetermined atomic parameters for rodalquilarite (based on the 90 positions by Dusausoy & Protas, 1969). 5.3 Original atomic parameters from Dusausoy & Protas (1969). 91 5.4 Atomic parameters for rodalquilarite (based on STRUCTURE TIDY 92 standardized positions). 5.5 Selected interatomic distances (A) and angles (°) for rodalquilarite. 93-95 5.6 Bond-valence arrangement in rodalquilarite. 96 6.1 Atomic positions for the proposed graemite substructure solved in Pna2\. 130 6.2 Atomic positions for the proposed graemite structure solved in Pmc2\. 131 vii Appendix A Commonly used terms and symbols. 156 Appendix B B.l Tellurite Minerals 158-159 B.2 Tellurate Minerals 160 B.3 Tellurium Oxysalt Minerals With Mixed Te4+ and Te6+ Valences 161 Appendix C Observed and calculated structure factors for dugganite in P321. 163-166 Appendix D Observed and calculated structure factors for choloalite in P4i32. 168-172 Appendix E Observed and calculated structure factors for rodalquilarite in P-1. 174-182 Appendix F Observed and calculated structure factors for graemite in PncQ.\. 184-187 viii LIST OF FIGURES Page 1.1 a) Three- and b) four-fold coordination of Te4+ (after Zemann 1969). Small 7 circles: Te; large circles: O. 1.2 Coordination figure showing four oxygen atoms around Te4+ (after 7 Zemann, 1971). Median distance of Te-Oa, Te-Ob, Te-Oc is 1.92 + 0.08 A; Te-Od varies from 2.08 to 2.98 A. 1.3 The coordination of Te4+ as depicted by Lindqvist (1973). a) and b) show 9 the idealized three- and four-fold coordinations including the lone electron pair. 1.4 Trigonal bipyramidal coordination showing in (a) the axial, a, and 12 equatorial, e, positions (after Gillespie, 1972). Possible locations for the lone electron pair, E, are shown in (b) and (c) with the preferred orientation being (c). 1.5 Possible octahedral configurations of Te (IV) (after Brown 1974). The 12 strength of the bond is correlated with the density of the line. 1.6 Back's (1990) depiction of Te4+coordination. The lettering is consistent 14 with Zemann (1971). 3.1 Coordination of the tellurium atom in dugganite. 43 3.2 Coordination of the arsenic atom in dugganite. 4 3.3 Coordination of the lead atom in dugganite. 45 3.4 Coordination of the zinc atom in dugganite. 6 3.5 The heteropolyhedral sheet in the dugganite structure, projected onto (001). 47 The Te06 octahedra are indicated by a regular dot pattern, and the PbOg polyhedra by a random dot pattern. 3.6 The tetrahedral layer in the dugganite structure, projected onto (001). The 48 AsC>4 tetrahedra are indicated with crosses and the ZnC>4 tetrahedra are ruled. ix 3.7 The dugganite structure projected onto (001). Te06 octahedra are shown 49 with a regular dot pattern, As04 tetrahedra with crosses, and ZnC*4 tetrahedra are ruled. The lead atoms are shown as spheres. 3.8 The dugganite structure projected onto (010). The shading is the same as 50 in figure 3.7. 4.1 The infrared transmittance spectrum of choloalite. The absorption bands at 60 3260 cm"1 and 1590 cm"1 are indicative of water in the structure of choloalite. 4.2 Coordination of the tellurium atom in choloalite. 75 4.3 Coordination of the copper atom in choloalite. 6 4.4 Coordination of the lead (1) atom in choloalite. 77 4.5 Coordination of the lead (2) atom in choloalite. 8 4.6a "Pinwheels" in the choloalite structure: (a) three Cufo polyhedra; (b) four 79 Pb(l)09 polyhedra. 4.6b "Pinwheel" in the choloalite structure. Seven Pb(2)0n polyhedra linked by 80 six Cu<j>5 polyhedra. 4.7 Three-dimensional network of Pb(l)Og polyhedra. The Te atoms are 81 shown as spheres. The positions of the 4\ axes are evident. 4.8 Three-dimensional network of Cufc and Pb(2)Oi2 polyhedra. The Te 82 atoms are shown as spheres. 4.9 Linkage of adjacent polyhedra to the TeC>6 octahedron. Bonds are shown 83 for the central Te06 octahedron and those adjacent polyhedra linked to it by shared edges. Only the central cation is shown for those polyhedra that link by shared corners. The Te atoms are shown as spheres with NE to SW ruling and the Cu atoms are shown as spheres with NW to SE ruling. The Pb(l) atoms are shown as spheres with a regular dot pattern, and the Pb(2) atoms as spheres with a random dot pattern. The O atoms are shown as shadowed spheres and the CI atoms as open, larger spheres. x 5.1 Chains of Fe06 octahedra in rodalquilarite projected onto the ftc-plane 98 (after Dusausoy and Protas, 1969). 5.2 Chains of FeC>6 octahedra in rodalquilarite projected onto the aft-plane 99 (after Dusausoy and Protas, 1969). 5.3 Projection of the rodalquilarite structure onto the ac-plane showing the 99 diverse bond types in the structure (after Dusausoy and Protas, 1969). 5.4 Eight-coordinated Te(l) and seven-coordinated Te(2) in rodalquilarite 101 (after Back, 1990). The proposed sites of the electron lone pair are shown as the shaded areas. 5.5 Coordination of tellurium (1) in rodalquilarite. Solid bonds show the three 105 short bonds on one side of the coordination polyhedron as found by Dusausoy and Protas (1969). Hollow bonds show the longer bonds not found in 1969. 5.6 Coordination of tellurium (2) in rodalquilarite. Shading of the bonds is the 106 same as that in figure 5.5. 5.7 Coordination of the iron atom in rodalquilarite. 107 5.8 Coordinaton of the chlorine atom in rodalquilarite. 108 5.9 Hydrogen-bonding in rodalquilarite viewed down the ft-axis. The hydrogen 109 bonds are shown as dashed lines. The bonds found by Dusausoy and Protas (1969) are shown as solid bonds. Fe atoms are shown ruled, Te(l) atoms have a regular array of dots, Te(2) have a random array of dots, CI atoms are shown as large open spheres, H atoms as small open spheres, and O atoms as shaded spheres. 5.10 Chains of edge-sharing iron octahedra parallel to the b-axis. 110 5.11 Te(l) and Fe polyhedra viewed down the a-axis. The Te polyhedra 111 (regular dot pattern) are shown with bonds < 3.0 angstroms. The longer bonds of one tellurium atom are shown as dashed lines. Fe octahedra are shown ruled, CI atoms as larger open spheres, O atoms as cross-hatched spheres, and H atoms as smaller open spheres. This figure shows Te(l) does not join the Fe octahedra in the c-direction. Notice the longer bonds to tellurium have a strong component in the a-direction. XI 5.12 Te(2) and Fe polyhedral sheet parallel to the 6c-plane. The Te polyhedra 112 (shown with dashes) are shown with bonds < 3.0 angstroms. The Fe octahedra are shown ruled and the CI atoms are shown as open spheres. The axes are in the same orientation as figure 5.11. 5.13 Connectivity of rodalquilarite as viewed down the c-axis. The unit cell is 113 shown with the a-axis roughly top to bottom and the 6-axis left to right. The longer (hollow) bonds connect planes of Te/Fe polyhedra in the a-direction. The shading of bonds and atoms is the same as in figure 5.9. 5.14 Linkage of adj acent cations to Te( 1) in rodalquilarite. The shading of 114 atoms is the same as in figure 5.13. Hollow bonds indicate linking by corners while the solid bonds indicate linking by edges or faces. 5.15 Linkage of adjacent cations to Te(2) in rodalquilarite. The shading of 115 atoms and bonds is the same as in figure 5.14. 6.1 Precession photograph of graemite showing hkO. Notice the streaking of 122 reflections, along the 6-axis, on odd /z-levels. 6.2 Precession photograph of graemite showing Okl. All reflections are sharp. 123 6.3 Precession photograph of graemite showing \kl. All reflections are 124 smeared along the 6-axis. 6.4 Precession photograph of graemite showing hk\. Reflections are smeared 125 on odd //-levels along the 6-axis. 6.5 The 6c-plane showing disorder in the proposed substructure of graemite in 132 Pna2\. Cu(l) atoms are shown as spheres with a regular pattern of dots, Cu(2) atoms as spheres with a random array of dots, Te(l) atoms as cross-hatched spheres, Te(2) atoms as spheres with NW to SE ruling, and Te(3) atoms with NE to SW ruling. Selected oxygen atoms are shown. 0(1) and 0(3) atoms are shown as shaded spheres and 0(7) atoms are shown as open spheres. The proposed disorder is between the Te(2) and Te(3) atoms and between the 0(1), 0(3), and 0(7) atoms. xii 6.6 The aft-plane of the proposed substucture of graemite in Pna2\. Disorder is 133 not apparent in this orientation. The shading of cations is the same as that in figure 6.5. All oxygens are shown. 0(7) atoms are shown as open spheres while the rest of the oxygens are shown as shaded spheres. 6.7 Disorder of Te(2) and Te(3) in the proposed graemite substructure in 134 Pnal\. Oxygen atoms bonded to either Te(2) or Te(3) are shown with hollow bonds. 6.8 Connectivity of the proposed graemite substructure in Pndl\ as viewed 135 down the c-axis. Hollow bonds show disorder between Te(2) and Te(3). The shading of the atoms is consistent with figure 6.5. 6.9 Connectivity of the proposed graemite substructure in Pna2\ as viewed 136 down the a-axis. The shading of bonds and atoms is the same as in figure 6.8. xiii PREFACE Two papers based on the work from this thesis have been submitted to the Canadian Mineralogist. "THE CRYSTAL STRUCTURE OF DUGGANITE, Pb3Zn3Te6+As20i4" by Anita E. Lam, Lee A. Groat, and T. Scott Ercit has been accepted and is presently in press. It will appear in volume 3, pages unknown, 1998. The procedure leading to and including crystal structure solution and refinement was done by Anita Lam. Dr. L. A. Groat was the thesis supervisor and gave a guiding hand in all aspects of the work. Dr. T.S. Ercit performed the electron microprobe analysis and also provided guidance. "THE CRYSTAL STRUCTURE AND REVISED FORMULA OF CHOLOALITE, Cu3Pb3Te4+60i8-(Cl,H20)" by Anita E. Lam, Lee A. Groat, Joel D. Grice, T. Scott Ercit, and Elizabeth Moffatt has been submitted but has not yet been accepted. The procedure leading to and including crystal structure solution and refinement was done by Anita Lam. Dr. L.A. Groat was the thesis supervisor and gave a guiding hand in all aspects of the work. Dr. T.S. Ercit performed the electron microprobe analysis and he and Dr. J. Grice also provided guidance when it was required. Elizabeth Moffatt performed the infrared analysis. xiv ACKNOWLEDGEMENTS A number of people have given me guidance, support, humour, and encouragement during the time it took to do this thesis. It has not been easy but it was worth it. I thank Lee Groat for his guidance, help, encouragement, and especially his patience. He was always encouraging and supportive even when times were bleak. He is one of the nicest, most accommodating people I know. I also thank him for those Yukon adventures that I will never forget and will remember as some of the best times of my life. The equipment and funding was provided by NSERC. The Canadian Museum of Nature provided many mineral samples. Thanks to Andy Roberts for providing the rodalquilarite and graemite crystal. Also, a thank you is extended to William Pinch for providing beautiful dugganite crystals. I have the deepest heartfelt thank-you for Joel Grice, Scott Ercit, and Bob Gault from the Canadian Museum of Nature. Bob, as a kindred spirit and the receiver of many of my queens of spades. I probably learned the most about crystallography as an art and a science from Joel and Scott and it is difficult to express the magnitude of appreciation that I have for them. During the course of this work, it was necessary to find a stress relief and I thank Bryon Cranston, Michelle Lamberson, Arne Toma, Lindsay Kelly, Dave Butler, and Sandy Stewart for introducing me to ice hockey. I thank Mati Raudsepp and Jim Trotter for their advice as members of my advisory committee and Greg Dipple and Tad Ulrych as members of my examining committee. Thanks to H. Meyer and W. Morgenroth for collecting the graemite synchrotron data. I also thank Malcolm Back for the loan of his thesis, and Mark Cooper and Andy McDonald for their advice. Thanks to Dave Dreisinger who gave me the opportunity to learn about hydrometallurgy. I have made many friends since the start of my thesis and I would like to thank these special people: Shannon, Julie, Ben, Mike Lo, Mike F., Ed, Nathan, Jacqueline, Lawrence, Felix, Gerdia, Kevin, Jesus, Ellen, Nathalie, Elisabetta, Cari, Laurel, and Heike. Be Wassink has been there for me through thick and thin and I am deeply grateful to him. I would also like to thank my parents, my great-aunt, my brothers Ray and Mike and my sister-in-law, Marina. A special thank-you goes to Pete(y7t) Daubeny for his love, humour, and support over the years. Many people have helped me along the way in this venture and I apologize if I neglected to mention your name. All of you are in my heart and have helped to shape the person that I am. Thank you. XV DEDICATION This work is dedicated to my parents, Wai Ying Lam and Chik Yuen Lam. It could not have been completed without their love and support. Thanks for working so hard for us and never giving me a rough time about what I was doing. xvi 1.0 INTRODUCTION This thesis examines the structures of one previously solved and three previously unsolved tellurium oxysalt minerals. A refinement of rodalquilarite (previously solved by Dusausoy and Protas 1969) and the structure solutions of dugganite and choloalite have been determined with the use of single crystal X-ray crystallography. A partial structure of graemite is proposed. This chapter will introduce tellurium as an element as well as the coordination of Te4+ and Te6+ in crystals. 1.1 General Overview of Tellurium The history of the discovery of tellurium, its chemistry, occurrence, and some of its uses are discussed. 1.1.1 Discovery of tellurium Tellurium, element 52 on the periodic table, was discovered by Austrian chemist Franz Joseph Mueller von Reichenstein in 1782. It was first encountered in the ores mined from the deposits of the Transylvania district. A different metal was extracted from a gold ore known then as aurum album (Heiserman, 1992) and specifically, from a mineral thought to be an alloy of bismuth and antimony which was referred to as white or grey gold. The unknown substance that was extracted was originally mistakenly identified as bismuth sulfide or antimony. Mueller von Reichenstein observed that the substance did not have the properties of antimony and concluded that it was an unknown metal that had an association with gold and he referred to it as 1 metallum problematicium or aurum paradoxum (Cooper, 1971). In 1784, Swedish chemist Torbern Bergman confirmed that the metal was not antimony. Mueller von Richenstein continued to work on the new metal and determined a number of its properties in 1785. Sixteen years after the initial speculation, Austrian chemist M. Klaproth confirmed the discovery with evidence that the metal had unique properties and gave Mueller von Richenstein full credit in a paper published in 1798. Klaproth named the element tellurium after the latin tellus meaning "earth". In 1789, tellurium was also discovered independently by P. Kitaibel, a Hungarian student of natural sciences. 1.1.2 General chemistry of tellurium Tellurium belongs to the group VIB family of elements along with oxygen, sulfur, selenium, and polonium. The elements of this group are known as "chalcogens" (derived from two Greek words "copper" and "born") as they form minerals that are an important source of metals. Moving down the group VIB column on the periodic table, we see that the atomic radius increases, the electronegativity decreases, and the reducing properties of the negatively charged ion increase. With increasing atomic weight the elements become more metallic: oxygen and sulfur are insulators, selenium and tellurium are semi-conductors, and polonium is a conductor. Tellurium is classed as a metalloid (having both metallic and non-metallic properties) and is found on the periodic table sitting immediately to the right of the diagonal line that separates the metals and non-metals. The electron configuration of this group can be summarized as ns2np4, two electrons short of a full shell or noble gas configuration; the configuration for tellurium is ls22s22p63s23p63d104s24p64d105s25p4 or [Kr]4d105s25p4. The common valence states of 2 tellurium are -2, 0, +4, and +6. In aqueous solution, Te is the most stable of the states. Notably, an oxidation state of+1 has also been demonstrated with the compound Te2i2-Compounds with Te2+ are unstable and the tellurium disproportionates to elemental Te and compounds of Te4+. The different classes of tellurium-bearing minerals are: native elements and intermetallic compounds, tellurides, oxides, tellurites, and tellurates (Vlasov, 1966). In this thesis, the crystal structures of tellurite and tellurate minerals are studied. 1.1.3 Geochemistry and occurrence of tellurium In nature, tellurium is closely associated with, and thus can be compared to, sulfur and selenium, two members of its family. Tellurium and selenium can be found in sulfide ores forming separate selenide and telluride minerals. Interestingly, selenium may substitute isomorphously for sulfur in sulfides because they are crystallochemically similar and have comparable sizes (Table 1.1). Tellurium, being larger in size, prefers to form independent telluride minerals often occurring as microsegregations in sulfide minerals. The most common form of tellurium in nature is that of tellurides. Sulfur, selenium, and tellurium are principal components of intrusive and extrusive magmas and of volcanic gases. Tellurium may be found in magmatic, pegmatitic, and hydrothermal deposits, especially if these are in close association with epithermal gold and silver deposits (Kroschwitz and Howe-Grant, 1997). 3 Table 1.1. Atomic radii of tellurium, selenium, and sulfur (Kudryavtsev, 1974). Element valence = 2- valence = 4+ valence = 6+ Atomic radius (A) Atomic radius (A) Atomic radius (A) Tellurium 2.22 0.89 0.56-0.61 Selenium 1.98 0.69 0.35 Sulfur 1.86 0.53 0.30-0.34 Tellurium is approximately the seventy-second most abundant element in the earth's crust with an abundance of 0.001 ppm compared with that of selenium at 0.05 ppm and sulfur at 340 ppm (Greenwood and Earnshaw, 1984.). Like selenium, tellurium mostly forms minerals with heavy metals and there are no naturally occurring light metal tellurides. The light metals prefer to combine ionically with oxygen and sulfur rather than with tellurium which has a prominent tendency towards covalent bonding (Vlasov, 1966). The elements that tellurium is known to form minerals with are: oxygen, sulfur, and the heavy elements of gold, silver, copper, mercury, nickel, iron, lead, bismuth, arsenic, and antimony. Tellurium is known to have close associations with gold, lead, and to some extent, silver and bismuth. Showing a tendency to combine with gold, the main source of tellurium comes from gold telluride ores. Some of the more common tellurides are: hessite Ag2Te, petzite Ag3AuTe2, calaverite AuTe2, sylvanite (Au,Ag)2Te4, altaite PbTe, tetradymite Bi2Te2S, rickardite C^Tes, and nagyagite PbsAu(Sb,Bi)Te2S6. Tellurium and selenium are widely disseminated without forming an ore and there are no reserves to speak of; large resources of tellurium and selenium are found in base metal sulfide deposits that are mined for copper, copper-nickel, copper-zinc, lead, silver, and gold. Weathering and oxidation of telluriferous minerals leads to the formation of rare tellurites and tellurates. 4 1.1.4 Uses of tellurium Commercial tellurium is recovered from anode slimes of electrolytic copper refining. It can be added to copper and steels to improve machinability; to rubber to improve vulcanization, aging, mechanical properties, and heat and abrasion resistance; to cast iron to control the chill depth; as a colourant for ceramics and glasses; and can be used to form specialty glasses for infrared transmission. 1.2 Tellurium Coordination and Structure in Minerals The coordination about Te4+ is complex, diverse, and difficult to describe, which has lead to a long history of interpretation. Conversely, the coordination about Te6+ is relatively simple to describe. Over the years the understanding of Te4+ coordination has grown from relatively simple three- and four-coordinate geometries to more complex models involving up to eight or nine bonds, including some long, weakly bonding interactions. Selected historical descriptions of tellurium coordination are summarized here. 1.2.1 Tellurium (IV) coordination Zemann (1968) noticed the varied coordination around Te4+ and attempted to categorize it as having either three- or four-coordination (Figure 1.1). Three-coordinated Te4+ results in a trigonal pyramid with Te4+-0 -1.95 ± 0.05 A and 0-Te4+-0 angles of -95°. Four-coordinated Te4+ exhibits a trigonal dipyramid with one corner of the equatorial plane unoccupied. Examining the bond angles in these two structures, he noticed that they deviated from the ideal 5 in both cases. He rationalized this effect as being the result of the lone pair of electrons occupying the free corner of the coordinate polyhedron (this is interpreted as the electron lone pair occupying the apex of the three-coordinated pyramid and occupying one corner of the equatorial triangle of the four-coordinated trigonal bipyramid.) Also suggested were intermediates between these two end-members which were described as having (3 + 1) coordination. These coordination polyhedra can be linked to form groups, chains, sheets, and framework structures. Zemann (1968) wrote that the one-sided coordination causes the formation of relatively open structures as the closest oxygen on the side with the electron lone pair is often longer than the minimum distance of ~2.7 A. In 1971, Zemann published an additional paper on the stereochemistry of Te4+ with respect to oxygen coordination. It was revealed that the three nearest neighbours to tellurium have fairly constant bond lengths (ranging from 1.78 to 2.15 A) and angles. He also noticed that the fourth bond length ranges from 2.08 to 2.98 A and that its direction is markedly constant (Figure 1.2) if Te-0 bonds ^ 2.75 A are excluded. Similarly, there is a directional component with additional oxygen atoms where Te-0 distances of up to 3.0 A occur; this is in addition to the shorter three or four Te-0 bonds. 6 1 0 Figure 1.1. a) Three- and b) four-fold coordination of Te4+ (after Zemann, 1969). Small circles: Te; large circles: O. Figure 1.2. Coordination figure showing four oxygen atoms around Te (after Zemann, 1971). Median distance of Te-Oa, Te-Ob, Te-Oc is 1.92 ± 0.08 A; Te-Od varies from 2.08 to 2.98 A. 7 For his dissertation, Lindqvist (1973) studied the coordinations of Te and Te . He found Te4+ to be either three- or four-coordinated forming pyramids and trigonal bipyramids (Figure 1.3). Many intermediates between these two forms were found as well. Occasionally, he found a fifth or sixth oxygen neighbour that interacted with tellurium. He reasoned that the inert pair of electrons requires a large space and thus limits the coordination of Te4+ to three or four strong bonds. The repulsions between the lone electron pair and the Te-0 bonds cause the polyhedra to distort away from its regular form. With regards to the directional component of the fifth and sixth oxygens as noted by Zemann (1971), Lindqvist stated that "Merely the fact of specific orientations of oxygen atoms at distances ranging from ~2.2 to3.0 A would suggest the presence of Te4+-0 interactions, these being, of course, weaker than those corresponding to the short bonds (1.85 to about 2.10 A)." He suggested that Te4+-0 distances less than 3.0 A should be considered as bonding distances. Hanke (1973) suggested a simple way of determining whether tellurium is strongly affected by the fourth oxygen neighbour. If the strong Te-0 bond opposite to the fourth neighbour is longer than the other two strong bonds and if the angle is substantially larger than the other two bond angles, then tellurium should be considered four-coordinated. 8 Figure 1.3. The coordination of Te4+ as depicted by Lindqvist (1973). a) and b) show the idealized three- and four-fold coordinations including the lone electron pair. 9 In describing the molecular geometry of the elements in the periodic table, Gillespie (1972) described various coordinations involving electron lone pairs. His work was based on the valence-shell electron-pair repulsion theory (VSEPR) and followed the rule "The pairs of electrons in a valence shell adopt that arrangement which maximizes their distance apart, i.e., the electron pairs behave as if they repel each other." With regards to the tetrahedral AX3E configuration (A = central atom, X = ligand, E = non-bonding or lone electron pair), Gillespie showed that the angles between the three ligands are less than that for an ideal tetrahedron (109.5°). This happens because the lone electron pair is larger and more spread out than the bonding pairs and so has more of a repulsive effect than if it were a bonding pair of electrons. This electron lone pair interaction with ligands is also seen in the trigonal bipyramidal AX4E configuration with resulting bond angles that are smaller than the ideal angles of 90° (axial-equatorial), 120° (equatorial-equatorial), and 180° (axial-axial). In AX4E, Gillespie (1972) also showed that while the lone electron pair may occupy either an axial or equatorial position (Figure 1.4) "non-bonding pairs will occupy the equatorial positions of a trigonal bipyramid arrangement because there is more room for them in these positions and because their interactions with neighbouring electron pairs are thereby minimized." Both the AX3E and AX4E configurations have been used to describe the coordination around tellurium (IV). Brown (1974) used the bond-valence method to study the irregular coordinations of the isoelectronic series: Sn(II), Sb(III), Te(IV), I(V), and Xe(VI). He described the cations as being at the center of octahedrons distorted by the lone pair of electrons. The distortion causes strong bonds to occur opposite weak bonds and intermediate bonds to be opposite each other. The lengthening of certain bonds results in five octahedrally-based configurations with three distinctive cases (4, C, £) and two intermediates (&, &) (Figure 1.5). Brown's A configuration, 10 otherwise depicted as AX4E (four-coordinated based on a trigonal bipyramid) has two strong, two intermediate, and two weak bonds. The C configuration (AX3E, three-coordinated, and based on a tetrahedron) has three strong and three weak bonds. The £ configuration (AX5E, five-coordinated, and based on an octahedron) has one strong, one weak, and four intermediate bonds. The configurations & and £ form intermediates between the others in a continuous series: It was noticed that in almost all the cases, two to four longer bonds are situated proximal to the direction of the lone pair. Using bond-valence arguments and the ligand fluorine, Brown (1974) concluded, for configuration £ only, that "the weak bond is replaced by 3 or 4 weak bonds, but the 5 stronger bonds remain close to the octahedral configuration". Although not explicitly stated by Brown himself, this is interpreted to mean that the coordinations about these cations can be up to nine-coordinated (5 stronger bonds and four weaker bonds arranged in the direction of the lone electron pair). Galy et al. (1975) studied the effect of the electron lone pair on the stereochemistry of the oxides, fluorides, and oxyfluorides of: Ge(III), As(III), Se(IV), Br(V), Sn(II), Sb(III), Te(IV), I(V), Xe(VI), T1(I), Pb(II), and Bi(III). For Te(IV), he found that the average Te-lone pair distance was 1.25 A and that neither the electron lone pair nor the Te cation lay on the equatorial plane of the trigonal bipyramid. This distortion was thought to be caused by the repulsive interactions between the electron lone pair and the neighbouring oxygen atoms. With respect to figure 1.2, Te(IV) was found to be displaced towards Oc. 11 a Figure 1.4. Trigonal bipyramidal coordination showing in (a) the axial, a, and equatorial, e, positions (after Gillespie, 1972). Possible locations for the lone electron pair, E, are shown in (b) and (c) with the preferred orientation being (c). XI XI XI X3 , XS X3 ' X5 Figure 1.5. Possible octahedral configurations of Te (after Brown, 1974). The strength of the bond is correlated with the density of the line. 12 In his study of tellurite minerals, Back (1990) used the bond-valence method to reveal the true tellurium coordinations of previously published structures. This was done because he noticed that many of the structures listed only the three or four shortest bonds (based on early interpretation of Te coordination) and neglected any of the intermediate or longer bonds. He found these intermediate and longer bonds to have important roles in holding some structures together. It was determined that tellurium could have a coordination anywhere from four to eight (Figure 1.6). It was also found that the longer bonds were directional although not as definite as the four shortest bonds. He summarize the coordination of tellurium as "distorted polyhedra with short bonds on one side and long bonds on the other side". Noticing that all the tellurites studied were lone pair stereoactive, he tried to locate these electrons with geometric arguments. The lone pair interaction with the oxygens creates longer bond lengths and angles in certain directions with the lone pair almost certainly on the side of the polyhedron with larger bond lengths and angles. Rossell (1992) reported the four tellurium atoms in Bi2Te40n to be six-, seven-, and eight-coordinated but stated that "In reality, however, the coordination polyhedra of all four tellurium atoms of this structure can be considered as distorted octahedra, the distortion being largely the result of lone-pair repulsions." Over time, the coordination of Te4+ has been described in terms of an increasing number of bonds. It has been shown (Back, 1990) that, in some cases, the longer, weaker bonds are important in holding structures together and thus, they must be accepted as bonding interactions with Te4+. 13 /Oh <3b< /Oh ! 0* On Figure 1.6. Back's (1990) depiction of Te4+ coordination. The lettering is consistent with Zemann (1971). 14 1.2.2 Coordination of tellurium (VI) Lindqvist (1973) found that Te6+ always tended to form octahedrons with oxygen and found no evidence that it forms other types of coordination polyhedra. The Te6+-0 bond lengths varied between 1.85 to 2.05 A with bond angles deviating by up to fifteen percent from the ideal octahedral values. Te6+ is always six-coordinated and forms regular octahedrons. There is no difficulty with large distortions of bond lengths or angles as that found with Te4+ because there is no stereochemically active lone pair of electrons. The known tellurate mineral structures all report six-coordinated Te6+ octahedrons with the average bond lengths of Te6+-0 -1.93 A and the average 0-Te6+-0 bond angles -90°. > 1.3 Known Tellurium Oxysalts and Structures To date, there are sixty-seven known tellurium oxysalt minerals, of which thirty-six are tellurites, twenty-four are tellurates, and seven are Te-oxysalts with mixed Te4+ and Te6+ valences. The complete list of tellurium oxysalts, formulae, and structure references is found in Table 1.2. The categorized lists are located in Appendix B. Thirty-one of these minerals structures are known (including dugganite and choloalite), twenty-four are tellurites, six are tellurates, and one is a mixed valence structure. The majority of known structures are of tellurites, probably because tellurites are more common and thus more accessible than tellurates when searching for single crystals. Zemann (1968) remarked that tellurium seemed to prefer the tetravalent state under the conditions for formation of natural tellurium oxysalts. This is 15 consistent with the fact that, in aqueous solution, Te4+ is the most stable valence state of tellurium. It should be pointed out that in the course of this research, there was significant difficulty in obtaining crystals large enough for use with the single crystal X-ray diffractometer. Even though there was access to museum quality minerals (from the Pinch collection at the Canadian Museum of Nature) many of the crystals were found as crusts, powdery aggregates, or crystals that were obviously not singular. The difficulty in procuring single crystals is one of the factors limiting the structure solution rate of tellurium oxysalts minerals. 16 Table 1.2. Tellurium oxysalt minerals. Name Formula Structure Reference balyakinite blakeite burckhardtite carlfriesite cesbronite chekhovicite cheremnykhite chiluite choloalite cliffordite cuzticite denningite dugganite dunhamite emmonsite eztlite fairbankite ferrotellurite frankhawthorneite girdite graemite jensenite juabite keystoneite khinite kinichilite kuksite CuTe03 Fe,Te03(?) Pb2(FeIMn)Te(Si3AI)Oi2(OH)2-H20 CaTe308 Cu5(Te03)2(OH)6-2H20 Bi2Te40n Pb3Zn3Te06(V04)2 Bi6Te2M02021 Pb3Cu3Te4+018(CI,H20) UTe309 Fe2Te06-3H20 (Ca,Mn)(Mn,Zn)Te4Oi0 Pb3Zn3Te6+As2014 PbTe03(?) Fe2(Te03)3-2H20 Pb2Fe6Te4Oi5(OH)10-8H2O PbTe03 FeTe04(?) (Cu2+)4Te6+04(OH)2 H2Pb3(Te03)(Te06) CuTe03H20 (Cu2+)3Te6+06-2H20 Cu5(Te04)2(As04)2-3H20 H0.8Mgo.8(Ni,Fe,Mn)2(Te03)3-5H20 Cu3PbTe04(OH)6 Mgo.5(Mn2+,Zn)Fe3+(Te03)3-4.5H20 Pb3Zn3Te06(P04)2 Lindqvist 1972 Effenberger et al. 1978 Rossel etal. 1992 Lam etal. 1998 Brandstatter 1981 Walitzi 1964 Lam etal. 1998 Pertlik 1972 Grice & Roberts 1995 Grice etal. 1996 Miletich 1995 17 Table 1.2 continued. Name Formula Structure Reference kuranakhite leisingite mackayite magnolite mcalpineite moctezumite montanite mroseite nabokoite oboyerite parakhinite paratellurite pingguite plumbotellurite poughite quetzalcoatlite rajite rodalquilarite schieffelinite schmitterite smirnite sonoraite spiroffite PbMnTeOe Cu(Mg,Cu,Fe,Zn)2Te6+06-6H20 FeTe205(OH) Hg2Te03 Cu3Te06H20 Pb(U02)(Te03)2 (BiO)2Te04-2H20 CaTe02(C03) Cu7Te04(S04)5KCI H6Pb6(Te03)3(Te06)2-2H20 (Cu2+)3PbTe6+06(OH)2 a-Te02 Bi6Te20i3 a-PbTe03 Fe2(Te03)2(S04)-3H20 Cu4Zn8(Te03)3(OH)i8 CuTe205 H3Fe2(Te03)4CI Pb(Te,S)04H20 (U02)Te03 Bi2Te05 Fe3+Te4+03(OH)H20 (Mn,Zn)2Te308 Margison et al. 1997 Pertlik and Gieren 1977 Grice 1989 Swihart 1993 Fischer et al. 1975 Pertlik & Zemann 1988 Burns et al. 1995 Thomas 1988 Mariolacos 1969 Pertlik 1971 Hanke etal. 1973 Dusausoy & Protas 1969 Meunier & Galy 1973 Loopstra & Brandenberg 1978 Don nay etal. 1970 Cooper & Hawthorne 1996 18 Table 1.2 continued. Name Formula Structure Reference teineite tellurite tlalocite tlapallite unnamed 604 unnamed 624 unnamed 625 unnamed 626 unnamed 627 unnamed 628 unnamed 629 utahite winstanleyite xocomecatlite yafsoanite yecoraite zemannite CuTe03-2H20 Te02 CuioZneTeaOn CI(OH)25-27H20 H6(Ca,Pb)2(Cu,Zn)3S04(Te03)4Te06 Au4Pb3Te20n Au2Te03 Au2Te06-2H20 Au2(Bi,Te)03 (Zn,Pb,Cu)3Te06-2H20 Au6(Pb03)2Te04 Au6Pb2(Pb03)2(Te04)3-6H20 Cu5Zn3(Te04)4(OH)8-7H20 TiTe308 Cu3Te04(OH)4 (Ca,Pb)3Zn3Te2012 Fe3Bi509(Te03)(Te04)2-9H20 (H,Na)2(Zn,Fe)2(Te03)3nH20 Zemann & Zemann 1962 Effenberger 1977 Beyer 1967 Meunier & Galy 1971 Jarosch & Zemann 1989 Matzat 1968 Miletich 1995 19 2.0 EXPERIMENTAL PROCEDURES This chapter will describe the experimental methods used to obtain single-crystal X-ray diffraction data. The general procedures are detailed in this chapter and deviations from these methods along with specific details are discussed in the individual chapter for each mineral. 2.1 Crystal Selection and Preparation The first step in the procedure of single-crystal X-ray diffractometry is to choose an appropriate crystal for data collection. The crystal size is important with recommended maximum and minimum dimensions of 50 pm and 10 pm, respectively (Mark Cooper, personal communication, 1996). For this project, smaller crystals were desired because of the high absorption of X-rays that heavy elements such as tellurium and lead are known for; larger crystals absorb more X-rays and so the diffracted data may be inferior to the data collected with smaller crystals (Joel Grice, personal communication, 1995). It is highly desirable that the mineral selected be a true single crystal so that problems associated with twinning do not have to be dealt with. The job of structure solution and refinement is difficult enough without added problems that could have been prevented by the better selection of a crystal. Rodalquilarite and graemite were provided as single crystals by Andrew Roberts of the Geological Survey of Canada. Dugganite and choloalite crystals were provided by the Canadian Museum of Nature (donated from the Pinch collection). The final data set for dugganite was collected on a crystal obtained directly from Mr. William Pinch of Rochester, New York, who generously provided beautifully formed octahedral crystals. 20 Single crystals of dugganite and choloalite were selected and the absence of twinning was confirmed by looking at the crystals under crossed polars of a polarizing microscope. Attempts to shape choloalite into a sphere were not successful as the crystals easily disintegrated in an air-driven, circular, abrasion grinder. The dugganite crystal used for data collection was not manually shaped because it was thought that its octahedral morphology would result in minimal problems with absorption and because earlier attempts at shaping dugganite crystals from the Canadian Museum of Nature were not successful due to disintegration of the crystals. Spherically-shaped crystals are highly desired for single-crystal X-ray crystallography because the absorption of X-rays is uniform. An absorption correction would still be required because it is unlikely that a perfect sphere could be generated, but the absorption correction would not be as influential on the final results. Both the choloalite and dugganite crystals were mounted on glass fibres with the use of "five-minute" epoxy. The rodalquilarite and graemite crystals were provided mounted and no attempts were made to shape them for fear of losing the crystals. The dimensions and origins of the crystals used in this study are located in their respective chapters. 2.2 Data Collection Two instruments were used for data collection: a Siemens P3 automated four-circle diffractometer using molybdenum X-radiation (located at UBC) was used for all four minerals and the four-circle diffractometer at HASYLAB beam line D3 (Hamburg, Germany), using synchrotron radiation, was used to collect an additional data set for graemite. 2.2.1 Single crystal X-ray diffraction using molybdenum X-radiation Each crystal was mounted on a Siemens P3 automated four-circle diffractometer equipped with a molybdenum-target X-ray tube (operating at 55 kV, 35 mA) and a precisely oriented graphite crystal monochromator mounted with equatorial geometry. The crystal was centered and the correct unit cell was selected from an array of real space vectors corresponding to potential unit cell axes. Least-squares refinement of these reflections, together with the orientation matrix relating the crystal axes to the diffractometer axes, produced the cell dimensions for each crystal. These dimensions were checked against the literature to be certain that the correct unit cell had been chosen. Intensity data were collected in the 0-29 scan mode, using ninety-six steps with a scan range from [20 (MoKa\)-l A°] to [20 (MoKa\)+\A°] and a variable scan rate between 0.5 and 29.3°/min depending on the intensity of an initial one second count at the centre of the scan range. Backgrounds were measured for half the scan time at the beginning and end of each scan. The stability of the crystal alignment was monitored by collecting two standard reflections every twenty-five measurements. Reflections uniformly distributed with regard to 20 were measured at 5° intervals of i|/ (the azimuthal angle corresponding to rotation of the crystal about its diffraction vector) from 0 to 355°, after the method of North et al. (1968). These data were used to calculate an absorption correction which was then applied to the entire data set. The data were also corrected for Lorentz, polarization, and background effects, averaged and reduced to structure factors. Data and absorption collection statistics for each crystal and any deviations from this procedure is described in the individual chapter of each mineral. 22 2.2.2 Single crystal X-ray diffraction using synchrotron radiation As previously mentioned, the final data collection for graemite was done using synchrotron light. This light is generated by accelerating electrons around a large circle at close to the speed of light. The electrons emit radiation in a continuous spectrum from 0.1 to 50,000 A and this radiation is directed through beamlines to workstations. A monochromator is used to filter through the desired radiation. Synchrotron radiation is a powerful light source and was used because of the perceived difficulties with the graemite crystal. The very small, tellurium-bearing crystal diffracted poorly and it was thought that with a more powerful light source, an improved data set could be obtained. At 295 K, single crystal X-ray diffraction data of graemite were collected with the four-circle diffractometer at HASYLAB beam line Fl. The wavelength used was 0.4959 A. The collection was done by H. Meyer and W. Morgenroth. The lattice parameters of graemite are a = 6.816, b = 25.627, c = 5.784 A, a = 90, p = 90, y = 90°. A continuous scan mode was used with the co axis rotated at a constant speed throughout the Bragg position. Scalers were recorded and cleared at fixed time intervals. After insertion of appropriate attenuator combinations, the scan speed was adjusted to record a maximum of 2500 counts, without exceeding measurement times of 0.1 to 1.0 s/step. A total of 3207 reflections (including test reflections) were recorded comprising four asymmetric units. Data reduction included normalization to the primary beam intensity monitor and an on line correction for the (measured) beam polarization, following the procedure of Kirfel and Eichhorn (1990). The data were corrected for absorption by approximating the shape of the 23 crystal with a polyhedron (eight faces). The unique data set (Ri„t = 2.7 %) comprised 3207 reflections. 2.3 Structure Solution and Refinement The Siemens SHELXTL PC system of programs was used throughout this study. Scattering curves for neutral atoms together with anomalous dispersion coefficients were taken from Cromer and Mann (1968) and Cromer and Liberman (1970). Miscellaneous collection and refinement data are given in Tables 3.2, 4.2, and 5.1. The procedure for the structure solution and refinement of each crystal was different and is detailed in each of their respective chapters. Generally, for structure solution, the heavy atoms of the mineral were located by using either Patterson or direct methods. This was followed by inputting the rest of the cations followed by the anions. Ultimately, the lowest R value was achieved with various steps including setting the cations and possibly anions anisotropic, restricting observed data to larger rj(F) values, omitting individual reflections, using a weighting factor, and refining atoms versus a substituting element. Elements not found in the empirical formulas but possibly present by substitution were found suggested in the original chemical descriptions of the crystals. For choloalite and dugganite, these and other elements were searched for with the electron microprobe. After structure solution and refinement, the program MISSYM(Le Page, 1987) was used in each case as a double-check to detect any missing symmetry that may have been present; none was ever found. Before the final refinements of the structures, the program STRUCTURE TIDY (Gelato and Parthe, 1987) was used to standardize the atomic positions according to the crystallographic conventions proposed by Parthe and Gelato (1984). 24 2.3.1 MISSYM The computer program MISSYM (Le Page 1987) was used, after structure refinement, to detect any symmetry elements that may have been overlooked in dugganite, choloalite, and rodalquilarite. Citing incidents of crystal structures published in subgroups of the correct space groups (reviewed by Marsh and Herbstein, 1983; Baur and Tillmanns, 1986), this program was developed to serve as a double-check against such errors in the future. Le Page (1987) recommended that MISSYM be routinely used on structural data about to be published. Using the atomic positions, the program is able to detect overlooked symmetry and quasi-symmetry. Inaccurate data or disorder of atoms may lead to incorrect results. MISSYM uses default errors of 1° (for the obliquity of metric symmetry elements)>and 0.25 A (for atomic positions); this serves to create a range that safeguards against slightly inaccurate data but it may also create problems by causing the detection of extra symmetry elements in a correct structure. The program is not able to prove the presence of symmetry elements nor is it able to discriminate symmetry from quasi-symmetry and so, it is up to the user to examine the experimental data to confirm the reality of these symmetry elements. 2.3.2 STRUCTURE TIDY Another program, STRUCTURE 77£>7(Gelato and Parthe, 1987), was used on the refined structural parameters of dugganite, choloalite, and rodalquilarite. The program was written to help standardize the way in which crystal structures are reported, according to an earlier set of rules proposed by Parthe and Gelato (1984). By reviewing atomic coordinates, this standardization of crystal structures enables the recognition of similar structures. 25 The input consists of a space group symbol, unit cell parameters, and atomic positions which the program uses to output a reordered list (based on Wyckoff letters) of standardized atomic positions in a standard space group setting. The origin and orientation of the structure is chosen as the setting with the minimum standardization parameter, r. Where: 1=1 N = number of representative atoms in the asymmetric unit x,y,z = atomic coordinates The standardization of slightly deformed structures or structures without well-defined atomic coordinates may give different results from isotypic structures. If so, it is suggested by Gelato and Parthe (1987) that all the possible settings be reviewed in an attempt to match the isotypic structures. Parthe and Gelato (1984) are careful to say that "standardized description should never replace any other description chosen to demonstrate a particular relationship to other structures, but should be given as an additional description". The work presented in this thesis is not fully standardized according to Parthe and Gelato (1984). The atomic coordinates have been changed in agreement to the program but the listing of atoms remains in the conventional way of cations first followed by anions. 2.4 Electron Microprobe Analysis Electron microprobe analyses for choloalite and dugganite were obtained using a JEOL 733 electron microprobe with Tracor Northern 5500 and 5600 automation. Dr. T. Scott Ercit of the Canadian Museum of Nature performed both analyses using the wavelength-dispersion 26 mode. The operating conditions were as follows: voltage 15 kV, beam current 20 nA, and beam diameter 5 pm. Data were reduced using a PAP routine (program XMAZNT by C, Davidson, CSIRO). The analyses are given in Table 3.1 for dugganite and Table 4.1 in for choloalite. 2.5 Infrared Analyses Choloalite and dugganite crystals were sent to Elizabeth Moffatt at the Canadian Conservation Institute for infrared analyses. The results for dugganite were inconclusive. Experimental details and results for choloalite are given in chapter four. 2.6 Introduction to Bond Valence After the final phase of structure refinement and electron microprobe analyses, the results for each crystal were subjected to bond-valence analysis. The strength of a bond can be quantified in terms of valence units (v.w.). The summation of the bond valences for all bonds to a central atom should result in a number equal to that atom's valence. This is expressed mathematically as: where: Vy = valence of bond between atoms i and j Vt = valence of atom i Values from Brown (1981) and Brese and O'Keeffe (1991) were used to generate bond-valence tables for each crystal. The results were then examined for deviations away from the formal valence of each atom. The equation used from Brown (1981) is: 27 s=(R/RoyN where: s - bond valence R = observed bond length #0 = bond length constant N = slope of the correlation curve (given). The equation used from Brese and O'Keeffe (1991) was based on Brown and Altermatt (1985) and is: v, =exp[(i?, -dv)lb] where: vtj = bond valence between atoms / and j Rtj = bond-valence parameter given in Brese and O'Keeffe (1991) dy = observed bond length b = universal constant, 0.37 A (Brown and Altermatt, 1985). The values from Brown (1981) presented an occasional problem as the paper does not contain constants for Te-Cl bonds. 28 3.0 DUGGANITE: CRYSTAL STRUCTURE AND REVISED FORMULA 3.1 Introduction Dugganite was first described by Williams (1978) from three mine dumps in the Tombstone District, Cochise County, Arizona. The type material was discovered at the Emerald mine dump, occurring as "spherules of water-green hexagonal prisms abundant in a sugary, vuggy quartz matrix". Numerous crystals of dugganite were discovered at this locality, associated with parakhinite and other Te-oxysalt minerals. At the Old Guard mine dump, crystals of khinite are replaced on the outside by a druse of minute dugganite crystals. Other minerals found at this site include chloroargyrite, chrysocolla, quetzalcoatlite, and tenorite. At both the Emerald mine and Old Guard mine dumps, dugganite crystals were found associated with bromargyrite, chlorargyrite, and numerous unidentified Te-oxysalt minerals in quartz or manganese oxide gangue material. At the dump of the Joe Shaft mine, dugganite was found with other Te-oxysalt minerals, cerussite, emmonsite, and rodalquilarite. Using Weissenberg and rotation photographs, Williams (1978) showed that dugganite is hexagonal, "perhaps" P6/mmm. Cell dimensions were refined from powder data: a 8.472(5), c 5.208(5) A. The average chemical composition (obtained using spectroscopic techniques) was found to be PbO 55.3, CuO 1.2, ZnO 17.6, As205 10.4, Te03 14.0, H20 (by the Penfield method) 1.5, total 100.0 wt %. Trace amounts of CO2, Mo, Ag, and Cd also were detected. Additional (partial) analyses showed some substitution of Te for As. The chemical formula suggested by Williams (1978) was Pb3Zn3(Te06)x(As04)2-x(OH)6.3x, with* in the range 0.94 to 1.33; the generally accepted formula for dugganite is Pb3(Zn,Cu2+)3(Te6+06)(As05)(OH)3. 29 A mineral resembling dugganite was also described by Kim et al. (1988) as a product of supergene oxidation in the Kuranakh deposit (central Aldan, Yakutia, Russia), where it is associated with calcite, cinnabar, gold, orpiment, altaite, clausthalite, descloizite, kuranakhite, naumannite, tiemannite, and yafsoanite. Single-crystal X-ray studies showed that the mineral is orthorhombic, with space group Cmmm, C222, C2mm, Cmlm, or Cmm2. Cell dimensions were refined from powder data: a 8.57(3), b 14.84(5), c 5.21(3) A. The authors noted that X-ray data from "normal" dugganite can also be indexed on this cell. The average chemical composition (based on seven electron microprobe analyses) was found to be (in wt. %) PbO 51.47, ZnO 18.82, Si02 0.96, P205, 0.70, V205 3.61, As205 12.16, Sb2Os 0.07, Te03 12.61, total 100.40. Note that this is not the average composition abstracted in ,4m. Mineral. 76, 1440, [1991]; that one was based on earlier analyses obtained using different standards and a non-standard data reduction routine. Recalculation on the basis of six Pb plus Zn atoms gave the formula Pb3Zn3Te(As,V,Si)2(0,OH)i4. Other analogues of this mineral that contain V + Si» As, or with significant substitution of P for As, were reported but not studied in detail by Kim et al. (1988). Kim et al. (1990) described cheremnykhite and kuksite, two new minerals associated with dugganite in the Kuranakh deposit. The formulae, determined from electron microprobe analyses, were Pb3Zn3Te06(V04)2 for cheremnyhkhite and Pb3Zn3Te06(P04)2 for kuksite. X-ray diffraction studies showed that both minerals are orthorhombic (Cmmm, C222, C2mm, Cm2m, or Cmm2), with cell dimensions similar to those previously determined for dugganite from the same deposit (Kim et al. 1988). Their conclusion was that cheremnykhite, kuksite, and dugganite, are isostructural. 30 Dugganite has also been described form the Centennial Eureka mine dump in Juab County, Tintic District, Utah, where it occurs with other secondary Cu-, Te-oxysalt minerals (Marty et al. 1993). 3.2 Experimental General details of the experimental methods used are found in Chapter two. The crystal used in this study is from the 400-foot level of the Empire mine, near Tombstone, Arizona. Fifty reflections with 20 7.83 to 45.69° were centered and from this the unit cell was derived. One sphere of reflections (3746 measurements, exclusive of standards) was collected from 3 to 60° 20. Eighteen of the reflections were rejected because of asymmetric backgrounds. Fourteen strong reflections were used for the absorption scan and the data (994 measurements) was used to calculate an absorption correction. The merging R index for the \|/-scan data set decreased from 8.5% before the absorption correction to 3.2% after the correction. Minimum and maximum transmissions were 0.030 and 0.068 respectively for the absorption-corrected data set. Of the 636 unique reflections, 558 were classed as observed [I > 3a(I)]. Electron microprobe data for Si, P, Ca, As, and Te were collected for twenty-five seconds; data for all other elements were collected for fifty seconds. The standards used were almandine (ALfoc), zircon (SLKcc), Pb7Ti(P04)6 (PKa), CaT^On (Ca£cc), VP207 (VKa), cuprite (CuKct), willemite (ZnKa), mimetite (AsZa), Te02 (Tela), and crocoite (PbMx). The elements Mg, Fe, Co, and Ni were sought but not detected. The analytical results are given in Table 3.1 together with those from Williams (1978) amd Kim et al. (1988). 31 Table 3.1. Chemical composition of dugganite. Williams (1978)* Kim et al.(1988)f This study* CaO wt. % negligible — 0.24 PbO 55.3 51.47 53.13 CuO 1.2 0.00 1.06 ZnO 17.6 18.82 17.25 Al203 - - 0.07 Si02 - 0.96 1.06 P205 - 0.70 4.90 v2o5 - 3.61 0.03 As205 10.4 12.16 8.28 Sb205 - 0.07 -Te03 14.0 12.61 13.48 H20 1.5 - -TOTAL 100.0 100.40 99.50 Ca2+ negligible - 0.06 Pb2+ 3.43 2.94 3.04 Cu2+ 0.21 0.00 0.17 Zn2+ 3.00 2.95 2.71 Al3+ - - 0.02 Si4+ - 0.20 0.23 p5+ - 0.13 0.88 v5+ - 0.51 0.00 As5+ 1.25 1.35 0.92 Sb5+ - 0.01 -Te6+ 1.11 0.92 0.98 H+ 2.31 - -o2- 14.25 14.02 13.90 Note: Oxides are expressed in weight percent; analyses are normalized on nine cations per formula unit. *Average of four AAS analyses for Pb, Cu, Zn, and three visible spectroscopy analyses for Te. As (two analyses) by UV spectroscopy. Trace Cd, Ag, Mo C02. Water by the Penfield method. fAverage of seven electron microprobe analyses. *Average of six electron microprobe analyses. 32 3.3 Structure Solution and Refinement Structure solution for dugganite was attempted with the recommended space group of P6lmmm but all trials failed to provide a good solution. Attempts with the space group P3 were promising but the final results were never satisfactory. To save time, it was decided to solve for the atomic positions in PI (refined to an R index of 7.8% for an isotropic displacement model) and input those positions into MISSYM (Le Page 1987) to see which symmetry elements were present; this would hopefully lead to the correct space group. Using all atoms, MISSYM showed that a three-fold and three two-fold axes were missing which would give P321 and P312 as possible space groups. Interestingly, inputting only cation positions resulted in symmetry elements that correspond to the originally described P6lmmm space group. Both P321 and P312 space groups were used to try to solve the structure and P32\ gave a very good model whereas P312 was never satisfactory. The assignment of phases to a set of normalized structure factors gave a mean value | E2-l | of 0.65, implying a non-centrosymmetric space group which agrees with the symmetry of the P321 space group but not with the centrosymmetric P6/mmm space group. Both direct methods and Patterson techniques were used to solve the structure. The structure was refined in P321 to an R index of 4.7% for an isotropic displacement model. Conversion to anisotropic displacement factors for all of the atoms in the structure resulted in convergence at R and wR indices of 2.7 and 2.9%, respectively (3.9 and 10.4% for all 636 data). Addition of an isotropic extinction correction did not improve the results. The program MISSYM (Le Page 1987) was used to search for additional symmetry elements; none were indicated. The program STRUCTURE TIDY was used to standardize the positions according crystallographic conventions and gave the final atomic positions. 33 Miscellaneous experimental information is given in Table 3.2. Positional coordinates and anisotropic and equivalent isotropic displacement factors are given in Table 3.3. Interatomic distances and angles are given in Table 3.4, and a bond-valence analysis in Table 3.5. Structure factors are listed in Appendix C. 34 Table 3.2. Miscellaneous information: dugganite. a (A) c V(A3) Space group Z 8.460(2) 5.206(2) 322.6(2) P321 1 Crystal size (mm) 0.1 x 0.08 x 0.05 u.(MoKa; mm"1) 49.89 R = H\F0-Fc\/ZFo ^=[HH^-^l)7l>Fo 0.5 Rad/mono MorCa/graphite Total reflections 3746 Unique reflections 636 Rint(%) 9.8 [l>3a(l)] 558 R (observed) % 2.7 Rw (observed) % 2.9 w = 1 35 3 , _ Lr? CD LO CD CN h-. CO LO LO CD T— LO a> CD CM LO 00 CD co CO CD CN CM oo CM CO CD 3 CO O CM CO GS' LO i CO LO i CM CO CD 00 C\) =5 , v oo" c\f o co LO CM, LO co CO co. co' oT co' oT ocT co" LO CD o o CM CO 5 ^ , co co —^ LO CD CM T— co CD co co CD co 00 ccT 00 LO CD o CD CO CO CO CM CM co CD CM 3 CD v-LO O CO co CM o oo CO CD CO CO CM 00 CO CD CO CO CD LO o , _ , ^ CO CO, CO, 00, CO LO LO' oT CO in C\f o CO LO CM o o CO CM CO co CO LO N CD CD CM LO CM 3 T— co CO CNJ co CM d d d CO CM CM CM CM CD O CM d CO CM CO CD, C\f CD LO CM, CD CD CM CM CM CM, CD O co CD CO •2 CO CM o CO O 36 Table 3.4. Selected interatomic distances (A) and angles (°) for dugganite. Te-0(1) x 6 1.925(8) 0(1)b-Pb-0(1)i 65.9(3) <Te-0> 1.925 0(1)b-Pb-0(2)b x 2 72.8(4) 0(1)b-Pb-0(2)j x 2 133.0(4) As-0(2)a x 3 1.64(1) 0(1)b-Pb-0(2)i x 2 85.4(3) -0(3) 1.51(2) 0(1)b-Pb-0(3)c x 2 78.2(2) <As-0> 1.61 0(1)b-Pb-0(3)f x 2 132.5(2) 0(1)i-Pb-0(2)j x2 113.4(3) Pb-0(1)b x 2 2.40(1) 0(2)-Pb-0(2)b x 2 53.5(5) -0(2) 2 3.00(1) 0(2)-Pb-0(2)j 100.0(5) -0(2)b x 2 2.70(1) 0(2)-Pb-0(3)c x 2 89.0(4) -0(3)c x 2 2.86(1) 0(2)-Pb-0(3)f x 2 70.0(4) <Pb(1)-0> 2.74 0(2)b-Pb-0(3)c x 2 113.4(5) 0(2)b-Pb-0(3)f x 2 74.3(5) Zn-0(1)d x 2 1.91(1) <0-Pb-0> 91.5 -0(2) 2 1.97(2) <Zn-0> 1.94 0(1)d-Zn-0(1)a 129.8(4) 0(1)d-Zn-0(2) x 2 103.8(5) 0(1)-Te-0(1)e x 6 89.2(3) 0(1)d-Zn-0(2)k x 2 101.5(4) 0(1)-Te-0(1)f x 3 85.5(5) 0(2)-Zn-0(2)k 117.8(8) 0(1)-Te-0(1)g x 3 96.8(5) <0-Zn-0 109.7 <0-Te-0> 90.2 0(2)a-As-0(3) x3 114.7(4) 0(2)a-As-0(2)h x 3 103.8(5) <0-As-0> 109.3 Note: <M-<|>> denotes the mean metal-ligand distance (A). Equivalent positions: a = y, x, z -1; b = y + 1, x-y, z; c = x, y-1, z; d = x +y, x,z;e = y,x-y,z;f = y, x, z;g=x,x+y, z;h = x-y, y+1,z+1;i=x+1, x+y, z;j = x-y, y,z;k = x-y, y,z+1. 37 Table 3.5. Bond-valence* arrangement in dugganite. Te Pb Zn Total 0(1) 0.98(2) xei 0.46(1) ,21 0.58(2) x24 2.02 0(2) 1.18(3) x34 0.092(5) x24x1 -> 0.48(3) x2 4 1.95 0.202(6) x2^x1-> 0(3) 1.67(9) 0.134(4) x24x3^ 2.07 Total 5.88 5.2 1.78 2.12 Calculated from the curves of Brese and O'Keeffe (1991). Calculated assuming 54% As and 46%P. 38 3.4 Description of the Structure There are four distinct cation sites in the dugganite structure. The coordinations of tellurium, arsenic, lead, and zinc are discussed followed by a description of the connectivity of the structure. 3.4.1 Tellurium coordination The atom at the Te site, special position la (0,0,0), is coordinated by six O atoms forming a slightly distorted octahedron (Figure 3.1). The Te-0 distances are 1.925 A, and the O-Te-0 angles range from 85.5 to 96.8° (mean 90.2°). The Te-0 distances are similar to those previously described for lesingite (1.922 A; Margison et al. 1997), jensenite (1.936 A; Grice et al. 1996), frankhawthorneite (1.939 A; Grice and Roberts 1995), parakhinite (1.92 A; Burns et al. 1995), yafsoanite (1.929 A; Jarosch and Zemann 1989), and carlfriesite (1.933 A; Effenberger et al. 1978). The variance in the octahedron angle is 18.45, the mean octahedral quadratic elongation (Robinson et al. 1971) is 1.0053, and the polyhedral volume is 9.43 A3. The electron-microprobe analyses, refined site-occupancy, and bond-valence analysis confirm that the site is completely occupied by Te6+. 3.4.2 Arsenic coordination The atom at the As site, special position 2d (1/3, 2/3 ,z), is coordinated by four O atoms forming a distorted tetrahedron (Figure 3.2). The As-0 distances are 1.64 A (x 3) and 1.51 A (mean 1.61 A), and the O-As-0 angles are 103.8° and 114.7° (mean 109.3°). The variance in 39 the tetrahedron angle is 35.93, the mean tetrahedron quadratic elongation is 1.0080, and the polyhedron volume is 2.11 A3. The average electron microprobe analysis indicates that the As site is occupied by As5+ (45%), P5+ (43%), Si4+ (11%), and Al3+ (1%). Refinement of the site occupancy for As and P shows 54(2)% As, 46(2)% P. The mean bond valence (Brese and O'Keeffe 1991) obtained using these proportions is 5.2 valence units (v.w.). The bond valence obtained using proportions from the average electron microprobe analysis is 5.0 v.w., and the values for the coordinating 0(2) and 0(3) atoms are 1.91 and 2.02 v.w., respectively. 3.4.3 Lead coordination The atom at the Pb site, at special position 3e (JC,0,0), is coordinated by eight O atoms forming a distorted snub disphenoid (Johnson 1965) (Figure 3.3). The Pb-0 distances range from 2.40 to 3.00 A (mean 2.74 A) and the O-Pb-0 angles vary from 65.9° to 133.0° (mean 91.5°). The polyhedral volume is 34.40 A3. The Pb site is almost completely occupied by Pb2+, although the electron microprobe results suggest a small amount of substitution (2%) by Ca2+. Pb2+ is commonly lone-pair stereoactive, which typically results in a very asymmetrical (one sided) coordination, with the lone pair of electrons positioned on the opposite side of the atom to the coordinating anions. However, the coordination of Pb2+ in dugganite is relatively symmetrical, and the difference-Fourier maps show no evidence of a lone pair of electrons. 3.4.4 Zinc coordination The atom at the Zn site, special position 3f (x,0,l/2), is coordinated by four O atoms forming a distorted tetrahedron (Figure 3.4). The Zn-0 distances range from 1.91 to 1.97 A 40 (mean 1.94 A); these are similar to the ^Zn-0 length (1.97 A) calculated using ionic radii from Shannon (1976). The O-Zn-0 angles range from 101.5 to 129.8° (mean 109.7°). There are two additional O(l) atoms at distances of 2.90 A; it is unlikely that they form bonds with the atom at the Zn position. The tetrahedral angle variance is 135.30, the mean tetrahedral quadratic elongation is 1.0363, and the polyhedral volume is 3.55 A3. The Zn site is almost completely occupied by Zn . The average electron microprobe results suggests a minor amount (6%) of substitution by Cu2+, although Cu2+ does not commonly occur in tetrahedral coordination (Eby and Hawthorne 1993). 3.4.5 Structure connectivity The TeC>6 octahedra and PbOg polyhedra share edges to form a heteropolyhedral sheet parallel to (001) (Figure 3.5). Each TeC*6 octahedron shares three edges, each with a different PbOg polyhedron; the lengths of the shared edges are 2.61 A. As expected, this is shorter than the unshared edges of the octahedron (2.70 A x 6 and 2.88 A x 3). Each PbOg polyhedron shares one edge with at Te06 octahedron, one edge with an As04 tetrahedron (length 2.58 A), and four edges with four other PbOg polyhedra. The length of the latter edges is 3.36 A, which is shorter than the mean (3.87 A) of the twelve unshared edges (3.04, 3.34, 3.47, 4.10,4.59,4.65 A, all x 2). The As04 and Zn04 tetrahedra share corners to form an interlinked, two- and three-connected two-dimensional net parallel to (001) (Figure 3.6). The two As04 tetrahedra in each unit cell point in opposite directions, with apical 0(3) atoms oriented ± z. The three basal 0(2) atoms are shared with different Zn04 tetrahedra. Each Zn04 tetrahedron shares two corners with As04 tetrahedra. The rather complex Schlafli symbol (O'Keeffe and Hyde 1980) for the 41 resulting net is (122.123)6. It is interesting to note that if the Te06 octahedra are considered as part of the net, the reultant Schlafli symbol is the much more conventional 63 (Figure 3.7). The heteropolyhedral sheets of PbOg and TeC>6 are linked by As04 and Zn04 tetrahedra (Figure 3.8). Each As04 tetrahedron shares an apical 0(3) atom with three PbOg polyhedra, and three basal As-0(2) edges (2.58 A) with three PbOg polyhedra in a different sheet. The As04 and TeOg polyhedra have no anions in common and thus are not directly joined. Each Zn04 tetrahedron shares two corners with two TeOg octahedra in different sheets, and four corners with six different PbOg polyhedra. The sheets of heteropolyhedral and layers of tetrahedra alternate along c to form the three-dimensional structure. 42 43 44 45 46 CD X> th CD ject x> ject an 0 c_ c c_ , CD CD 4-> -M C_ D O o_ true dot in c_ CD D qani CD CD t_ cn D O ~a 0 _Q JZ XI CD +J c O CJ heet ire indi tern. co ire indi O — o o_ D C_ a XI £_ o <D X x> JZ CD oly O lorn o_ O x> o o c L o CD CD i_ et TeO o JZ TeO CD CD _C Th O 1— Th edr LO . * CO o o o CD Q_ b ° 00 Ll_ O Q_ 47 o o CD O L_ c o o CD CD o o CD (_ > i-> O CD L. 4-> Q_ (J 3 i_ 4-> if) CD c o CD X c a in CD CD 0) CD D ~U CD 4-> if) o o 4-> CD o CD O o c CD L. O a L. ~U <D _C D O <i> -fc ^ CD It CD oo o to CD < L_ ~o 3 CD CD Li_ I— t-48 49 3.5 Discussion The ideal formula of dugganite is Pb3Zn3TeAs20i4. The electron microprobe and bond-valence analyses imply that there is little to no OH or H20 in the dugganite structure. The empirical formula, based on the average results of the microprobe analyses, and calculated on the basis of nine cations per formula unit, is (Pb3.o4Cao.o6) This is similar to the formula based on the structure analysis, which is Pb3Zn3Te(Asi.o8Po.92)i2.ooOi4. The empirical formulae calculated from the analyses in Williams (1978) and Kim et al. (1988) (on the basis of nine cations per formula unit) are Pb3.44(Zn3.ooCuo.2i)i3.2iTei.iiAsi.250ii.94OH2.3i and Pb2.94Zn2.95Teo.92(Asi.35Vo.5iSio.2oPo.i3Sbo.oi)i2.2oOi4.o2, respectively. Note that in each study, As is the dominant cation in the As position. As noted above, minerals with V (cheremnykhite) and P (kuksite) dominant at the As site have been described by Kim et al. (1990), and are presumed to be isostructural with dugganite. For comparison purposes, the indexed X-ray powder patterns are listed in Table 3.6 and are indexed according to P321 for UBC data, P6lmmm for Williams (1978), and a C-centered cell for Kim et al. (1988). Kim et al. (1988, 1990) chose an orthorhombic unit cell {a ~ 8.6, b ~ 14.8, c ~ 5.2 A) for all three minerals, and suggested Cmmm, C222, Clmm, Crrilm, or Cmrnl as possible space groups. The orthorhombic cell can be derived from a hexagonal unit cell by using the formula borth « 2ahex'cos30°. However, it would only be necessary to use this cell if there were ordering e.g., of As between pseudo-equivalent As positions, and there is no evidence for this. In addition, the space groups proposed by Kim et al. (1988, 1990) are neither subgroups or supergroups of P321. Without studying the samples described by Kim et al. (1988, 1990), it is 51 suggested that dugganite, cheremnykhite and kuksite are isostructural, and crystallize in the hexagonal system with space group P321. 3.6 Conclusions The formula of dugganite is revised to Pb3Zn3TeAs20i4 from Pb3(Zn,Cu2+)3(Te6+06)(As04)(OH)3. Dugganite crystallizes in the space group P321 and is probably isostructural with cheremnykhite and kuksite whose formulae are similar. The structure of dugganite is made up of heteropolyhedral sheets of lead and tellurium polyhedra, parallel to (001), alternating along c with layers of zinc and arsenic tetrahedra. 52 Table 3.6. Indexed* powder diffraction patterns for dugganite. UBC dmeas Intensity hkl Williams dmeas I hkl Kim ef al. dmeas I hkl 5.206 20.45 00 1 5.204 4 00 1 5.21 2 00 1 4.230 19.13 -12 0 4.233 4 1 1 0 4.27 2 2 0 0; 1 3 0; 0 2 1; 1 1 1 3.663 15.74 020 3.666 3 200 3.71 1 0 4 0; 2 2 0 3.283 100.00 -1 2 1 3.284 10 1 1 1 3.30 10 1 3 1; 20 1 2.996 40.76 -2 2 1 2.997 8 20 1 3.01 9 22 1; 04 1 2.996 44.58 02 1 2.773 5 1 2 0 2.80 3 1 5 0; 2 4 0; 3 1 0 2.769 26.69 -13 0 2.603 4 002 2.605 4 002 2.603 19.70 002 2.446 6 1 2 1 2.468 4 0 6 0; 3 3 0; 1 5 1; 24 1; 3 1 1 2.448 9.11; -1 3 1 2.215 4 1 1 2 2.442 1 1 1 2; 0 2 2; 0 6 1; 4.67 -2 3 1 33 1 2.442 17.51 030 2.121 4 220 2.220 3 III 1 32; 2 02 2.217 8.15 -12 2 2.035 4 1 3 0 2.129 3 III 2 6 0; 4 0 0; 0 4 2; 222 2.122 6.41; -2 2 2 1.963 0.5 2 2 1 2.056 2 1 2 0; 1 7 0; 3 5 0 6.52 022 2.032 17.45 -14 0 1.896 6 1 3 1 2.027 1 1.960 2.90 -2 4 1 1.783 4 302 1.904 8 2 4 2; 1 5 2; 3 1 2 1.897 11.33; -13 2 1.734 0.5 003 1.867 1 III 080 9.07 -2 3 2 1.893 11.63 -3 4 1 1.687 1 1.790 3 3 32; 062 1.893 11.02 -1 4 1 1.644 1 1.706 1 2 8 0; 5 1 0; 3 7 0 1.781 8.55; -3 3 2 1.603 6 1.609 7 3 5 2;422;1 77; 7.70 032 20 3; 1 33 1.735 1.48 003 1.569 3 1.569 2 0 4 3; 22 3 1.681 4.35 -2 5 0 1.530 0.5 1.477 1 III 1 5 3; 2 4 3; 3 1 3 53 Table 3 continued. UBC Williams Kim et al. dmeas Intensity hkl dmeas I hkl dmeas I hkl 1.642 2.81 -2 4 2 1.469 2 1.424 2 III 2 8 2; 5 1 2; 0 6 3; 333 1.606 8.87 -12 3 1.413 3 1.400 1 6 2 0; 4 8 0; 2 10 0; 2 6 3; 4 0 3 1.600 9.92; 9.48 -3 5 1 -2 5 1 1.387 1 1.356 1 62 1;48 1; 2 10 1; 2 6 3; 4 0 3 1.568 AAA; 5.24 -2 2 3 023 1.364 1 1.324 1 1 7 3; 3 53; 42 3 1.341 2 1.29 1 III 0 102; 5 52 1.321 3 1.236 1 III 6 6 0; 0 12 0 1.303 1 1.214 2 2 8 3; 3 7 3; 5 1 3 1.279 3 1.181 1 2 4 4; 3 1 4; 1 5 4 1.242 1 1.125 1 0 10 3; 5 53 1.225 3 1.039 1 82 1; 0 14 1; 77 1 1.209 4 1.117 5 *UBC indexed based on P321, Williams based on P6/mmm; Kim et al. based on a C-centered cell. 54 4.0 CHOLOALITE: CRYSTAL STRUCTURE AND REVISED FORMULA 4.1 Introduction According to Williams (1981), choloalite was first found in Arabia with a host of other unknown tellurium minerals. An X-ray powder pattern was taken and the material was then discarded. The type specimen of choloalite was described by Williams (1981) from waste rock in the tunnel at the Mina La Oriental, Moctezuma, Mexico. The type piece consists of a matrix of intensely sericitized rhyolite vitrophyre with veins of crystalline crusts and choloalite crystals. Soon after the discovery of the type material, samples with tiny crystals of choloalite were found between the dumps of the Joe and Grand Central shafts at Tombstone, Arizona. According to Williams (1981), the crystals occur with cerussite, emmonsite, and rodalquilarite within fragments of severely-brecciated shale replaced by opal and granular jarosite. The breccia matrix is vuggy quartz. A thin section showed large (1 mm) subhedra of choloalite corroded by fibrous crusts of emmonsite. From textural evidence, Williams (1981) obtained the paragenetic sequence, beginning with the first to crystallize: rodalquilarite, choloalite, emmonsite, cerussite. According to Williams (1981), crystals of choloalite from both Mina La Oriental and Tombstone are invariably simple octahedra. Crystals viewed in thin section show sectoring into polygonal domains. Some are isotropic, others show birefringence up to 0.011, but with variable optical character. Using powder X-ray diffraction data, Williams (1981) showed that choloalite is isometric. The refined cell dimensions were a 12.519 for the type specimen, 12.586 for the Arabian material, and 12.576 A for the Tombstone sample. The larger cell edge of the 55 Tombstone specimen was attributed to the presence of minor amounts of antimony. Wet chemical analysis of the type material gave the empirical formula CuPb(Te4+03)2-H-20. Choloalite was also described by Roberts et al. (1994) from the McAlpine mine, Tuolumne County, California. Associated nonmetallic phases are annabergite, azurite, calcite, chlorargyrite, goethite, hematite, keystoneite, malachite, mcalpineite, mimetite, muscovite (mariposite), and a host of unidentified crusts, both crystalline and amorphous. Associated metallic minerals include acanthite, altaite, electrum, galena, hessite, owyheeite, pyrargyrite, pyrite, native silver, and sphalerite (Roberts et al. 1994). The formula of choloalite was revised to CuPb(Te03)2 by Powell et al. (1994). Crystals with this formula were synthesized by fusion of stoichiometric amounts of CuO, Te02, and PbO. No weight loss was detected with heating to 400°C, and infrared spectroscopy was used to confirm the absence of water. Powder X-ray diffraction spectra of the synthetic material were similar to those obtained from type choloalite, with some additional weak reflections. Powell et al. (1994) concluded that choloalite is anhydrous, and that the water determined by Williams (1981), using only 156 ug of material, was adsorbed on the surface of the mineral particles. The cell dimension obtained from the synthetic phase was a 12.514 A, and indexed reflections suggested possible space groups P23, Pm3, P4 32, P43m, or Pm3m (none of which would result in systematic absences). Powell et al. (1994) also suggested an additional occurrence of choloalite. This was based on the original description of balyakinite (Spiridonov 1980), which occurs with teinite and two unnamed Cu, Pb tellurites with formulae CuPb(Te03)0 and CuPb(Te03)2 (from microprobe analyses). The latter formula is the same as that obtained by Powell et al. (1994) for their synthetic material. 56 4.2 Experimental Two data sets were collected because the absorption correction for the first set was not satisfactory. Structure refinement was attempted with the original, combined, and duplicate data sets; statistically, the results were always better using the duplicate data set with the better absorption correction. The final structure refinement was made with the second data set and unless otherwise specified, its experimental conditions are described. The crystal used is from the Mina La Oriental locality (Canadian Museum of Nature sample MI58777). Data collection is as described in Chapter two with a few differences. In the original data collection, fifty reflections with 20 11.30 to 28.39° were centered using an automated search routine and from these results the unit cell was determined. In the second data set, one octant of reflections (3186 measurements, exclusive of standards) was collected from 3 to 60° 20; 64 reflections were rejected because of asymmetric backgrounds, and one because of peak asymmetry. Fifteen strong reflections were used for v)/-scan and this data (920 measurements) was used to calculate an absorption correction. The merging R index for the u> scan data set decrease from 5.1% before the absorption correction to 2.1% after the absorption correction. This correction was then applied to the entire data set; minimum and maximum transmissions were 0.88 and 0.68 respectively. Of the 956 unique reflections, 455 were classed as observed [I > 3a (I)]. Microprobe data for Ca, Cu, Sb, and Te were collected for twenty-five seconds; data for CI, Zn, and Pb were collected for fifty seconds. The standards used were scapolite (ClKxx), CaTa40n (CaKa), cuprite (CuKa), ZnW04 (ZnXa), stibiotantalite (SbZa), and PbaTeaOg (Tela and PbMoc). The analysis is given in Table 4.1, together with that of Williams (1981). 57 The infrared spectrum of choloalite was obtained using a Spectra-Tech IR-Plan microscope connected to a Bomem Michelson MB 100 Fourier-transform infrared spectrometer equipped with a mercury cadmium telluride (!) detector. A small amount of the mineral was mounted in a diamond anvil microsample cell, then pressure was applied to crush the sample and cause it to spread as a randomly-oriented powder. Two hundred scans were collected from 4000 to 400 cm"1 then coadded to generate the transmittance spectrum (Figure 4.1). The spectrum of an empty diamond cell collected with the same parameters was used as a reference. The spectrum shows a broad absorption band at approximately 3260 cm"1 (due to O-H stretching) and a weaker band at approximately 1590 cm"1 (due to H-O-H bending). These confirm the presence of H2O in the crystal structure of choloalite. 58 Table 4.1. Chemical composition of choloalite. Williams (1981)* This study1" CaO wt. % trace 0.50 PbO 33.0 31.22 CuO 11.0 11.81 ZnO — 0.37 Sb205 trace 1.10 Te02 50.7 51.81 CI — 1.19 H20 3.4 0.34 OCI - -0.27 TOTAL 98.1 98.07 Ca2+ trace 0.17 Pb2+ 2.53 2.65 Cu2+ 2.37 2.81 Zn2+ — 0.09 Sb5+ trace 0.13 Te4+ 5.44 6.14 CI" - 0.64 H+ 6.46 0.72 O2" 19.00 18.36 Note: Oxides are in weight percent; analyses are normalized on 19 anions per formula unit. *Average of four wet chemical analyses for CuO, and three for PbO and Te02. Water by the Penfield method. tH20 is calculated to give one (CI + H20) per formula unit. 59 1—I—1—i—I—I—I—I—I—I—I—1—I—I—I—I—I—I—I—I—I—I—I—1—|— o aouBmujsueJi Figure 4.1 The infrared transmittance spectrum of choloalite. The absorption bands at 3260 cm"1 and 1590 cm"1 are indicative of water in the structure of choloalite. 60 4.3 Structure Solution and Refinement The mean value of | E2-l | was 0.85, which is indicative of a non-centrosymmetric space group (Joel Grice pers. comm., 1998). Systematic absences in the original data set suggested space groups P43 2 and P4j32. In the second data collection, the reflections required to acknowledge these space groups were dismissed for having bad backgrounds and consequently gave the possible space groups as P2i3 and P4232; structure solution and refinement using these space groups were attempted but there was no success. Upon closer scrutiny of the data, it was confirmed that the reflection conditions for a 4\ or 43 screw axis [(0,0,/) with / = 4n] were indeed met. The structure was solved by Patterson and direct methods and refined in P43 2 to an R index of 6.9 % for an isotropic displacement model. The refined atomic positions were used in the normalization program STRUCTURE TIDY (Gelato and Parthe 1987), which suggested space group P4i32, with an origin shift of 1/2,1/2,1/2 and a redefined orientation matrix (by -1 0 0, 0 -1 0, 0 0 -1). Accordingly, the structure was refined in P4\32 to an R index of 6.9% for an isotropic displacement model. Conversion to anisotropic displacement factors for all cations and CI resulted in convergence at R and wR indices of 5.2 and 5.9%, respectively (13.0 and 28.3% for all 956 data). Conversion to anisotropic displacement factors for the oxygen atoms resulted in convergence at an R index of 5.1% (due to "smearing" of the electron density), but did not improve the model. Addition of an isotropic extinction correction did not improve the results. The program MISSYM(Le Page 1987) was used to search for additional symmetry elements; none were indicated. Miscellaneous experimental information is found in Table 4.2. Positional coordinates and anisotropic and equivalent isotropic displacement factors are given in Table 4.3. Interatomic distance and angles are given in Table 4.4, and a bond-valence analysis in Table 4.5. Initially, bond-valence values were calculated using the curves of Brese and O'Keeffe (1991), 61 but the sums were poor. Bond-valence values calculated using the "correction" terms given by Wang and Liebau (1996) for Te4+ were consistently too high. The curves of Brown (1981) were found to give the best sums for bonds to oxygen atoms (when the correct R0 value of 1.951 was used for Te4+, as shown by Back 1990). Structure factors are listed in Appendix D. 62 Table 4.2. Miscellaneous information: choloalite. a (A) V(A3) Space group Z 12.520(4) 1963(2) P4i32 4 Crystal size (mm) 0.04 x 0.04 x 0.05 u. (MoKoc; mm"1) 35.6 wR = [}Z{w-\F0-Fc\)2 I ^.F0! 0.5 Rad/mono Total reflections Unique reflections [I > 3 a (I)] R (observed) % Rw (observed) % MoKa/graphite 3186 956 455 5.2 5.9 ,w = 1 63 o IT) oo CD, CO, 00 CO CM h- CD CO CM T— 00 CN CM o in oo CM 2-co 3 2-in CM CM, T— CO CO 2-CM 2-CD CM 00, m 00 2-CM cn, co CM CM >— . m 00 T- oo 2-h-CM 2-ccT CM co 3 o CM CM, oo' CD CO 00 m CO CM 00 m in 3 ^ ^ R T— CM, T— LO CO co' LO CD o CO CM oo CM oo m in CO T— co T— NT CM OO LO O CO N- CO CM 00 CM oo in m N cu CO c\T CO T— o CN CD 00 m d d • d CO T— CO T— N-o CNJ CM 00 O) CM O d d CM CNT „ T— 00 oo ^ o 3 o CM CD 00 oo 00 co oo oo CM So CM ^— X— CM OO oo CO oo x— CD CO CM oo CN d d d co" 00 CO CM ^— ^— CD o O o CM CN CN oo in d d d oo" 00 CM T— x— T— CD CD in m CM CO O d d d CM O oo, O 00 co oo o T3 CD +-» </> 2> CO <n CD _g co > ^> T3 C CO * 64 Table 4.4. Selected interatomic distances (A) and angles (°) for choloalite. Te-0(1)a 1.87(3) 0(2)e-Cu-0(3)f x 2 94.0(1.0) -0(1 )b 2.95(3) 0(2)e-Cu-0(3)h x 2 85.7(1.0) -0(2) 1.90(2) 0(2)e-Cu-CI x 2 93.4(7) -0(3) 1.92(2) 0(3)f-Cu-CI x 2 92.3(7) -0(3)c 2.71(2) <0-Cu-0> 90 -0(3)d 3.05(2) <0-Cu-0.CI> 91.4 <Te-0> 2.40 0(1)-Pb(1)-0(1)i x 3 98.9(9) Cu-0(2)e x 2 1.92(2) 0(1)-Pb(1)-0(1)j x 3 65.1(1.0) -0(3)f x 2 1.86(2) 0(1)-Pb(1)-0(1)a x 3 67.9(6) -CI 2.53(6) 0(1)-Pb(1)-0(2) x 3 81.3(8) <Cu-0> 1.89 0(1)-Pb(1)-0(2)i x 3 115.0(8) <Cu-0,CI> 2.02 0(1)g-Pb(1)-0(1)j x 3 119.4(0.1) 0(1)g-Pb(1)-0(2) x 3 122.3(7) Pb(1)-0(1) x 3 2.46(3) 0(1)g-Pb(1)-0(2)i x 3 81.7(7) -0(1 )g x 3 3.14(3) 0(1)g-Pb(1)-0(2)k x 3 55.1(7) -0(2) x 3 2.83(2) 0(2)-Pb(1)-0(2)i x 3 68.1(7) <Pb(1)-0> 2.81 <0-Pb(1)-0> 87.5 Pb(2)-0(2) x 6 2.56(2) 0(2)-Pb(2)-0(2)i x 6 76.5(8) -0(3) x 6 3.31(2) 0(2)-Pb(2)-0(2)d x 3 116.9(1.0) <Pb(2)-0> 2.94 0(2)-Pb(2)-0(2)l x 3 93.8(1.0) 0(2)-Pb(2)-0(3) x 6 55.1(6) 0(1)a-Te-0(1)b 79.0(6) 0(2)-Pb(2)-0(3)i x6 54.4(6) 0(1)a-Te-0(2) 94.9(1.1) 0(2)-Pb(2)-0(3)k x 6 115.4(6) 0(1)a-Te-0(3) 97.5(1.1) 0(2)-Pb(2)-0(3)d x 6 68.6(6) 0(1)a-Te-0(3)c 78.1(1.0) 0(2)-Pb(2)-0(3)m x6 142.5(6) 0(1)b-Te-0(3) 71.2(9) 0(2)-Pb(2)-0(3)l x6 107.2(6) 0(1)b-Te-0(3)c 127.6(7) 0(3)-Pb(2)-0(3)i x 6 108.7(4) 0(1)b-Te-0(3)d 99.8(7) 0(3)-Pb(2)-0(3)d x 3 53.0(8) 65 0(2)-Te-0(3) 0(2)-Te-0(3)c 0(2)-Te-0(3)d 0(3)-Te-0(3)d 0(3)c-Te-0(3)d <0-Te-0> 94.3(1.0) 65.1(8) 82.1(8) 68.6(9) 113.0(9) 89.3 0(3)-Pb(2)-0(3)m x 3 92.3(8) <0-Pb(2)-0> 90.6 Note: <M-<t)> denotes the mean metal-ligand distance (A). Equivalent positions: a = z + 3/4 -1, y + 1/4, x + 1/4; b = x, y + 1/2, z + 1/2; c = z + 1/4, y + 3/4 -1, x + 1/4; d = y + 3/4, x + 3/4, z + 3/4; e = x, y, z -1; f = z, x, y -1; g = y + 1/4, x + 1/4, z + 3/4 - 1; h = z + 1/4, y + 3/4 - 1, x + 1/4 -1; i = z, x, y; j = x + 1/4, z + 3/4 -1, y + 1/4; k = y, z, x; I = z + 3/4, y + 3/4, x + 3/4; m = x + 3/4, z + 3/4, y + 3/4. 66 Table 4.5. Bond-valence arrangement in choloalite. Te Cu Pb(1) Pb(2) Total 0(1) 1.21 0.36 x 3 4 1.82 0.16 0.09 x3i 0(2) 1.13 0.55x24 0.17 x34- 0.26 x64 2.11 0(3) 1.07 0.66 x2l 0.07 x6i 2.16 0.23 0.13 CI 0.26 x 3-* 0.78 Total 3.93 2.68 1.86 1.98 *Calculated from the curves of Brown (1981), as modified by Back (1990) for Te, and those of Brese and O'Keeffe (1991) for bonds to CI. 67 4.4 Description of the Structure The structure of choloalite is a difficult one to describe because of the intricate way in which the structure is connected together. The coordinations around each cation is discussed followed by a description of the complex structure connectivity. There are four distinct cation sites in the choloalite structure: Te, Cu, Pb(l), and Pb(2). The coordination polyhedra of these cations are shown in Figures 4.2 - 4.5. 4.4.1 Te coordination The Te site is completely occcupied by Te4+, as shown by the electron microprobe analysis, refined site occupancy, and bond-valence analysis. The atom at the Te position is coordinated by at least four oxygen atoms at distances of 1.87, 1.90, 1.92, and 2.71 A (Figure 4.2). In accordance with Zemann (1968, 1971) and Lindqvist (1973), these atoms can be described as forming a trigonal dipyramid, with a lone-pair of electrons occupying one corner of the equatorial triangle. Brown (1974), however, assumed that the coordination environment of Te4+ (and Sn2+, Sb3+, I5+, and Xe6+) is an octahedron distorted by a lengthening of some of the bonds on one side. Rossell (1992) demonstrated that the coordination polyhedra of the four Te4+ atoms in the crystal structure of BiaTe^n can be described as distorted octahedra. In the crystal structure of choloalite, two additional O atoms at distances of 2.95 and 3.05 A can be considered to form bonds with the atom at the Te position contributing 0.16 and 0.13 v. u. respectively. The resulting polyhedron is a distorted octahedron, with three weak bonds occurring opposite three strong bonds. As suggested by Brown (1974), the bond-valence sum of each trans pair is approximately equal. The environment corresponds to type of Brown 68 (1974) with three strong and three weak bonds. The mean Te-0 distance is 2.40 A, and the O-Te-0 angles range from 65.1 to 127.6°, with a mean value of 89°. The octahedral angle variance is 354.12, the mean octahedral quadratic elongation (Robinson et al. 1971) is 1.2296, and the polyhedral volume is 14.47 A3. The lone-pair of electrons is probably located on the side of the Te atom opposite the three closest O atoms, and within the volume defined by the Te atom and the three O atoms with the largest Te-O distances and O-Te-0 angles. It is unlikely that the atom at the Te position forms a bond with the atom at the nearest CI site, given the distance (3.701 A), the possible bond-valence contribution (0.03 v.w.), and the presence of Cu sites at distances of 3.206 and 3.330 A. 4.4.2 Copper coordination The atom at the Cu site, special position \2d (l/SyxA/4+x), is coordinated by four oxygen atoms at distances of 1.86 and 1.92 A (both x 2), and by the atom (CI) or molecule (H2O) at the CI site, at a distance of 2.53 A. The resulting coordination sphere (Figure 4.3) is almost a square pyramid (actually a very distorted trigonal dipyramid; the oxygen atoms deviate from a common plane by ± 0.02 A), with a mean Cu-§ = unspecified anion) distance of 2.02 A, a mean O-Cu-((> angle of 91.4°, and a polyhedral volume of 6.3 A3. The structure refinement shows that the Cu site is predominately occupied by Cu . The electron microprobe analysis suggests 92.7% Cu, 4.3% Sb, and 3.0% Zn at the Cu site. The structure refinement shows 93(4)% Cu and 7(4)% Sb at the Cu position. According to Shannon (1976), the ionic radii of Cu and Sb in five-fold coordination, and of Sb5+ in six-fold coordination, are 0.65, 0.80, and 0.60 A, respectively. This suggests that the Sb at the Cu position is pentavalent. In addition, the CI in choloalite serves to balance the excess positive charge introduced by Sb, and the chemical formulae obtained from 69 both the electron microprobe and crystal-structure analyses are only charge-balanced with pentavalent Sb. The results of the crystal structure refinement (using 93% Cu and 7% Sb) suggest that the bond-valence sum of the Cu site should be 2.21 v.u.. In fact, the sum is 2.68 v.u. including a contribution from CI plus H2O at the CI position of 0.26 v.u. This suggests that the bond-valence curves are not optimal for use with Cu in five-fold coordination. This is not surprising, since existing bond-valence curves are based primarily on Cu in six-fold coordination. It is interesting to note that of the ninety-four Cu-oxysalt minerals listed in the compendium by Eby and Hawthorne (1993), only eleven show Cu in five-fold coordination. Eight of the former and two of the latter also contain Cu in six-fold coordination. Of the eleven Cu-oxysalt minerals with Cu in five-fold coordination, ten contain Cufo square pyramids that share edges to form [Cu2<|>5] dimers. In fingerite the coordination polyhedron is a triangular dipyramid. Only in clinoclase are there "isolated" Cufo square pyramids, and these share edges with Cu(|>8 octahedra. Therefore the coordination of Cu in the crystal structure of choloalite is virtually unique. The results of the crystal structure refinement show that the CI site is occupied by 81(4)% CI and 19(4)% H2O, corresponding to 0.64 and 0.34 atoms (molecules) per formula unit, and 1.19 and 0.34 wt.%, respectively (Table 4.1). However, the infrared spectrum (Figure 4.1) suggests a higher H2O content. This could be real (the spectrum was collected from different material, but from the same sample, as that used in the crystal structure analysis), or could be due to adsorbed H2O. It is interesting to note that the maximum possible amount of H20 in the choloalite structure is one molecule per fomula unit (i.e., the CI site completely filled with H2O), corresponding to 0.97 wt.% H2O, and a total of 97.78 wt.% for the analysis in Table 4.1. 70 4.4.3 Lead(l) coordination The atom at the Pb(l) site, special position 8c (x,x,x), is coordinated by nine oxygen atoms (Figure 4.4) forming a triaugmented trigonal prism. The Pb(l)-0 distances are 2.46, 2.83, and 3.14 A (all x 3; mean 2.81 A), and the 0-Pb(l)-0 angles range from 55.1 to 122.3° (mean 87.4°). The lengths of the polyhedral edges are 2.78, 3.07, 3.17, 3.18, 3.46, 3.74, and 3.92 A (all x 3). The polyhedral volume is 40.6 A3. The coordination polyhedron is somewhat distorted, suggesting the presence of a lone-pair of electrons. The results of the crystal structure refinement show that the Pb(\) site is completely occupied by Pb2+. 4.4.4 Lead(2) coordination The atom at the Pb(2) site, special position 4a (3/8,3/8,3/8), is coordinated by twelve oxygen atoms forming a distorted icosahedron (Figure 4.5). The Pb(2)-0 distances are 2.56 and 3.31 A (both x 6; mean 2.94 A), and the 0-Pb(2)-0 angles range from 53.0 to 142.5° (mean 90.7°). The lengths of the polyhedral edges are 2.95 and 4.77 A (both x 3), and 2.76, 2.80, 3.17, and 3.37 A (all x 6). The polyhedral volume is 57.9 A3. The electron microprobe analysis suggests that the Pb(2) site is occupied by 79% Pb and 21% Ca. The structure refinement shows 70(2)% Pb and 30(2)% Ca at the Pb(2) position. Other minerals with twelve-coordinated Pb2+ include osarizawaite (Giuseppetti and Tadini 1980), plumbojarosite (Szymanski 1985) and senaite (Grey and Lloyd 1976). All show six equal short and six equal longer Pb-0 distances, with mean values of 2.82 to 2.92 A (Table 4.6). Although the Pb(2)-0 distances in choloalite show a larger range, the mean value is close to those for the other minerals. 71 Table 4.6. Bond lengths of twelve-coordinated lead icosahedra in different minerals. Mineral short Pb-0 bonds (each x 6), (A) long Pb-0 bonds (each x 6), (A) average Pb-0 length (A) osarizawaite 2.784(4) 2.846(4) 2.815 plumbojarosite: Pb(1) 2.862(1) 2.965(1) 2.914 plumbojarosite: Pb(2) 2.690(1) 2.953(1) 2.822 senaite 2.786 2.849 2.817 choloalite 2.56(2) 3.31(2) 2.94 72 4.4.5 Structure connectivity The intricately connected structure of choloalite makes its description a difficult job. To begin, the polymerization of coordination polyhedra by simple rotation around an atom (generally a central cation), at a special position, is considered. The CI site, at special position Ab (1/8,1/8,7/8), lies at the intersection of one two-fold and one three-fold rotational axes. The atom or molecule at this site forms bonds with three Cu atoms (each of which is on a two-fold rotational axis). Because of this, each Cu<j>5 square pyramid is attached to two others by corner-sharing of the atom or molecule at the CI site, forming a "pinwheel" (Figure 4.6a). In addition, each Cu(|)5 polyhedron shares two trans 0(2)-0(3) edges (length 2.57 A) with two Te06 octahedra, and the other trans 0(2)-0(3) edges (length 2.76 A) with two Pb(2)Oi2 polyhedra. The lengths of the unshared 0(2)-Cl and 0(3)-Cl edges are 3.26 and 3.20 A, respectively. Each Cu<j>5 polyhedron is also linked by corner-sharing to additional Te06 octahedra (x 4) and Pb(l)09 polyhedra (x 2). The Pb(l) sites lie on three-fold rotational axes. Each Pb(l)09 polyhedron shares edges with three others, forming an additional "pinwheel" (Figure 4.6a). The "pinwheels" polymerize to form a three-dimensional network (Figure 4.7). Like the CI sites, the Pb(2) positions are at intersections of one two-fold and one three fold rotational axes. Individual Pb(2)Oi2 polyhedra are not joined; however, each is linked by the shared 0(2)-0(3) edges to six Cu(j)5 polyhedra. Each Cu§5 polyhedron is then joined through the trans 0(2)-0(3) edge to an additional Pb(2)Oi2 polyhedron. The result is yet another "pinwheel" (Figure 4.6b). These polymerize to form an additional three-dimensional network (Figure 4.8). 73 The two three-dimensional networks are linked by the two trans 0(2)-0(2)-0(2) faces (edge length 3.17 A, x 3) of each Pb(2)Oi2 icosahedron, which are shared with adjacent Pb(l)09 polyhedra. The spaces are filled with Te06 octahedra (note that the Te atom, alone of the cations in the choloalite structure, is not on a rotational axis). The linkage of the TeC>6 polyhedra with neighbouring polyhedra is shown in Figure 4.9. Each TeC>6 octahedron shares one triangular 0(2)-0(3)-0(3) face with a Pb(2)C*i2 polyhedron; the lengths of the shared edges are 2.80, 2.95, and 3.37 A. In addition, each TeC>6 polyhedron share one 0(2)-0(3) edge (2.57 A) with an adjacent Cufo square pyramid, and one 0(3)-0(3) edge (2.95 A) and two 0(l)-0(3) edges (2.96 A x 2) with three different TeC>6 octahedra. Furthermore, one 0(1)-0(1) (3.18 A) and one 0(1)-0(2) (2.78 A) edges are shared with adjacent Pb(l)09 polyhedra. This leaves only three unshared edges (lengths 4.60, 4.81, and 5.08 A). Finally, each Te06 polyhedron is linked by corner-sharing to additional Cx\§$ (x 2), Te06 (x 2), Pb(l)09, and Pb(2)Oi2 polyhedra. 74 75 76 77 78 79 CM O CN _£) Q_ C CD > CD CO CD c_ D 4-> U D L_ 4-> co CD O _o O o CD 4-> D C_ "O CD _c o Q_ m •©-15 O CD CO c _Q CD "D CD C D CD CD C_ _C O 80 c CD Te > Te CD CD CD Th. JD to CD D X L. a X> CD T JZ >~ pol he 4-> co <+-O O x _Q to D_ c o u-O 4-> to o Q_ O CD _c CD 1— C ~D to C CD o t_ to CD c _C CD Q_ £ to to l D CD CD C -C o \— _c to CD ar CD to ur £ CD o CN o~ CN _Q Q_ ~o C D co ?_| <-> •&. <4- to to D c o t_ o 4-> c to "O CD c c_ O D to to c £ 0) o l« i CD CD C_ CD CD C-CD CD C_ _C D >-O 82 c o JZ "D CD t_ D CO CD £_ O CO X c o CQ c o £_ X CD _C o o O 4-> X CD c X CD C_ O JZ CO J3 c co § CO 4-> CD D C_ O Q_ CD JZ CO c C_ CD O <•> 4-> o D t_ O X L. CD X JZ <D >~ JZ O 6| COJZ c co 3 CD £- c_ D co co E o o 4-> 4J D LU O x £ o "a c o i_ JZ CO CD C_ CD C CD o_ O CO D co E o o CD CD JZ <oaozPx — ^ CD c CD O D CD CO O JZ x ° c_ o o 4-> a £_ X CD JZ >• c o o a_ c CD co o JZ X 4-> c o CD Xi U CD .^JZ o 4-> o o X c o JZ CO CO c o D o ~o c_ CD o CD <-> CO <D a CD c CO CD JZ 4-> D CD C <~> O CD CD JZ L. ^ CO CD cn x CD 4-> £ a> JZ co h— CD c_ CD cb JZ c Q_ ~ CO Z5 l_ CO D UJ CO c £ o o ^ ^1 co * E co O CD -<-> L. d CD CD i— CO <D CO JZ O I— c CO o t- JZ CD CO c t- CD o c_ u o ^ JZ 9-"^ CO X CO c o a CO E o 4-> a co CD c_ CD JZ CN ' S" rfx CD CD £ JZ O ^ X 6 "> - CO C D C_ CD C 4-' $ D O Q_ JZ CO I J C_ a co Z5 E CO § CD £ • C- O CO CD O O L. £ ® Jz - JZ CL $ I— CO 4.5 Discussion The ideal formula of choloalite is Cu3Pb3Te4+60ig-(Cl,H20). The empirical formula, based on the microprobe analysis, and calculated on the basis of nineteen anions per formula unit, is (Cu2.8iSbo.i3Zno.o9)z3.03(Pb2.65Cao.i7)z2.82Te6.i40i8.oo (Clo.64H2Oo.36)si.oo- This is similar to the formula based on the structure analysis, which is (Cu2.79Sbo.2i)s3.oo(Pb2.7oCao.3o)z3.ooTe6.ooOi8.oo(Clo.8iH2Oo.i9)zi.oo- The empirical formula calculated from the analysis in Williams (1981) (on the basis of 19 anions per formula unit) is Cu2.37Pb2.53Te5 440i5.77-(H20)3.23. The results show a CI position that is fully occupied by CI plus H2O, unlike the material synthesized by Powell et al. (1994), which presumably contains no CI and is anhydrous. Choloalite is one of five cubic Te-oxysalt minerals; the others are cliffordite, mcalpineite, winstanleyite, and yafsoanite. Only the crystal structures of cliffordite and yafsoanite (Jarosch and Zemann 1989) are known. Brandstatter (1981) showed that there are three distinct cation sites in the crystal structure of cliffordite. The atom at the Te position, which is completely occupied by Te4+, is coordinated by five (Brandstatter 1981) or more (Back 1990) O atoms. There are also two U positions in the crystal structure of cliffordite; each is coordinated by eight O atoms forming hexagonal bipyramids. The crystal structure of yafsoanite was most recently studied by Jarosch and Zemann (1989), who showed that it is a garnet-type oxide with Ca, Te6+, and Zn atoms coordinated by eight, six, and four O atoms, respectively. 84 4.6 Conclusions The fomula of choloalite is revised to Cu3Pb3Te 60i8-(Cl,H20) which is different from earlier formulas of CuPb(Te4+03)2H20 (Williams 1981), and CuPb(Te03)2 (Powell et al. 1994). Microprobe and infrared analyses and structure refinement show that choloalite does contain water. The structure consists of two three-dimensional nets, one net contains only Pb(l) polyhedra and the other consists of Pb(2) and Cu polyhedra; these nets are joined together by TeC>6 octahedra. 85 5.0 RODALQUILARITE, A REFINEMENT OF THE STRUCTURE 5.1 Introduction Rodalquilarite was first discovered by J. Sierra Lopez et al. in 1968 during a general study of the gold-bearing Rodalquilar deposit in the province of Almeria, Spain. Named after the deposit, it was determined to be an unknown chlorotellurite of iron. Associated with jarosite, emmonsite, and rarely with native gold, rodalquilarite was found in the oxidation zone of the gold-bearing field. Rodalquilarite occurs as tiny crystals often smaller than 0.1 mm forming crystalline crusts covering quartz geodes. The crystals are squat with a greasy lustre and the colour ranges from brass green to emerald green. Sierra Lopez et al. (1968) describes rodalquilarite as a possible alteration product of gold tellurides. The cell parameters, determined with a precession camera, were: a = 8.89 A b = 5.08 A c = 6.63 Aa= 103°10' p = 107°5' y = 77°52' and V = 275.9 A3. The crystal system was found to be triclinic and the space group PI. The original chemical, thermogravimetric, and microprobe analyses of rodalquilarite gave the formula Fe23+(TeO327(TeO3H")3/Cl")-0.5 H2O. However, these analyses could not confidently define the CI to H2O ratio and Sierra Lopez et al. (1968) suggested that crystal structure analysis would resolve any questions about the formula. The crystal structure of rodalquilarite was originally solved using film methods (Dusausoy and Protas 1969) to a final R index of 9.2%. Crystal structure analysis gave the revised formula as H3+Fe23+(Te03)42"Cl" allowing the conclusion be drawn that rodalquilarite is an anhydrous chlorotellurite of iron. It was decided that a refinement of the crystal structure of rodalquilarite be done using a single crystal X-ray diffractometer. It was thought that with better data, the R index would be 86 reduced resulting in a better structural model which could allow the hydrogens and their bonds to be located with confidence. 5.2 Experimental Forty reflections with 29 11.29-49.36° were centered using an automated search routine. One sphere of reflections (3342 measurements, exclusive of standards) was collected from 3 to 60° 20. No reflections were rejected. Eleven strong reflections were used for the \|/-scan and the data (395 measurements) was used to calculate an absorption correction. The merging R index for the \|/-scan data set decreased from 8.30% before the absorption correction to 3.39% after the absorption correction. This correction was then applied to the entire data set; maximum and minimum transmissions were 0.958 and 0.425 respectively. Of the 1672 unique reflections, 1555 were classed as observed [I > 3a(I)]. 5.3 Structure Solution and Refinement The structure was solved by direct methods in the space group PI but the atomic positions were not the same as that published by Dusausoy and Protas (1969). The published atomic positions were put into the problem and the structure was refined to an R index of 5.3% for an isotropic displacement model and to R = 4.1 % and wR = 4.7% using anisotropic displacement factors for the two tellurium atoms, iron, and chlorine. Using all 1672 data, R is 4.6% and wR is 6.4 %. A hydrogen atom was tentatively located using the listing of possibly bonded atoms in the listing file. Previous results indicated that 0(3), 0(4), and 0(1) may be bonded to hydrogens 87 and knowing that 0(3) had the most deficient bond-valence sums, unassigned atoms that were joined to 0(3) were the ones most likely to be hydrogen atoms. Luckily, only one unassigned atom appeared to be joined to both 0(3) and 0(4) and this atom was assigned as a hydrogen. The bond-valence sums improved for 0(3), 0(4), and O(l) with the addition of this atom although there was no improvement in the R index. Knowing that one of the hydrogens must lie on a special position, a hydrogen atom was located at a site proposed by Dusausoy and Protas (1969). The bond-valence sum for 0(1) improved but again there was no improvement in the R index. No additional symmetry was detected when the program MISSYM was used on the redetermination (based on the 1969 atomic positions). The program STRUCTURE TIDY-was used to standardize the atomic positions but, for comparison purposes, it was decided that the redetermination be described using the atomic positions based on Dusausoy and Protas (1969). Miscellaneous experimental information is given in Table 5.1. Positional coordinates and anisotropic and equivalent isotropic displacement factors are given in Tables 5.2, 5.3, and 5.4 respectively for the refined, original (Dusausoy and Protas, 1969), and "STRUCTURE TIDY" refinements. Interatomic distances and bond angles are found in Table 5.5. A bond-valence table is given in Table 5.6. Structure factors are listed in Appendix E. 88 Table 5.1. Miscellaneous information: rodalquilarite a (A) 9.021(1) Space group PI b(A) 5.1170(7) p (MoKa; mm"1) 13.00 c(A) 6.6539(8) Rad/mono MoKa/graphite an 103.23(1) Total reflections 3342 P(°) 106.66(1) Unique reflections 1672 7(°) 78.07(1) [I > 3 a (I)] 1555 V(A3) 283.15(6) R (observed) % 4.1% Z 1 Rw (observed) % 4.7% Crystal size (mm) 0.19 x 0.13 x 0.05 R = H\F0-FC\ I £F0 WR = [£HF0-FC|)2 / Zw-F? 0.5 ,w = 1 89 3 00 CM co CVJ 3 N c\T c\T ^" CN CN CN 1 CO co CN CD O CN 00 CO co LO co OO CO CT> CO o o o LO CO co' o c\T oo' CNT T— 1 co" o CN 1 CN co • o CD 1 If? oo' o oo 00 LO o CN LO" o co CD CM CN co co 2-ur> co co co co CM co CD co, ocT co co co co oo co CN co d ^ ^ , _ •~ CN CO Tel 1? JD, O 00 ^ CN 00 LO co LO 00 o CM o o o ^— CO T— CD LO CO Oi co CO CN co 00 d d d CM CvT 00 o LO CN o CO LO CO CN o oo, CO CO CO o 00, CM CO CN o oo, CNT CO CO LO LO o CM CD co' 00 ' * co" ^— CD "ST 00 CO T— o CO T— o co CN a> CD o d d d d d d d i ^~ CD o CM O o CO CO co 00 T— T— LO LO CD CD d d d d d d d 00, CO d CD O CD, C\T 1^ CM 90 CM < CQ N o CM" C\T CO CO CD co' o T— CM CN o co co f^" CM CO o ^3-CO LO CO CO CO d d d o CM CM, CM CO CM CD 5, O CO 00 CO CD O O CM CM LO OO co, CD CD d o CM CO c\f CD LO 00 d 00 o CD T— CO o CM o CM 5, CM LO CM ^, LO o CD CM T— CO oo CM CD CM LO co CD LO oo CO CO CM o co CO ^2" CM LO CM CO LO CD CD, CD, CO, CO CD c6" erf CM o 00 LO CO CM CM CD CD CD LO O LO LO T— CD d d d d d d d 00 CD CD CO CM CO d oo CM d CD o CD 1^ co 00 CD oo CNT co" o T— O o T— 00 o' CD o T— CD CD CM X— CM LO d d d d 0 CO .2 CM 2? CM o co O O LO, O CO O * CM 91 CO CO c\T co If) CD O crT 00 T— 1 C\f 1 CM CM CO CD O CM CM CM LO CM O CD CM O CD O co co o' to LO LO co o oo LO CM CM CN, CN T— CO o co , v "3" CM, CN LO, o' CD co" O CD o o T— CM <N 3 CM, o' LO co o lO, CO o CN * T— , _ , ^ CN, CM, JO, co" c\f LfT L0" CD CO CN N co , c\f T— CO r--CD 00 CD CO d d d , _ oo CN oo o CN CD CD LO CO CD co d d d o' o' LO N" 00 CN CN LO CO 00 CD CO LO LO CN d d d d d 00 CN d CD co^ CD CO o d ^r" oo^ CD p -CN CD CD co CD CO CO CO LO T— CN CO d d d d co^ CD CO, oT CN LO d M" T— LO" O CO CO CN CO CN co d d d P p P P T— p o> Cvf c\f CD CD CO CD O T— co LO LO d d d d d d co, d CD -*—* CO 1- CN i5 o CN O co cT O LO O CO O 3: I 92 Table 5.5. Selected interatomic distances (A) and angles (°) for rodalquilarite. Te(1)-0(1) -0(2) -0(4) -0(3)g -0(3) -0(6) -CI -Clb <Te(1)-0>3 closest <Te(1)-0/CI> Te(2)-0(3) -0(5)d -0(6) -0(1 )a -0(2)b -0(5)b -Clb <Te(2)-0>3 closest <Te(2)-0/CI> Fe-0(2)b -0(2)e -0(4) -0(5)e -0(6)e -0(6) <Fe-0> H(1)-0(1)b -0(3)f -0(4) 1.879(6) 1.912(6) 1.890(8) 3.109(7) 3.139(7) 2.963(6) 3.082(1) 3.486(1) 1.894 2.683 1.937(8) 1.886(6) 1.931(7) 2.531(8) 3.174(8) 2.719(7) 3.115(1) 1.918 2.470 2.037(6) 2.092(6) 1.941(7) 1.946(8) 2.010(6) 2.114(8) 2.023 2.08(3) 1.15(4) 1.75(4) Cl-Te(1)-0(1) CI-Te(1)-0(2) CI-Te(1)-0(3) CI-Te(1)-0(4) CI-Te(1)-0(6) Cl-Te(1)-Clb CI-Te(1)-0(3)g 0(1)-Te(1)-0(2) 0(1)-Te(1)-0(3) 0(1)-Te(1)-0(4) 0(1)-Te(1)-0(6) 0(1)-Te(1)-Clb 0(1)-Te(1)-0(3)g 0(2)-Te(1)-0(3) 0(2)-Te(1)-0(4) 0(2)-Te(1)-0(6) 0(2)-Te(1)-Clb 0(2)-Te(1)-0(3)g 0(3)-Te(1)-0(4) 0(3)-Te(1)-0(6) 0(3)-Te(1)-Clb 0(3)-Te(1)-0(3)g 0(4)-Te(1)-0(6) 0(4)-Te(1)-Clb 0(4)-Te(1)-0(3)g 0(6)-Te(1)-Clb 0(6)-Te(1)-0(3)g Clb-Te(1)-0(3)g <0-Te(1)-0> 0(3)-Te(2)-0(6) 0(3)-Te(2)-Clb 0(3)-Te(2)-0(1)a 87.0(0.3) 84.2(0.2) 73.6(0.2) 175.9(0.2) 119.7(0.2) 102.2(0.0) 62.0(0.2) 95.7(0.3) 160.5(0.3) 90.0(0.3) 143.1(0.3) 131.3(0.2) 74.7(0.3) 80.8(0.2) 98.9(0.3) 65.1(0.2) 132.5(0.2) 144.9(0.3) 109.5(0.2) 52.1(0.2) 57.3(0.1) 97.1(0.1) 64.3(0.2) 77.7(0.2) 114.4(0.2) 71.3(0.1) 138.8(0.2) 68.5(0.1) 99.0 87.9(0.3) 74.2(0.2) 76.6(0.3) 93 H(2)-0(1),c Cl-Te(1),i -Te(1)h,g -Te(2)h,g <CI-Te> 0(1)-H(2)-0(1)c 0(4)-H(1)-0(1)b 0(4)-H(1)-0(3)f 0(3)f-H(1)-0(1)b Te(1)-CI-Te(1)h Te(1)-CI-Te(1)g Te(1)-CI-Te(1)i Te(1)-CI-Te(2)h Te(1)-CI-Te(2)g Te(1)h-CI-Te(1)g Te(1)h-CI-Te(1)i Te(1)h-CI-Te(2(h Te(1)g-CI-Te(2)g Te(1)g-CI-Te(1)i Te(1)g-CI-Te(2)h Te(1)i-CI-Te(2)g Te(1)i-CI-Te(2)h Te(1)h-CI-Te(2)g Te(2)-CI-Te(2)g <Te-CI-Te> x2 1.256(7) x2 3.082(1) x2 3.486(1) x 2 3.115(1) 3.228 180 107.9(1.7) 126.5(2.8) 117.8(2.8) 102.2 77.8 180 87.5 92.5 180 77.8 72.7 107.3 102.2 107.3 72.7 92.5 87.5 180 108 0(3)-Te(2)-0(2)b 0(3)-Te(2)-0(5)b 0(3)-Te(2)-0(5)d 0(6)-Te(2)-Clb 0(6)-Te(2)-0(1a) 0(6)-Te(2)-0(2)b 0(6)-Te(2)-0(5)b 0(6)-Te(2)-0(5)d Clb-Te(2)-0(1)a Clb-Te(2)-0(2)b Clb-Te(2)-0(5)b Clb-Te(2)-0(5)d 0(1)a-Te(2)-0(2)b 0(1)a-Te(2)-0(5)b 0(1)a-Te(2)-0(5)d 0(2)b-Te(2)-0(5)b 0(2)b-Te(2)-0(5)d 0(5)b-Te(2)-0(5)d <0-Te(2)-0> 0(4)-Fe-0(6) 0(4)-Fe-0(2)b 0(4)-Fe-0(2)e 0(4)-Fe-0(5)e 0(4)-Fe-0(6)e 0(6)-Fe-0(2)b 0(6)-Fe-0(2)e 0(6)-Fe-0(5)e 0(6)-Fe-0(6)e 0(2)b-Fe-0(2)e 0(2)b-Fe-0(5)e 0(2)b-Fe-0(6)e 126.9(0.2) 166.4(0.2) 96.0(0.3) 94.2(0.2) 164.0(0.3) 61.7(0.2) 85.6(0.3) 98.5(0.3) 78.2(0.1) 66.7(0.1) 118.1(0.1) 163.7(0.2) 125.6(0.2) 110.4(0.2) 86.9(0.3) 59.3(0.2) 128.7(0.3) 73.3(0.3) 102.0 84.8(0.3) 104.6(0.3) 172.2(0.3) 93.9(0.3) 90.8(0.3) 85.8(0.3) 88.0(0.3) 177.9(0.3) 80.3(0.3) 77.9(0.3) 93.0(0.3) 158.3(0.2) 94 0(2)e-Fe-0(5)e 93.4(0.3) 0(2)e-Fe-0(6)e 84.9(0.2) 0(5)e-Fe-0(6)e 101.3(0.3) <0-Fe-0> 105.8 Equivalent positions: a = x, y + 1, z + 1; b = x, y + 1, z; c = x, y, z;d = x +1, y + 1, z +2; e=x+1,y+1,z+1; f = x, y, z-1; g= x, / +1, z +1; h = x, y-1,z; i = x, y, z +1. 95 Table 5.6. Bond-valence* arrangement' in rodalquilarite. Te(1) Te(2) Fe H(1) H(2) Total 0(1) 1.30 0.22 0.07 0.44x24 2.03 0(2) 1.19 0.04 0.47 2.11 0.41 0(3) 0.04 1.11 0.76 1.96 0.05 0(4) 1.27 0.61 *> 0.07 1.95 0(5) 0.13 0.60 2.01 1.28 0(6) 0.07 1.13 0.38 2.09 0.51 CI 0.15 x2^ 0.13x2^ 0.66 0.05 x 2^ Total 4.12 4.04 2.98 0.90 0.88 *Based on the curves of Brese and O'Keeffe (1991). TAtomic positions refined based on those found in Dusausoy and Protas (1969). 96 5.4 Description of the Structure Based on Earlier Work The structure of rodalquilarite was originally solved and described by Dusausoy and Protas in 1969. Further work using the original atomic positions was performed by Back (1990), mostly concentrating on bond valence and the coordination around tellurium. 5.4.1 Original structure description by Dusausoy and Protas (1969) Rodalquilarite was described as consisting of chains of edge-sharing FeC"6 octahedra extending along the 6-axis with triangular Te(2)03 pyramids linking these chains in the c-direction (Figures 5.1 and 5.2). Planes of FeC*6 octahedra and TeC>3 pyramids are therefore formed parallel to the 6c-plane. Between these planes lie the chlorine and hydrogen atoms that connect the planes in the a-direction (Figure 5.3). The Te(l)03 pyramids do not serve to join chains or planes together as each Te(l)03 pyramid is only attached to a single chain of FeC"6 octahedra. Also described is hydrogen-bonding between 0(4) and 0(3) which are joined to the triangular pyramids of Te(2) and Te(l) respectively. Another hydrogen is located symmetrically between two 0(l)'s, probably on a center of symmetry at (0,0,0). 97 Figure 5.1. Chains of FeC>6 octahedra in rodalquilarite projected onto the bc-plane (after Dusausoy and Protas, 1969). 98 Figure 5.2. Chains of Fe06 octahedra in rodalquilarite projected onto the afo-plane (after Dusausoy and Protas, 1969). Figure 5.3. Projection of the rodalquilarite structure onto the ac-plane showing the diverse bond types in the structure (after Dusausoy and Protas, 1969). 99 5.4.2 Previous work done by Back (1990) Back (1990), in his general study of tellurites, performed some additional work on rodalquilarite using the results from Dusausoy and Protas (1969). The data was input into the NRCVAX structure program to determine bond lengths and angles so that bond-valence calculations could be done. Extra bonds were found for Te(l) [0(3), 0(6), and CI] and for Te(2) [0(1) and 0(5)]. Bond-valence sums using the tables from Brown (1981) were found to be too high for Te(l), Te(2), 0(1), 0(2), 0(4), and 0(6). The bond-valence sums were too high for Te(l) and Te(2) even without CI coordination. Similar problems were found with Te(2), 0(1), 0(2), and 0(6) using the tables of Brown and Altermatt (1985). In calculating these sums, Back (1990) had to estimate the valence contributions of the hydrogens and that fact may explain the problem sums for 0(1) and 0(4). Figure 5.4 shows the polyhedra drawn by Back (1990) assuming that Te(l) is eight-coordinated (with two CI atoms) and Te(2) is seven-coordinated (with one CI atom). He states that these Te4+ polyhedra have similar topologies to seven and eight-coordinated Te4+ in other tellurites. He also noticed that the chlorine atom takes up a normal oxygen position despite the 0.49A difference in size between the ionic radii of the two ions. According to Back (1990), the roles of chlorine and hydrogen-bonding in the structure are unclear. If these roles were defined, the difficulties with the bond-valence sums and the correct coordinations around Te(l) and Te(2) could be resolved. In his conclusions, Back (1990) recommended a redetermination of the structure using a difractometer. 100 Te(l) Polyhedron Atom Labels 1 2 3 4 5 6 7 8 9 Te(l) 0(1) 0(2) 0(3) 0(3) ' 0(4) 0(6) CI CI' 1.91 A 1.86 A 3.12 A 3.08 A 1.91 A 2.93 A 3.46 A 3.06 A Te(2) Polyhedron 3 Atom Labels 1 2 3 4 6 7 8 9 Te(2) 0(1) 0(2) 0(3) 0(5) 0(5) • 0(6) CI 2.54 A 3.10 A 1.88 A 2.61 A 1.91 A 1.87 A 3.07 A (Oc) (Oa) (og) (Of) (Ob) (Od) (Oh position) (Oe position) (Od) (Oe) (Oa) (Of) (Ob) (Oc) (Og position) Figure 5.4. Eight-coordinated Te(1) and seven-coordinated Te(2) in rodalquilarite (after Back, 1990). The proposed sites of the electron lone pair are shown as the shaded areas. 101 5.5 Description of the Refined Structure In the redetermination of rodalquilarite, modifications are made to the coordination of the two Te4+ atoms, the hydrogen positions are confirmed and their bonds are detailed, and the role of chlorine is clarified. 5.5.1 Coordination of tellurium The results of the redetermination were used to create a new bond-valence table (Table 5.6) using the values from Brese and O'Keeffe (1991). The values from Brown (1981) were comparable, however, it did not have constants for Te-Cl bonds which presented a problem. With the evolution of the interpretation of the coordination around Te4+, the description of the Te4+ in rodalquilarite should be brought up to date. Te(l) may be described as eight-coordinated with two CI bonds; the eighth bond is to CI at 3.486 A away which is slightly more distant than an Fe atom that is 3.426 A away. Te(2) is seven-coordinated with one chlorine bond. Both of these coordinations to Te agree with the results from Back (1990). The interatomic bond lengths and angles found in Table 5.5. Both telluriums have the typical three close bonds of ~1.9 A on one side of the coordination polyhedra while the remaining more distant bonds can be found on the other side of the polyhedra (Figures 5.5 and 5.6). As Back (1990) described, the lone electron pairs probably reside on the side opposite to the three close bonds. 102 5.5.2 Coordination of iron The coordination around iron is unchanged with respect to its initial description in 1969. It remains coordinated with six oxygens to form octahedra (Figure 5.7). There is no evidence that iron is eight-coordinated (as suggested by Back in 1990). The bond lengths do not differ by much, ranging from 1.942 to 2.114 A (average 2.024 A). The polyhedral volume is 10.7573 A3, the octahedral angle variance is 62.8457, and the mean octahedral quadratic elongation is 1.0190. 5.5.2 Coordination of chlorine Chlorine is six-coordinated with bonds of 3.082 and 3.486 A to Te(l) and 3.115 A to Te(2) (all x 2) (Figure 5.8). Bond-valence analysis shows the absence of some valence but this is not a new problem as there were also difficulties with bond valence with regards to chlorine in the structure of choloalite. 5.5.3 Hydrogen-bonding Using Pauling's rules, Dusausoy and Protas (1969) rationalized which oxygen atoms the hydrogens would be bonded to. Bond-valence results support their choices of oxygen atoms by exposing which oxygen atoms were deficient in valence sums. It is also known that bond valences of oxygen, as the hydrogen donor, typically have sums of ~1.2 v.u. while H-acceptors are not as evident having sums of ~1.8 v.u. (Brown, 1981). Looking at the bond-valence table, it can then be proposed that 0(3) is a H-donor and that 0(4) and 0(1) could be H-acceptors. The hydrogen, H(2), appears to be on special position a (0,0,0) exactly the same distance away, 1.256 103 A, from two 0(1)'s; however, hydrogen could be disordered about this site. The hydrogen, H(l), in the general position is closely bonded to 0(3), (1.053 A) and distantly bonded to O(l), (1.949 A) and 0(4), (1.954 A). This would make 0(3) a hydrogen donor and 0(1) and 0(4) hydrogen acceptors with respect to H(l). The hydrogen-bonding scheme is shown in Figure 5.9. 5.5.4 Structure connectivy With the added coordination around the telluriums atoms the structure connectivity is harder to describe although the overall changes could be considered minor. Edge-sharing iron octahedra (each sharing two edges) continue to form chains along the 6-axis (Figure 5.10). The difficulty in description comes with the added coordinations around the tellurium atoms. Looking at the Te-0 bonds less than 3 A long (this results in four-coordinated Te(l) and five-coordinated Te(2) as compared to three-coordinated Te's described by Dusausoy and Protas, 1969), the chains of Fe-octahedra are connected in the odirection by these Te-0 bonds to form relatively strongly held planes of iron and tellurium polyhedra parallel to the 6oplane (Figure 5.11 and 5.12). The more distant Te-0 and Te-Cl bonds (> 3 A) help to connect the structure in the a-direction (Figure 5.13). Thus the original structure description of planes of iron octahedra and tellurium polyhedra parallel to be held together by weak Te-Cl and H-O(l) bonds still basically holds true. The refinement served to locate additional weak Te-0 bonds that help to hold these 6c-planes together in the a-direction. Te(l) shares faces with one Te(l) and one Te(2) atom, edges with two Te(2) and two Fe atoms, and is corner-sharing with four Te(l), two Te(2), and one Fe atom (Figure 5.14). Te(2) shares edges with three Te(l), one Te(2), and two Fe atoms and is also corner-sharing with two Te(l), one Te(2), and two Fe atoms (Figure 5.15). 104 CO o CD O CD C JZ — -i—> show q pun' t four ds o no c CO CO o D X c c o c_ o -— J=> o X te. S lyhe^ nger te. S o o — Q_ c_ O c CD D o JZ cr 4^ O D r~ x L_ o o X JZ (_ L_ co o C o CO o X -—. c CD o JZ _Q £ Z> c_ o o Z5 — CD o CD X zc CO <4-O (Dm C O +-> o c CD c o c o CO 4-> LO O CD 0 U_ 4-> cn co CD CO O o c_ Q_ X C o >~ o CO Z5 C CD CO z> a co CD 105 CN O CD O CO ~o c o _Q CD _c 4-> CD C O _C CO CD _o '5 _cr a TJ O L. CO O O CN £ ^ CD L_ I! CD O c ^ .2 c 4-> — D C J-J .*= D "O _C L. 4-> O O CO O D CD - I LO CO CD CD h£ CD iT CO 106 107 108 CD «4-C_ o CD _ cnco o c P CD c_ CD c_ o D_ >— ^ CO ar CD CD 5 Z5 CO c_ CO JZ o CO o 1- L_ CD CD 0_ t_ CO er co "g o D JZ CD c o_ X D CO a > CD JZ c $ o ~a -a CD CD > CD c_ _D D _Q" O O C_ o co ZJ D CO D Q >-_Q ' -O I C D O o JZ co £ o CD CO "D C o CD JZ CO CD c _CD D L. O JZ co CD c_ D CO E o O o CO o CO c -a o JZ CO CD o CO £ o CD ~D O JZ co co D co £ o D c D CO CD c_ CD o C O _Q i C CD CO o >~ ZLZ CO LO CD JZ CO a CO D c o JZ to CD t_ o E o c o C_ c CD Q_ o CD L — " - 1 to to "O c o _Q ® to 5 Li_ JD O CO CO O c o JZ to CD > D JZ CO E o 4-> D CO D CO E o D 5X CD CO H- CD OT ® 4-> JZ O D_ ~D CO to X D i _Q CD o 4-> _CD ~6 L. o Q_ O c_ CD _c o o o c o CJ> c c_ D _c to I CD CD "O CD O (0 c o _c o o LO 0 L. 3 cp LJ_ ti CD CD L. 4-> D © L. C ~~o o JZ ^ o to Q--D „ C <D o CO c_ _o to o to £ o o o c o o CD t_ c CD Q_ _ o x> <_> _C CD CD I— cn^ S 2 c 0 JZ o 1 I— _c c to t_ _CD "o E to to o I o CD L. sis q-b CD X> £ o C <D — -C 4-> to X c j2 CD CD CD JZ 4-> tO <D ! b L D L. CO -o cn a, 4-> ^ o u CD CO ° > v © c o CD c o "O "O CD CO CD L_ C C o o_ E -i- o CD ° c o t_ 4-> to 4-> o c to x> to CD c CD JZ _>^- _ O JZ — Q_ 4-» x> *i C CO _ o JZ to to o CD x> c ' b c $ o O CD S b O 4-> Ll_ X> 0 to XI CD > JZ CO D O CD ^ O I"8 § tO CD ^ P ' CD O CO $ o or to *-g E <u £ O L ° -u h JD ° <_ o to CD CD c o LO CD t_ D CD •> to to -<D £ " L. <~ CD CD JZ • JZ Q_ if) 4-> tO CD „ C_ CD C CD O CD JZ -M Q_ Q_ O O (0 Z o t_ X CD CD C_ JZ o o o c_ Q_X CD CD JZ 1— D 4-> CD O JZ o 1— CD LL CD CD C JZ _o 1— i bc-10 £ CD o JZ C_ U) O cn c D a oo 4^ CO ® o -£ -° c a % * * i oj X ° c — o co CD CN -C — CO CD o I— -o • JZ CN •*-> CD £ a to CD JZ 4J D to CD X a CD JZ to CD i_ CD JZ Q_ 10 c CD Q_ O to a c o JZ to CD L. a to £ o D ^_ O LO CD CD CO XI <zz c a to o LO 3 O CDJZ ,T CO X 3 o D C 4-» £ C o 3> JZ c_ to o 112 — CO CD £ CO I— CO £ . <D co CO c_ O c X o D i 4-> 4-> u 4-> o <J— CD CD _CD c_ X 4-3 CO 1 o wn X o 1 CD o JD JZ x CD 4-> x JZ c CD 4-> iew D iew x> C_ iew c X > a CD CO JZ CO E ^LO o CD tto pol igure 4-> o Fe igure £_ JD Fe igure o ilqu o_ Te c oda to <4-o as c_ CO CD <4- JZ CD E O CO Z5 c D D CO ity O c_ o_ CD tiv CO o th o X CD CD o c CO c 1 o c C o CO o CD o E o JZ ids o J-J ids 4-> o 00 JZ c o X LO JD UD CD c ds igur 0 ds igur ho ~o /— on LL CO J_ JD CD c CO CD c X o JZ CO CD JZ c_ o CJ >~ JD CO CD £ 4-> _Y C_ C _o — '5 CD CT 4^ ^1 Pi 9 co • -rj CO p C ® 3 0 O CD _S O £ <2 5 CO o CO C =LZ CD .2 .-g> •g <r> CD 4-. -Q £ CD CD CD C_ C U Z) .— cp_* X <4_ — D — <4_ •— CD 0 CO o CD O O O £ C £ g co _i U) x c CD O £ -Q x "5 co LO CO ?> co b E CO O CD — 4-> JZ Ll_ D 4-> CD c O _C CO CD JZ CD _o D D O C_ C CN CD h— LO O 4-5 CD co ur c CD o <4-4-> D c O 4-> CO c D CD CD U O "0* O DS <4- CD o JZ x-> CD CO CD O CO c ~o _l c o XI LO "O LO UD CD CO e D £ CD o 4-> u_ a 5.6 Conclusions About the Refinement of Rodalquilarite The original structure description of planes of iron and tellurium octahedra parallel to be held together by weak Te-Cl and H-O(l) bonds still basically holds true. The refinement served to locate more weak Te-0 bonds that help to hold these planes together in the a-direction. Te(l) and Te(2) are described as eight- and seven-coordinated respectively and both have three short Te-0 bonds on one side of the coordination polyhedra. Chlorine is bonded to six tellurium atoms and help to bond the Fe/Te polyhedral planes in the a-direction. A hydrogen-bonding scheme is proposed; the hydrogen that appears to be on special position a (0,0,0) may be disordered about the site but there is no way of knowing for sure as there is not enough material for neutron diffraction. 116 6.1 Introduction 6.0 GRAEMITE The type specimen of graemite (CuTe03-H20), originally described by Williams (1975), was found in 1959 by Richard Graeme in an ore car at the Cole shaft at Bisbee, Arizona. The rock sample, which bears about 500 mg of graemite, measures 2.5 x 2.5 x 2 inches and "is a loose spongy aggregate of cuprite crystals embedded in a dense matted matrix of tiny malachite needles." Embedded within the malachite are several large (8 mm) teinite prisms with corroded and pitted surfaces. Cuprite and graemite are found on these surfaces and in two cases graemite totally replaces two large teinite crystal (one was 20 mm long and the other had an 8 mm cross section). The graemite replaces the teinite as "divergent platy, bladed crystals arranged in a random fashion. In the stoutest teinite relic they show a radial divergence but on the surface of both pseudomorphs they tend to lie with their long axes [100] near parallel to the prism axis of the teinite." Bisbee is known for its copper oxide ores and it is uncertain where the tellurium, required to form teinite and graemite, is found. Rickardite, Cu7Tes, could be the source as traces of it was detected in the ores. A second locality for graemite was found at a small prospect in the Dome Rock Mountains, Yuma County, Arizona. Samples consist of massive chalcocite in a quartz-tourmaline gangue with small corroded blebs of bornite and traces of weissite embedded within the chalcocite. Brochantite and malachite film the fractures that are lined with crystalline goethite and gold. Small cavities housing goethite, gypsum, teineite, and graemite are found by breaking the chalcocite where it is fresh, not at the brocanthite-filled fractures. At both the Bisbee and Yuma County localities, teinite is corroded and graemite appears to be replacing it, 117 probably through a partial dehydration of teinite. The species description by Williams (1975) was based on the Bisbee material only. Chemically, Williams (1975) found graemite to be Cu9.77(Te03)9.62T 1.42H20 or CuTe03-H20. Cu was analyzed by atomic absorption, Te colorimetrically, and water was determined by the Penfield method. The initial result of 9.5% H20 was considered incorrectly high because a small particle was ejected from the tube during decrepitation. Emission spectrographic analysis showed a trace amount of silver. The test specific for tellurite was positive and the test for tellurate was negative. Tests for halogens and sulfate were also negative. Williams (1975) describes the X-ray powder data of graemite as that of a typically layered mineral. Weissenberg level photographs taken with CuKor radiation showed strong sets of Okl reflections and very weak hOl reflections. Pcmm, the proposed space group, is far from being a certainty because of the problem of recording many hOl reflections. A good cleavage was found on {010} and a pronounced parting on {100}. There was no evidence either morphologically or optically that graemite is not orthorhombic 2mm. Cell edges, refined from powder data, are a = 6.805 A ± 0.006, b = 25.613 ± 0.015, c = 5.780 ± 0.006. The calculated density is 4.24 g/cm , measured specific gravity is 4.13, and Z =10. 6.2 Experimental The crystal used in this study was provided by Andy Roberts, of the Geological Survey of Canada, who stated that this was the "best graemite crystal in the world". The crystal was mounted on a Siemens P3 automated four-circle diffractometer equipped with a molybdenum-target X-ray tube (operating at 55 kV, 35mA) and a precisely oriented graphite crystal 118 monochromator mounted with equatorial geometry. Two sets of data were collected but, due to power fluctuations, parts of both sets of data were lost. The second data set was interrupted six times and all confidence was lost that this was a consistent set of data. Problems with structure solution also lead to suspicions that the data sets were at fault. Initial precession photos showed that the crystal did not diffract well at all. A third data set was collected using synchrotron light in hopes that the poor diffracting qualities of the crystal could be overcome as well as achieving one consistent set of data. In the first graemite data collection at UBC, fourteen reflections with 20 6.34 to 17.41° were centered using an automated search routine, and the correct unit cell was selected from an array of real space vectors corresponding to potential unit cell axes. One octant of reflections (1558 measurements, exclusive of standards) was collected from 3 to 60° 20. Details of the synchrotron collection are given in Chapter 2. 6.3 Structure Solution and Refinement Initial attempts at solving the structure of graemite with the suggested space group Pcmm (William 1975) led to poor results and it was decided that precession work be carried out on the crystal to see which space groups are likely. These photographs also provided information on the crystallinity of the crystal, apparently there is some disorder present. 6.3.1 Determination of possible space groups Precession photographs of MO, Okl, Ikl, and hkl were taken (Figures 6.1 to 6.4), however, the planned photographs of hOl and of the second levels could not be obtained because 119 the X-ray generator was destroyed by a power surge. This difficulty was somewhat overcome by using the program XPREP to look at the reflections in reciprocal space. It was determined from the three data sets that the reflection conditions for hOl was l = 2n and this would be the limiting factor in determining possible space groups for graemite. These space groups are: non-centrosymmetric Pmc2\ (#26 in the International Tables of X-ray Crystallography), P2cm (#28, Pmdl is the standard setting), and centrosymmetric Pmcm (#51, Pmma is the standard setting). Of course if the condition hOl I = 2n is not real, then the space group choices would increase and involve the ones with less symmetry such as P222 (#16), P222] (#17), P2i2]2 (#18), P2i2i2i (#19), Pmm2 (#25), and Pmmm (#47). The MO precession photograph showed that the reflections of the odd h levels were smeared along k. This indicates a disordering of atoms (Joel Grice, personal communication 1997) along the 6-axis. There was no smearing on the Okl photograph but everything on the Ikl photograph was smeared along k. It should be pointed out that the smearing was only detected on film and that the XPREP program showed the smears in reciprocal space as spots. This was very misleading and kept in mind when XPREP was used as the sole method for looking at systematic absences. It was also noticed that the spots on the MO photograph were present when h+k = 2n+l. This is not a reflection condition useful for the determination of space groups; however, if the a-axis is reduced by half, this now becomes h + k - 2n which is a valid reflection condition and leads to possible space groups for a reduced unit cell. Attempts at solving the structure with the space group Pcmm as suggested by Williams (1975) never gave satisfactory results. It should also be noted that no acceptable space groups could be determined on any of the data sets by the computer program using its default parameters; the intensity/sigma gap had to be reduced to <0.2 to generate possible space groups. 120 Several other space groups were tried without success and it was decided that the problem should be approached from a new direction. The prominence of the reflection condition h + k = 2n for hkO when a is reduced by half gave some hope that this structure could be solved by using a space group for a smaller cell. It was also encouraging because a appears to be the axis that is most affected by the disorder and reducing it's length could possibly make it easier to model a sub-structure which could then be extrapolated to the full structure in the proper unit cell. In reducing a by half, additional reflection conditions for the reduced cell were met with hOl I = 2n, hOO /z = 2n (only 2 spots were found), OkO k = 2n, and 00/ / = 2n. These lead to possible space groups of non-centrosymmetric P2\cn (#33, Pna2\ is the standard setting) and centrosymmetric Pmcn (#62, Prima is the standard setting). 121 122 Figure 6.2. Precession photograph of graemite showing Okl. All reflections are sharp. 123 Figure 6.3. Precession photograph of graemite showing fkj. All reflections smeared along the 6-axis. 124 Figure 6.4. Precession photograph of graemite showing hk\. Reflections are smeared on odd ft-levels along the b-axis. 125 6.3.2 Structure solution Using the reduced cell, structure solution was attempted with both space groups and both gave similar results. To convert the synchrotron data to the standard space group settings, the orientation matrix (0 0 1, 0 -1 0, 0.5 0 0) was used for Pna2\ and the orientation matrix (0 0 1, -0.5 0 0, 0 -1 0) was used for Pnma. A final R index of ~9.3 % was achieved with Pnma and 7.7 % for Pna2\. Refinement of anisotropic temperature factors was attempted and actually reduced the R value for both space groups but many of the cations and oxygen atoms became "non-positive definite" indicating that the anisotropic temperature factors could not be satisfactorily refined. The two space group models both have a Te-Te distance of approximately 1 A, which is probably where the disorder is located. The | E2-\ | statistic of 0.812 shows that the structure is most likely non-centrosymmetric and upon closer scrutiny of the actual bond lengths, the non-centrosymmetric structure appears to be a better model. Other factors such as the better R value for Pna2i and the chemistry of the models also point to the structure as being non-centrosymmetric . Using the proper unit cell, the structure of graemite was refined in non-centrosymmetric Pmc2\ to an R value of 6.9 %. Refinement of anisotropic temperature factors lead to a lower R value but once again the atoms showed that this refinement could not be performed satisfactorily. Like the reduced cell models, there is a Te-Te distance of ~1 A which is probably due to disorder. The results here are not final as some of the occupancies were allowed to refine freely, many of the temperature factors had to be fixed at reasonable values because they were unstable, and there are still questions regarding the chemistry of the crystal; it is however the best model to date using the full unit cell and it is expected that many questions will be answered with chemical analyses from the electron microprobe. 126 Knowing that the synchrotron data collection is probably the best data set that could be achieved with this crystal, the ^?jnt is 2.7% which is very good, and the fact that precession photographs show smearing of spots on selected levels, it is likely that the atomic disorder is the reason the R values are so high. The model using the full unit cell still has many problems associated with it and at this time the sub-structure appears to be the most definitive model, albeit of only part of the structure, of graemite that is possible with this crystal. Structure factors are listed in Appendix F. 6.4 Description of the Proposed Structure of Graemite Two structural models are proposed, one in the reduced cell (a 5.78, b 25.63, c 3.41 A, a = P = y = 90°) with space group Pna2\ and one with the proper unit cell (a 6.82, b 25.62, and c 5.78, a = P = y = 90°) with the space group Pmc2\. Until further work is completed with regards to upper level precession photographs and electron microprobe analysis, questions about the correct space group and chemistry of graemite still remain. 6.4.1 Description of the proposed substructure in Pna2j The atomic positions used to refine the space group Pna2\ to an R value of 7.7% is listed in Table 6.1. Te(2) is about 1 A away from Te(3) and 0(7) is very close to 0(1) at 1.4 A and to 0(3) at 1.9 A away. The disorder appears to be related to these atoms. Figure 6.5 shows how these atoms may be presented as smeared reflections along the 6-axis on the ftc-plane (remembering that a 6.82 A has been transformed so that it is c 3.41 A). The clustering of these atoms is not as prominent in the aft-plane (Figure 6.6) which is consistent with the fact that no 127 reflections are smeared on the precession photograph of this plane. Figure 6.7 shows how Te(2) and Te(3) may be bonded to six common oxygen atoms and it can be imagined that only one of the sites may be occupied at any one time. No figure of the aoplane is depicted but, because of the 25.63 A long 6-axis, one can see why Williams (1975) had trouble recording hOl reflections. Figures 6.8 and 6.9 show the connectivity of the proposed structure looking down the c- and fl axes respectively. There are still many problems with the substructure even if the disorder of Te(2) and Te(3) as well as that of 0(1), 0(3), and 0(7) is accepted. The Te(2) and Te(3) sites have been fixed at half occupancy but the Te(l) and Cu(2) sites also appear to be half-occupied. The 0(1), 0(3), and 0(7) sites seem to be half-occupied, 0(7) being present when 0(1) is not, but it is unclear how 0(3) is related although logically it should be present when 0(7) is not. The 0(5) site is partially occupied and it has been tentatively assigned as a hydroxyl group. The chemistry of this substructure does not match the accepted formula as no water molecule has been located and both copper and tellurium each sum up to six in the half unit cell when there should be only five of each. With all these problems, one can see that there is still more work to be done in determining the roles of all the atoms. It was hoped that solving the substructure would lead to the solution of the full structure but it was too difficult a task to project the full structure from the substructure. 6.4.2 The proposed structure in Pmc2j The atomic positions used to obtain an R value of 6.9% in Pmc2\ are listed in Table 6.2. There are many unanswered questions with regards to the chemistry and occupancy of sites. With the large 6-axis dimension and Z = 10, there are many atomic positions to work out. 128 Without knowing if there are elements substituting for copper and/or tellurium and with the effect of disorder causing some sites to be partially occupied, no definite conclusion of the model can yet be made. No figures will be shown using the space group Pmc2\ because, to this date, much of it is speculation based on chemical assumptions and experimentation with various elements in the cation sites. 129 Table 6.1. Atomic positions for the proposed graemite substructure solved in Pna1\. Atom X y z K fUeq Cu(1) 0.1505(9) 0.6651(2) 0.02260* 1 87(15) Cu(2) 0.522(2) 0.2562(4) -0.028(7) *0.5 31(27) Te(1) 0.888(1) 0.4489(2) -0.025(6) *0.5 154(17) Te(2) 0.377(1) 0.3617(2) -0.027(5) *0.5 72(15) Te(3) 1.253(1) 0.3904(2) 0.026(5) *0.5 89(14) 0(1) 0.200(8) 0.301(2) 0.03(3) *0.5 39(103) 0(2) 0.782(6) 0.261(1) 0.399(8) 1 88(96) 0(3) 0.686(8) 0.334(2) 0.05(2) 0.59(6) *100 0(4) 0.985(6) 0.404(1) -0.41(1) 1 148(101) 0(5) -0.16(1) 0.511(2) -0.45(3) 0.50(7) *100 0(6) 0.436(6) 0.356(1) 0.62(1) 1 185(101) 0(7) 0.500(9) 0.169(2) -0.04(3) *0.5 39(103) Ueq are listed x104. *Fixed value. 130 Table 6.2. Atomic positions for the proposed graemite structure solved in Pmc21. Atom x y z K *Uea Te(1) 0 0.1989(4) 0 0.5 62(19) Te(2) 0 0.1130(4) -0.479(3) 0.5 78(24) Te(3) 0.25000 0.0836(8) 0.041(4) *0.5 132(44) Te(4) 0.227(2) 0.3898(6) 0.277(3) *0.5 82(35) Te(5) 0.275(1) 0.3598(6) 0.143(3) *0.5 MOO *Ru 1/2 0.8594(6) 0.139(3) 0.5 *400 Cu(2) 0 0.5856(7) 0.237(4) 0.5 15(42) Cu(3) 1/2 0.587(1) 0.241(5) 0.5 228(60) *Rb 1/2 -0.0073(4) 0.870(3) 0.5 MOO Cu(5) 0.218(2) 0.301(1) -0.231(4) 0.52(2) MOO 0(1) 0.22(1) 0.419(4) 0.60(1) 0.66(3) *800 0(2) 0.17328 0.152(2) 0.90(1) 1 *800 0(3) 0.326(8) 0.107(2) 0.458(9) 1 *800 0(4) 72 0.086(3) -0.11(1) 0.5 *1000 0(5) 1/2 0.492(3) -0.34(1) 0.5 *1000 0(6) 0.232(7) 0.445(2) 0.087(8) 1 *800 0(7) 0 0.239(3) -0.27(1) 0.5 *1000 0(8) 0.331(7) 0.012(2) 0.11(1) 1 *800 0(9) 0 0.351(3) -0.13(2) 0.5 *800 0(10) 0 0.082(4) 0.24(1) 0.5 *800 0(11) 1/2 0.396(4) 0.32(1) 0.5 *800 0(12) 1/2 0.347(3) -0.09(1) 0.5 *1000 0(13) 0 0.479(3) -0.34(1) 0.45(3) *800 H20 0.288(5) 0.499(2) 0.423(7) 1 *800 H20a 0 0.015(2) 0.37(1) 0.5 *800 H20b 1/2 0.199(2) 1.01(1) 0.5 *1000 Ueq are listed x10 . *Fixed value. *Ru and Rb were used to emulate scattering powers between that of copper and tellurium in an attempt to see if silver, tellurium, or other elements were substituting in this site. 131 GD O @ O co o 8 o GO o 9 o GO CO O 8 O co Qp o o o cb dp o o CO CO O 8 O CO E ••-> CD O O „ b,Sj o 4-> CO C _Q C-D CD co fi CD u" CO i_ o o /-\ —7 Q_ CD CD X> CD CD , CO TJ CO C CD O C ^ ,A CD C ^ _C ~ CD CL D C_ tO C- CD "D ^ Q_ CD CO CO O O ~® -t-> 4_> CD O "O -C LU O O -M CO b z ° to CO > o| TJ c o CD CD D JZ ^ JZ CO E ° o — CD CO CD Q CD JZ c CD CD 4-> CD J3 to L. CD "U c_ O to -a CD to £ o 4-> CD i_ CD TJ c_ O to CD L. CD 4^ ^ to CD to to J? CD CO c „ O CD ^b ^ CO TJ E •-co - a co , ° tf CD 'S .^2 ~Z3 ° O ^ "O D O 10 O O — ^x <D C JZ a ro to O CD -o 8-® i o JD CD JZ LO CD to E o x-> D CD _ CD c U_ Q_ a to * ? o_ co co CD C- CO CD O JZ CL CO to E „ o CO 4J a o c o JZ CO c <D C 9- a O CD CO ^ b ^ x o c to JZ o E co o D 0 C_ o to o CD CO CD E CO >- o —' X 4J (D o a I— 132 o o 0 o o O O 0 O Q Q O o o o o O 9 © o o o Q o o o © o Q o o o © o © o o o o o o © o o o © 6 o o 9 o 0 Q o o © o o cu "D £_ o c CO • Q 4-> o JZ C\T CO D D c Q_ 0 £ C o CO cu 0 £ JZ CD D CO C_ • — CD (0 c O o CD -L> D ur o -M O D o t_ CO CO c _Q "C Z> D CO JZ CO "O CD 0 CO JZ O 1— o_ O C_ D_ c o CD 4-> _C D c <4— o 0 L_ CD O c CO D o_jz i 4-> _Q O c CD JZ c 1— 0 t_ D CD Q_ o_ CD Q CD i_ o D c CO U_ CO 0 JZ 0 CO 0 L_ 0 JZ Q_ CO c 0 o_ o CO o c CO o 0 JZ c_ co 0 JZ 0 o_ c_ CO o ~U CO 0 E TJ toi O JZ o CO as o c o o w JZ CO 0 c_ a CO 0 o CO E o 0 D CO r-X o 0 CO _ X < ° 0 LO "£ CD <+_ 0 ° L. 4J Z3 CO CD Q) <J_ C_ 133 o oo o to ~o c o _o ~o JZ cu c_ D 4-> O Z5 t_ to _Q Z> to CU r CO „, 15 6 to — o cu CD w JZ — r CU 00 £r • CD ® JZ I 4-> XI '<•> § o 4-> CN X i- c o JO CD X c_ O CO co to E o D C CU CO X • o cu b ™ LL Q_ 134 "o c gx» > D CD _C > to tO CD O JZ CN O c Q_ CO c i-CD C b D 4-> .—. <J CN —1 -Z> to z> to CD CD CD CD 4-> ±? CD £ -Q CD , CD to CD CD LO CO "O O <•*- o O _Q L. D CD 4-> if o co > = w CD c o CO X O CO -! CD ^ CD i- C Z> > ^ O LT) O O oo CD 135 CD — ^ Li. "O 136 6.5 Discussion The magnitude of the task of solving the graemite structure becomes clear when one thinks of it as attempting to model disorder; add to that a relatively large unit cell, not knowing the correct space group, and unconfirmed chemistry of the crystal, and the problem can be seen to be immensely difficult. It is already incredible that the disorder can be modeled to the point that it is logical and consistent with the precession photographs. As stated earlier, every space group that gave a somewhat acceptable model had two cations (usually Te-Te) 1 A apart. It is hoped that with future work in obtaining upper level precession photographs and chemical analysis with the electron microprobe, some of the questions will be cleared up enabling some conclusions to be drawn about the structure. As this is the "best graemite crystal in the world" there is a reluctance to possibly ruin it in the procedure of electron microprobe analysis. It would certainly be unwise to do so before all precession photographs are satisfactorily obtained and that cannot be done until the new X-ray generator arrives and is up and running (September 1998). Thus the crystal structure of graemite remains unsolved although inroads have been made in solving this mystery. 6.6 Conclusions The crystal structure of graemite remains unsolved although a substructure using a 5.78, b 25.63, c 3.41 A, a = P = y = 90°, and the space group Pna2\ has been proposed. The full structure is probably non-centrosymmetric and probably crystallizes in the orthorhombic space group Pmc2\ with a 6.82, b 25.62, c 5.78, a = p = y = 90°. This is different from the originally proposed centrosymmetric space group of Pmma. There is disorder in the mineral that shows up 137 in precession photographs of the MO, \kl, and Ml planes but not in the Okl plane. The smearing of reflections is always along the 6-axis. This disorder appears to be caused by two cations approximately 1 A apart from one another and possibly by some disordered oxygen as well. Upper level precession work and a complete chemical analysis by the electron microprobe remain to be completed. 138 7.0 CONCLUSIONS The intent of this thesis was to study, by single crystal X-ray crystallography, the structures of a number of tellurium oxysalt minerals. It was fortunate that there was an opportunity to work intimately with both tellurate and tellurite minerals because it afforded the chance to learn about the coordination of both Te6+ and Te4+ by way of contrast and comparison. The main reason behind the structural difference between these two valence states is the presence of a lone electron pair that distorts the coordination polyhedra of Te4+ and the absence of it in Te6+. The coordination of Te6+ is straightforward as it is six-coordinated to form a regular octahedron. As discussed in the introduction, the interpretation of the coordination around Te4+ has progressed from what was originally thought to be three- or four-coordination to recent descriptions of eight-coordinated Te4+. The earlier descriptions, using the three and four closest coordinations, are still valid but the added coordination brings a better understanding of how the structures are connected by the addition of weaker bonds that previously have been neglected. 7.1 Dugganite, Choloalite, Rodalquilarite, and Graemite The formula of dugganite is revised to Pb3Zn3TeAs20i4 from Pb3(Zn,Cu2+)3(Te6+06)(As04)(OH)3. Dugganite was solved to an R value of 2.7% in the hexagonal (trigonal) space group P321 which differs from the space group suggested by Williams (1978) of P6/mmm. The parameters are a 8.460(2), c 5.206(2) A, V 322.6(2) A3, Z 1. The structure of dugganite consists of heteropolyhedral sheets of lead and tellurium polyhedra parallel to (001) joined together in the c-direction by AsC^ and Zn04 tetrahedra. The revised 139 formula of dugganite is similar to that of cheremnykhite, Pb3Zn3TeV20i4, and kuksite, Pb3Zn3TeP20i4, and it is proposed that these minerals are isostructural. The formula of choloalite has been revised as well to CU3PD3 Te£+ Ois'CCl^O) from the original formula of CuPb(Te4+03)2-H20 (Williams, 1981) and the recently revised formula of CuPb(TeC>3)2 (Powell et al. 1994). Electron microprobe and infrared analyses and structure refinement show that choloalite contains water. Choloalite crystallizes in the cubic space group P4j32 with a 12.520(4) A, V 1963(2) A3 and Z4. The structure consists of two three-dimensional nets, one net contains only Pb(l) polyhedra and the other consists of Pb(2) and Cu polyhedra; these nets are joined together by distorted Te06 octahedra. Choloalite was solved to a final R value of 5.2%. The original structure description of rodalquilarite by Dusausoy and Protas (1969) still basically holds true. It consists of planes of iron and tellurium octahedra parallel to be held together by weak Te-Cl and H-O(l) bonds. The refinement served to locate more weak Te-0 bonds that help to hold these planes together in the a-direction. Rodalquilarite crystallizes in the triclinic space group PI, a 9.021(1) b 5.1170(7), c 6.6539(8) A, a 103.23(1)°, (3 106.66(1)°, y 78.07(1)°, V 283.15(6) A3, Z 1. Eight-coordinated Te(l) and seven-coordinated Te(2) both have three short Te-0 bonds on one side of the coordination polyhedra. Chlorine is bonded to six tellurium atoms and help to bond the Fe/Te polyhedral planes together in the a-direction. Finally, a hydrogen-bonding scheme has been proposed. The redetermination of rodalquilarite gave a final R index of 4.1% which is improved from the original value of R 9.2% obtained by Protas and Dusausoy (1969). Although excellent data was collected using synchrotron light, graemite has not been structurally refined to satisfaction. The problem appears to be disordering along the b-axis which shows up in the M0, Ikl, and hkl precession photographs. In all attempts at structure 140 solution, two atoms (usually tellurium) were found approximately one angstrom away from each other. The cell obtained from the synchrotron data is a 6.816, b 25.627, c 5.784, and with all angles 90°. The structure has been refined in Pna2\ using a reduced cell (Vi a) to an R index of 7.7%. This is probably a substructure of the full structure. Using the full cell, the structure has been refined in Pmc2\ to an R value of 6.9% but the atoms are not as "well-behaved" as that for the substructure. Further study of graemite is required to rationalize the problem with disorder before any final structure model can be accepted. 7.2 A Comment on Experimental Procedures As mentioned in Chapter one, crystals of tellurium oxysalt minerals suitable for single crystal X-ray diffractometry are difficult to obtain. This fact along with original descriptions that are often incorrect means that future structure solution and refinement of these minerals will probably continue to be quite difficult. Simply put, the easy crystals have been solved and the ones that remain unsolved are usually associated with some sort of difficulty such as: poor crystal quality, misleading original description of the chemistry and/or space group, and other unforeseen problems. Structure solution and refinement becomes even more difficult when these problems are compounded. In this thesis, crystal quality was a problem for dugganite and graemite, the published chemistry was wrong for dugganite and choloalite, and published space groups that were incorrect were misleading for dugganite, choloalite, and graemite. Unforeseen problems were also encountered with graemite. As discussed earlier, these tellurium-bearing minerals absorb more X-rays than light element-bearing crystals and thus lead to long data collection times. The crystals could not be 141 shaped into spheres because of their brittleness so, to combat absorption problems, more data was collected than needed. The absorption scan became very important with regards to the success of the final refinement and so extra reflections were collected for the y-scan which added to the total collection time. Also, because the crystals usually diffracted poorly, longer than normal peak scan times were used. These factors combined to result in data collection times (including the absorption collection) of six to eight weeks. In the case of graemite, these long collection times were detrimental to the success of the final result because power fluctuations over the six week period lead to a loss of a significant amount of data in the first collection. In the second collection, six power interruptions lead to loss of data and cohesion as six individual parts of the collection had to be combined together to form a complete data set. With these power fluctuations, the confidence in the data set was undermined. With the inability to solve the structure of graemite using these two data sets, it was not known whether the problem lay with the crystal or with the data itself, although it was suspected that the data was at fault. After data collection with synchrotron light, it was determined that the crystal was probably at fault. Precession work was initially attempted with the graemite crystal but it diffracted very poorly and no helpful information was gleaned from the work. Finally, after the synchrotron collection, (with much appreciated help from Joel Grice) useful precession photos were taken (24 to 36 hour exposure times) which showed disorder in the crystal; this disorder is probably the cause of the problems with structure solution. From the experience of these difficulties, it is recommended that precession work be one of the first procedures carried out in crystal structure analysis. It will provide information on the quality of the crystal, its cell dimensions, and help to confirm or disprove possible space groups. It will also determine if the crystal is twinned and whether or not disorder is present. This is 142 definitely a more scientific route than that of trial and error with suggested space groups from a computer program based on reflections that may be in error. This recommendation is certainly not a new one and has been personally communicated by Joel Grice and Scott Ercit of the Canadian Museum of Nature and by Mark Cooper, a crystallographer at the University of Manitoba. The importance of this kind of work has also been emphasized by Stout and Jensen (1989) who, in comparing photographic film methods to automated diffractometers, say: "nothing can supplant photographic methods for the purpose of obtaining a general view of the geometry and symmetry of the reciprocal lattice. A disturbing number of errors have arisen recently in space group and lattice assignments. Many of these could have been avoided if photographs of the crystal lattice had been taken rather than depending solely on individual reflections found by an automated diffractometer." An increasing number of incidents of erroneous space groups and lattice assignment, probably resulting from the blind confidence in the automated diffractometer, have been documented (Marsh and Herbstein, 1983; Baur and Tillmans, 1986) which subsequently prompted Yvon Le Page to develop the program MISSYM in an attempt to counteract this problem. It is also recommended that additional chemical analysis be performed to confirm the chemistry of the crystal in question. Methods include the use of the electron microprobe for exact microchemical analysis, infrared analysis (commonly used to detect water and hydroxyl groups), and the scanning electron microscope for a quick scan of the elements that may be present in the crystal. 143 7.3 Crystal Structure Analysis as a Means For Chemical Analysis of Crystals In the course of this work, it has come to attention and confirmed by Joel Grice (personal communication 1997) that crystal structure analysis can be a powerful tool with regards to determining the chemistry of minerals. Crystal structure analysis as a chemical analytical method has been documented for light elements by Hawthorne and Grice (1990). In the case of dugganite, structure refinement revealed that arsenic occupied a special position that would give two times the amount of arsenic that should be present. The problem became more perplexing when bond-valence analysis of arsenic at this site yielded extremely poor sums. By reviewing the literature, it was determined that there could be significant substitution at this site. Upon further bond-valence analysis and structure refinement, it was predicted that the site (and therefore the extra cation) was real and fully occupied and that the site had approximately fifty percent substitution by phosphorus. Chemical analysis by the electron microprobe confirmed the prediction almost exactly. With choloalite, the site that is occupied by water and chlorine was either supposed to contain nothing (using the formula of Powell, 1994) or only water (using the formula of Williams, 1981). Structure refinement showed that the site definitely had something scattering X-rays but that it was heavier than water. The site refinement indicated that chlorine was probably present however, if it were so, then the crystal would not be charge-balanced. The original description suggested that antimony may be present which would require an anion, like chlorine, to balance its charge. Another prediction of the chemistry was made based on structure refinement with antimony refining versus copper in the copper site and chlorine versus water in the water site. Once again the chemical analysis obtained from the electron microprobe was very close to that predicted by structure analysis. 144 With regards to rodalquilarite, Dusausoy and Protas (1969) used crystal structure analysis to redefine the chemistry of the mineral as being anhydrous. The work in this thesis found no reason to disagree with their conclusions. Earlier work by Sierra Lopez et al. (1968) had shown rodalquilarite to be hydrous. It is therefore a conclusion that a good structure refinement of a crystal can be chemically definitive. One problem is that only two elements can be refined versus one another and if a site contains more than two elements, these elements cannot be refined for. However, when crystal structure analysis is used in cooperation with other chemical analysis techniques that scan and analyze for the whole range of elements, many difficulties with the chemistry of minerals can be alleviated. 145 8.0 CONSIDERATIONS FOR FUTURE RESEARCH In the process of completing this thesis, future research in this and related topics were considered and are now proposed. 1. Solve the structure of graemite. A complete chemical analysis and a full set of precession photographs should be obtained. 2. Determine the crystal structures of cheremnykhite and kuksite to learn if they truly are isostructural with dugganite. Compare the three structures and note the different effects, if any, that arsenic, vanadium, phosphorus, and silicon have on the structures. Research the genesis of these three minerals to gather information on the similarities of the geochemical environment. 3. Solve the structures of the rest of the Te-oxysalt minerals. This is a logical continuation of this thesis which will help determine the behaviour of tellurium in minerals. 4. A complete study of tellurium structurally with oxidation states from -2 to +6. This could lead to a structural classification scheme for tellurium-bearing minerals. 5. The formal coordination of Te4+ should be standardized with the known tellurite structures redrawn with these coordinations for comparison purposes. Back (1990) surveyed the then known structures of the tellurite minerals with substantial work done on calculating bond valences and determining coordinations around Te4+. However, the work was never published outside of his thesis and tellurites continue to be described with various coordinations because there are no set rules. 6. The lone electron pair of Te4+ in tellurite minerals needs to be studied in detail. Back (1990) stated that all the tellurites in his study involved stereochemically active lone 146 electron pairs and he attempted to define the locations of the electron lone pairs based on differences in Te-0 bond lengths and O-Te-0 bond angles. Work by Wang and Liebau (1996) may help in decisively locating these electron lone pairs. 7. A study of the geochemical conditions for formation of Te-oxysalts. To learn which conditions lead to the formation of tellurites, tellurates, and mixed valence Te-oxysalt minerals. 8. The determinations of the crystal structures of selenates and selenites. This would be a logical progression in future studies as selenium is similar to tellurium in its electronic configuration and in its place on the periodic table. It would be of great interest to compare the structures of selenium-bearing and tellurium-bearing minerals to see if there are any isostructural minerals and to determine whether the elements have similar roles in the crystal structures. As discussed in the introduction, there are some differences in the primary occurrences of selenium and tellurium-bearing minerals; the difference in the atomic radii allows selenium to substitute isotypically with sulfur whereas tellurium forms its own discreet minerals. A look at the electronic lone pairs and ligand coordinations around Se and comparing it to Te would provide more information on these complex subjects. 9. In a larger scheme of research, it would be of interest to compare the structures of Group VIB oxysalt minerals to see what conclusions can be drawn with regards to the location of the elements in the family. 10. A standardization of previous minerals with the program STRUCTURE TIDY for comparison purposes. 11. The use of crystal structure analysis as a chemical analytical method should be further investigated. The work should complement that done by Hawthorne and Grice (1990). As one can see, there is much more work to be done on tellurium oxysalt minerals and related topics. As this author has discovered, research into a specific topic leads to questions in myriad of other subjects and quite often there are unanswered questions in these other topics. Research itself seems to be a self-propagating venture. 148 9.0 REFERENCES BACK, M.E. (1990): A Study of Tellurite Minerals: Their Physical and Chemical Data Compatibility, and Structural Crystallography. Master's thesis. University of Toronto, Canada. BAUR, W.H., and TILLMANNS, E. (1986): How to avoid unnecessarily low symmetry in crystal structure determinations. Acta Cryst. B42, 95-111. BEYER, H. (1967): Verfeinerung der kristallstruktur von tellurit, dem rhombischen Te02. Zeitschriftfur Kristallographie 124, 228-237. BRANDSTATTER, F. (1981): Non-stoichiometric, hydrothermally synthesized cliffordite. Tschermaks Min. Petr. Mitt. 29, 1-8. BRESE, N.E. and O'KEEFE, M. (1991): Bond-valence parameters for solids. Acta Cryst. B47, 192-197. BROWN, I.D. (1974): Bond valence as an aid to understanding the stereochemistry of O and F complexes of Sn(II), Sb(III), Te(IV), I(V) and Xe(VI). Journal of Solid State Chemistry 11,214-233. BROWN, I.D. (1981): The bond-valence method: An empirical approach to chemical structure and bonding. In Structure and Bonding in Crystals II (M. O'Keeffe and A. Navrotsky, eds.). Academic Press, New York (1-30). BROWN, I.D. and ALTERMATT, D. (1985): Bond-valence parameters obtained from a systematic analysis of the inorganic crystal structure database. Acta Cryst. B41, 244-247. BURNS, P.C, COOPER, M.A., and HAWTHORNE, F.C. (1995): Parakhinite, Cu" 3PbTe° 06(OH)2: crystal structure and revision of chemical formula. Canadian Mineralogist 33, 33-40. COOPER, M.A. and HAWTHORNE F.C. (1996): The crystal structure of spiroffite. Canadian Mineralogist34, 821-826. COOPER, W.C. editor (1971): Tellurium. Van Nostrand Reinhold Company, Toronto. CROMER, D.T. and MANN, J.B. (1968): X-ray scattering factors computed from numerical Hartree-Fock wave functions. Acta Cryst. A24, 321-324. CROMER, D.T. and LIBERMANN, D. (1970): Relativistic calculation of anomalous scattering factors for X-rays. J. Chem. Phys. 53, 1891-1898. 149 DONNAY, G., STEWART, J.M., and PRESTON, H. (1970): The crystal structure of sonoraite, Fe3+Te4+03(OH)H20. Tschermaks Min. Petr. Mitt. 14, 27-44. DUSAUSOY, P.Y. and PROTAS, J. (1969): Determination et Etude de la structure cristalline de la rodalquilarite, chlorotellurite acide de fer. Acta Cryst. B25, 1551-1558. EBY, R.K. and HAWTHORNE, F.C. (1993): Structural relations in copper oxysalt minerals. I. Structural hierarchy. Acta Cryst. B49, 28-56. EFFENBERGER, H. (1977): Verfeinerung der kristallstruktur von synthetischem teineit, CuTe03-2H20. Tschermaks Min. Petr. Mitt. 24, 287-298. EFFENBERGER, H., ZEMANN, J., and MAYER, H. (1978): Carlfriesite: crystal structure, revision of chemical formula, and synthesis. American Mineralogist 63, 847-852. FISCHER, R, PERTLIK, F., and ZEMANN, J. (1975): The crystal structure of mroseite, CaTe02(C03). Canadian Mineralogist 13, 383-387. GALY, J., MEUNIER, G., ANDERSSON, S., and ASTROM, A. (1975): Stereochimie des Elements Comportant des Paires Non Liees: Ge (II), As (III), Se (IV), Br (V), Sn (II), Sb (III), Te (IV), I (V), Xe (VI), Tl (I), Pb (II), et Bi (III) (Oxydes, Fluorures et Oxyfluorures). Journal of Solid State Chemistry 13, 142-159. GELATO, L.M., and PARTHE, E. (1987): STRUCTURE TIDY - a computer program to standardize crystal structure data. J. Appl. Cryst. 20, 139-143. GILLESPIE, R.J. (1972): Molecular Geometry. Van Nostrand Reinhold Company, Toronto. GIUSEPPETTI, G. and TADINI, C. (1980): The crystal structure of osarizawaite. N. Jahrbuch f. Mineralogie, Monatshefte 9, 401-407. GREENWOOD, N.N. and EARNSHAW, A. (1984): Chemistry of the Elements. Pergamon Press, Toronto. GREY, LE. and LLOYD, D.J. (1976): The crystal structure of senaite. Acta Cryst. B32,1509-1513. GRICE, J. (1989): The crystal structure of magnolite, Hg21+Te4+03. Canadian Mineralogist 27, 133-136. GRICE, J., and ROBERTS, A.C. (1995): Frankhawthorneite, a unique HCP framework structure of a cupric tellurate. Canadian Mineralogist. 33, 649-653. GRICE, J.D., GROAT, L.A., and ROBERTS, A.C, (1996): Jensenite, a cupric tellurate framework structure with two coordinations of copper. Canadian Mineralogist 34, 55-59. 150 HAHN, T. editor (1996): International Tables For Crystallography. Volume A Space-Group Symmetry. Fourth edition. Kluwer Academic Publishers, Boston. HANKE, K., KUPCIK, V., and LINDQVIST, O. (1973): The crystal structure of CuTe205. Acta Cryst. B29, 963-970. HAWTHORNE, F.C. and GRICE, J. (1990): Crystal-structure analysis as a chemical analytical method: application to light elements. Canadian Mineralogist 28, 693-702. HEISERMAN, D.L. (1992): Exploring Chemical Elements and Their Components. McGraw-Hill, Blue Ridge Summit, PA. JAROSCH, D. and ZEMANN, J. (1989): Yafsoanite: a garnet type calcium-tellurium (Vl)-zinc oxide. Mineralogy and Petrology 40, 111-116. JOHNSON, N.W. (1965): Convex polyhedra with regular faces. Can. J. Math. 18,169-200. KIM, A.A., ZAYAKINA, N.V., and MAKHOTKO, V.F. (1990): Kuksite Pb3Zn3Te06(P04)2 and cheremnykhite Pb3Zn3TeOe(V04)2 - New tellurates from the Kuranakh gold deposit (Central Aldan, southern Yakutia). Zapiski Vses. Mineral. Obshch. 119, 50-57 (in Russian). KIM, A.A., ZAYAKINA, N.V., LAVRENT'EV, Yu.G., and MAKHOTKO, V.F. (1988): Vanadian silician varitety of dugganite - the first find in the USSR. Mineralog. Zhurnal 10, 85-89 (in Russian). KIRFEL, A. and EICHHORN, K. (1990): Accurate structure analysis with synchrotron radiation: The electron density in Al203 and CU2O. Acta Cryst., A46, 271-284. KROSCHWITZ, J.I. and HOWE-GRANT, M. editors (1997): Kirk-Othmer Encyclopedia of Chemical Technology. Fourth edition. Volume 23. John Wiley & Sons, Toronto. KUDRYAVTSEV, A.A. (1974): The Chemistry and Technology of Selenium and Tellurium (translated from the second Russian edition and revised by E.M. Elkin). Collet's Ltd., London. LAM, A.E., GROAT, L.A., and ERCIT, T.S. (1998): The crystal structure of dugganite, Pb3Zn3Te6+As20i4. Canadian Mineralogist. In press. LAM, A.E., GROAT, L.A., GRICE, J., ERCIT, T.S., and MOFFATT, E. (1998): The crystal structure and revised formula of choloalite, Cu3Pb3Te4+60ig-(Cl,H20). Canadian Mineralogist. In Press. LE PAGE, Y. (1987): Computer derivation of the symmetry elements implied in a structure description. J. Appl. Cryst. 20, 264-269. LINDQVIST, O. (1973): The Oxygen Coordination Of Tellurium (IV) And Tellurium (VI). Dissertation, University of Goteborg, Sweden. 151 LINDQVIST, O. (1972): The crystal structure of CuTe03. Acta Chemica Scandinavica 26, 1423-1430. LOOPSTRA, B.O. and BRANDENBURG, N.P. (1978): Uranyl selenite and uranyl tellurite. Acta Cryst., B29, 1251-1255. MARGISON, S.M., GRICE, J.D., and GROAT, L.A. (1997): The crystal structure of leisingite, (Cu2+,Mg,Zn)2(Mg,Fe)Te6+06-6H20. Canadian Mineralogist 35, 759-763. MARIOLACOS, K. (1969): Die kristallstruktur von PbTe03. Anz. Oesterr. Akad. Wiss. Math. - Naturwiss., Kl, Nd. 06, 129. MARSH, R. and HERBSTEIN, F.H. (1983): Some additional changes in space groups of published crystal structures. Acta Cryst. B39, 280-287. MARTY, J., JENSEN, M.C., and ROBERTS, A.C. (1993): Minerals of the Centennial Eureka Mine, Tintic District, Eureka, Utah. Rock and Minerals 68, 406-416. MATZAT, E., (1967): Die kristallstruktur eines unbenannten zeolithartigen telluritminerals, {(Zn, Fe)2[Te03]3}NaxH2.x-yH20. Tschermaks Min. Petr. Mitt. 12, 108-117. MEUNIER, G. and GALY, J. (1971): Sur une deformation inedite du reseau de type flourine. Structure cristalline des phases MTe308 (M=Ti,Sn,Hf,Zr). Acta Cryst., B27, 602-608. MEUNIER, G. and GALY, J. (1973): Structure cristalline de la schmitterite synthetique UTe05. Acta Cryst. B29, 1251. MILETICH, R. (1995): Crystal chemistry of the microporous tellurite minerals zemannite and kinichilite, Mg05[Me2+Fe3+(TeO3)3]4.5H2O, (Me2+ = Zn;Mn). Eur. J. Mineral. 7, 509-523. NORTH, A.C.T., PHILLIPS, D.C., and MATHEWS, F.S. (1968): A semi-empirical method of absorption correction. Acta Cryst. A24, 351-359. O'KEEFFE, M.O. and HYDE, B.G. (1980): Plane nets in crystal chemisty. Phil. Trans. R. Soc. London 295A, 553-618. PARTHE, E. and GELATO, L.M. (1984): The standardization of inorganic crystal-structure data. Acta Cryst. A40, 169-183. PERTLIK, F. (1971): Die kristallstruktur von poughit, Fe2[Te03]2[S04]-3H20. Tschermaks Min. Petr. Mitt. 15, 279-290. PERTLIK, F. (1972): Der strukturtup von emmosit, {Fe2[Te03]3-H20}-xH20 (x = 0-1). Tschermaks Min. Petr. Mitt. 18, 157-168. 152 PERTLIK, F. and GIEREN, A. (1977): Verfeinerung der kristallstruktur von makayit, Fe(OH)[Te205]. N. Jahrbuch f. Mineralogie, Monatshefte 145-154. PERTLIK, F. and ZEMANN, J. (1988): The crystal structure of nabokoite, Cu7Te04(S04)5-KCl: The first example of a Te(IV)04 pyramid with exactly tetragonal symmetry. Mineralogy and Petrology 38, 291-298. POWELL, D.W., THOMAS, R.G., WILLIAMS, P.A., BIRCH, W.D., and PLIMER, I.R (1994): Choloalite: synthesis and revised chemical formula. Mineralogical Magazine 58, 505-508. ROBERTS, A.C, ERCIT, T.S., CRIDDLE, A.J., JONES, G.C, WILLIAMS, R.S., CURETON II, F.F., and JENSEN, M.C. (1994): Mcalpineite, Cu3Te06H20, a new mineral from the McAlpine mine, Tuolumne County, California, and from the Centennial Eureka mine, Juab County, Utah. Mineralogical Magazine 58, 417-424. ROBINSON, K., GIBBS, G.V., and RIBBE, P.H. (1971): Quadratic elongation: A quantitative measure of distortion in coordination polyhedra. Science 172, 567-570. ROSSELL, H.J., LEBLANC, M., FEREY, G., BEVAN, D.J.M., SIMPSON, D.J., and TAYLOR, M.R. (1992): On the crystal structure of Bi2Te40n. Aust. J. Chem. 45, 1415-1425. SHANNON, R.D. (1976): Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Cryst. A32, 751-767. SIERRA LOPEZ, J., LEAL, G., PIERROT, R, LAURENT, Y., PROTAS, J., and DUSAUSOY, Y. (1968): La rodalquilarite, chlorotellurite de fer, une nouvelle espece minerale. Bull. Soc. fr. Mineral. Cristallogr. 91, 28-33. SPIRIDONOV, E.M. (1980): Balyakinite, CuTe03, a new mineral from the zone of oxidation. Doklady Akademii Nauk SSSP 253, 1448-1450. STOUT, G.H., and JENSEN, L.H. (1989): X-ray Structure Determination. A Practical Guide. Second edition. John Wiley & Sons, Toronto. SWIHART, G.H., GUPTA, P. K. S., SCHLEMPER, E. O., BACK, M. E., and GAINES, R.V., (1993): The crystal structure of moctezumite [PbU02](Te03)2. American Mineralogist 78, 835-839. SZYMANSKI, J.T. (1985): The crystal structure of plumbojarosite Pb[Fe3(S04)2(OH)6]2. Canadian Mineralogist 23, 659-668. THOMAS, P.A. (1988): The crystal structure and absolute optical chirality of paratellurite, a-Te02. J. Phys. C: Solid State Phys. 21,4611-4627. VLASOV, K.A. editor (1966): Geochemistry and Mineralogy of Rare Elements and Genetic Types of Their Deposits. Volume 1. Daniel Davey & Co., Inc. New York. 153 WALITZI, E.M. (1964): Die kristallstruktur von denningit, (Mn,Ca,Zn)Te205. Ein biespiel fur koordination um vier wertiges tellur. Tschermaks Min. Petr. Mitt. 10, 241-255. WANG, X. and LIEBAU, F. (1996): Influence of lone-pair electrons of cations on bond-valence parameters. Zeitschrift fur Kristallographie 211, 437-439. WILLIAMS, S.A. and MATTER III, P. (1975): Graemite, a new Bisbee mineral. Mineralogical Record 6, 32-34. WILLIAMS, S.A. (1978): Khinite, parakhinite, and dugganite, three new tellurates from Tombstone, Arizona. American Mineralogist 63, 1016-1019. WILLIAMS, S.A. (1981): Choloalite, CuPb(Te03)2-H20, a new mineral. Mineralogical Magazine 44, 55-57. ZEMANN J. (1971): Zur stereochemie des Te(IV) gegenuber sauerstoff. Monatshefte fur Chemie 102, 1209-1216. ZEMANN, J. (1968): The crystal chemistry of the tellurium oxide and tellurium oxosalt minerals. Zeitschrift fur Kristallographie 127, 319-326. ZEMANN, V.A. and ZEMANN, J. (1962): Die kristallstruktur von teineit. Ein beispiel fur die korrektur einer chemischen formel auf grund der strukturbestimmung. Acta Cryst. 15, 698-702. 154 APPENDIX A. COMMONLY USED SYMBOLS AND TERMS 155 A.1 Commonly used symbols and terms. tellurite Tellurium oxysalt mineral containing Te4+. tellurate Tellurium oxysalt mineral containing Te6+. 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. M- Linear absorption coefficient. R R = ^\F0~ FC\/Z~1 FO ' indicates how closely your model matches the true model. Rw Weighted R. Rint Integrated R. Rad/mono Type of radiation and monochromator used. Value of 0.968 indicates centrosymmetric, 0.736 indicates non-centrosymmetric. Intensity. u Displacement factor. < > Indicates average values on the tables of bond lengths and interatomic angles. Corneas Measured distance between planes. flcalc Calculated distance between planes. F0 Observed structure factor. Fc Calculated structure factor. 156 APPENDIX B. CATEGORIZED TELLURIUM OXYSALT MINERALS 157 B.l Tellurite Minerals Name Formula balyakinite blakeite burckhardtite cesbronite chekhovicite choloalite cliffordite denningite dunhamite emmonsite fairbankite graemite keystoneite kinichilite mackayite magnolite moctezumite mroseite nabokoite paratellurite pingguite plumbotellurite poughite quetzalcoatlite rajite rodalquilarite schmitterite CuTe03 Fe,Te03(?) Pb2(Fe,Mn)Te(Si3Al)0,2(OH)2-H20 Cu5(Te03)2(OH)6-2H20 Bi2Te40n Pb3Cu3Te4+0I8(Cl,H20) UTe309 (Ca,Mn)(Mn,Zn)Te4Oi0 PbTe03(?) Fe2(Te03)3-2H20 PbTe03 CuTe03H20 Ho.8Mgo.8(Ni,Fe,Mn)2(Te03)3-5H20 Mg05(Mn2+,Zn)Fe3+(TeO3)3-4.5H2O FeTe205(OH) Hg2Te03 Pb(U02)(Te03)2 CaTe02(C03) Cu7Te04(S04)5KCl a-Te02 Bi6Te20i3 a-PbTe03 Fe2(Te03)2(S04)-3H20 Cu4Zn8(Te03)3(OH)18 CuTe205 H3Fe2(Te03)4Cl (U02)TeQ3 158 Tellurites continued smirnite Bi2Te05 sonoraite Fe3+Te4+03(OH)H20 spiroffite (Mn,Zn)2Te308 teineite CuTe03-2H20 tellurite Te02 unnamed 624 Au2Te03 unnamed 626 Au2(Bi,Te)03 winstanleyite TiTe308 zemannite (H,Na)2(Zn,Fe)2(Te03)3nH20 159 B.2 Tellurate Minerals Name Formula cheremnykhite Pb3Zn3Te06(V04)2 chiluite Bi6Te2Mo202i cuzticite Fe2Te06-3H20 dugganite Pb3Zn3Te6+As20,4 ferrotellurite FeTe04(?) frankhawthomeite (Cu2+)4Te6+04(OH)2 jensenite (Cu2+)3TeD+06-2H20 juabite Cu5(Te04)2(As04)2-3H20 khinite Cu3PbTe04(OH)6 kuksite Pb3Zn3Te06(P04)2 kuranakhite PbMnTe06 leisingite Cu(Mg,Cu,Fe,Zn)2Te6+06-6H20 mcalpineite Cu3Te06H20 montanite (BiO)2Te04-2H20 parakhinite (Cu2+)3PbTe6+06(OH)2 schieffelinite Pb(Te,S)04-H20 utahite Cu5Zn3(Te04)4(OH)8.7H20 unnamed 604 Au4Pb3Te20ii unnamed 625 Au2Te06-2H20 unnamed 627 (Zn,Pb,Cu)3Te06-2H20 unnamed 628 Au6(Pb03)2Te04 unnamed 629 Au6Pb2(Pb03)2(Te04)3-6H20 xocomecatlite Cu3Te04(OH)4 yafsoanite (Ca,Pb)3Zn3Te2012 160 B.3 Tellurium Oxyalt Minerals With Mixed Te and Te valences Name Formula carlfriesite CaTe308 eztlite Pb2Fe6Te4Oi5(OH)10-8H2O girdite H2Pb3(Te03)(Te06) oboyerite H6Pb6(Te03)3(Te06)2-2H20 tlalocite Cuj 0Zn6Te3011 Cl(OH)25 -27H20 tlapallite H6(Ca,Pb)2(Cu,Zn)3S04(Te03)4Te06 yecoraite Fe3Bi509(Te03)(Te04)2-9H20 161 APPENDIX C. STRUCTURE FACTOR TABLES FOR DUGGANITE 162 T-CNT-T-CNCN-,-T-T-CNJT-C^C>JT-T-C^ ODCO<OOeOON(DO)NOO(0^(*)(DNrOOO)U)T-0>000)OlflOrt\|0000)COO)0^0)ON CO CNCniOT-CNlfiT-CDr- COCNCM^^CNT-U^LOLOC^OJLOLOTTCNCOC^ i^oocx)T-r^a)cx>c^cncN<Dc^ CO CM CO if) CN if) T- (D r- CDCMCM^^CNCNtf3inLOCOCM(OLnT|-CMCOCOCNCO T-COCOCDTI-CSICNCSI COCOMCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOC^ WCDCDtDCDCDCflCDCOcDcDCDCDCDCDCDNSSNSNNNSNNSNNeOCOCOCOW tf)Oc»cpr^«pup^cocMT^o^cMco^oc» CsjT-T-CNlCO-^-COCOTj-CDCOCO^-COCOCSlT-T-^-cOT-Tt COT-T-I-CMCNT-IOT-CMCMT-T-T-co LO r*~- CD LO r**~ TJ- LO cr> T- oo r*~- co CD LO r~- LO CD LO co co LO CM CD cz) co co r^- LO co CD CSl-»--r-CMCO4c0eO'*CDC0C0T|-C0COCMT- T- CO 4 T-4 nrrt-NWT-WNCVT-r-r-CNCNCNCNCNCNCNCNCMCNCMCNC^ SNS(X)eOC0O300»COCOC00000(O00(OCOO)CS©WCnO)OT CNCOTfT-OOTCCf^CjOLOTj-COC^ CN t- CVI^CVICNT-CNjT-OJr-T-COCOCNJC^Tj-T-T-CNtOCO^-^CO CN CN T- CM CM CN CM TfO)NCDCOC^O^LONOT-LncOCDCMCDCO(DNT-NCD^r-(DM ^^r^(Mr^T-T-(N|T-T-CNI^T-NNCOOOCOOT-(OU)01WOW^ONNCONCOrtCONCnif) CM t-T- T- T— V"* Y"" U)C»CJCOCO(OT-IOCMCDCO^CDT-COT-IOOCO(DOCDCDCMOO^C\|COCN| ^^^^^^^r-r-T-T-^T-T-T-CMCMCMCMCMCMCSICVICMCMCMCMCSINCMN OOOOOOOT-T-^X-V-T-T-T-O^^CNCNCMCMCNCMCOCOCOCOCOCOW CflOTj-COCMr-OQCONCOU)^COWOOT-n T-CO^CMi-OfT-CNCMT-T-T-lf)r^CNT-T-^T-rT- CMCM^-T-CMCMt-CM T-T-r (Mr r^CX)OCMr^l^TTCN>ta3CMOCOTtTfT-CDCO ^•^-COT-CMCOCD^-OO ^S^CO^COCMCOCM^CD^T-^T-T-COCON COCOCMNCOCMNCOCOT-r-r^CDCNCX>COCX)CN|^OLOCNOTfLOTfC» ^•T-CDT-CNCOCO^OO TTS^CO'«trMCOCOCO^CD't'-Ttr- CO CO N COCOCMNCOCNJNCOCOT-T-UO LO LO LO LO LO LO UD LO LO LO LO LO LO LO CD CO CO CO CO CO CO CO CO CO CD CO CO CO CO CO CO ^cocNT^OT-cN<r}Tfc^cor^ LOcX)^M-CNOCOr^LOCOCNr^CNOOLOTff^ T-c»ooOTCMcocNiocor^oooco^inco^inoou>^coc^^^cDcocoTr ^^lOt-T-cocoitin^ CNCNI^TfCMLOOCT>^a>TtOTlOOr^ cMOooocorocoLnxj-r^ooocoiciooo^-inoocD^-coo>^- CO CO CO ^ lO T- CO CO TT LO CO ooooooooooooooooooooooooooooooooooooooooo T-T-r>icMCNCNicococococo^^^^^^^inininwu)u)u)iococoo Or-r-O^CNr-OT-NCONr-OT-CMCO^CMr-Ot-CMn^incOCM^Ot-^ 163 COCNT-CNCNCOCNT-COT-CNCOCOCOCNCOCOCNCNT-CN1*-^CONCl)0«C35^NCOCOCXOr-CNO)Lnc\C^ CO CM CO CM CN CO CO CN^^OT-C0T-©T-T-W(DC0^^(0C0^t0Q(0(DC0(DU)U)n^W LOCJ5SNOTfCNLnN^COCNJC^CNJOOOTfCOOCSJSSnC^ CO CM CO W r- CMCOCOT-T-^-V-COT-COCMCO T-lOCDN^^(DCOCO<OoOCDCDCOCDTfU)W^M cococococococococococococoeococococo COCOOO^C^OTO)CJ)CJ)a)CnroOOOOO T-CNC^CON(DUp^fO(Nr-OCONO T-C\|^CNinT^^T|-C>jTfTflOT-T-COCOCNC^ ^T-ONN^COi-OfOCOO)N©ir)(DOC^O)COO)^COLOT-lDNOCOCOC^ CN O COCOSCNlCVICOCO^OQCDeO^ncOcONCOWCN 0)incOCOCNlOCN(D-T-CNincOO)CN lOTTT-CDCDCOffiCOSNOO^CfiNT-^tDOOCOCOCNICOmroCDCOO r r CM r O) CONCO^T-cOCOTrOO)U)COlOCOCOCOCNCO^C\J O)tO00C\IC\llf)^-CDT-COir)fOO)CN CNCNCNCNCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCO ^^T-^o^T-T-r>jcNCNc\cNCNncocococoncorom CDW^COOT^O^COCN^OT-CNU^x|-nCN T-CNT--V-CNT-C>JT-IOT-^C>JT-CNC^ C^CDCOOCOCDr-CNCNT-OOCONCOCN^OCDNC^ CO CO LO ^NCM^^IOSCOCMT-N^T-IO^-T-WCOCO CM N S CO r- TJ- CN LO T- T- CO LO ^WWCO^^O^OW(OCMOOCO(OOCOSlO^CMCOCOCD(ClOCOCOn CO CO TT TT TfNCMTf^mNCOCM NCOr-lfiT-T-^cOCO CN Is- CO •«- <<J- CN r- T-T- CO LO CNCNCNCNICNCNCNCNCNCNCNCNCNCNCNCNCNC^ CNCNCNT-T-T-CNCN N^lONCOCftCMOJNSSr-OOJNlOODOT-ONOJT-ON^OOCnojCOCDOJQ CN ^" CO CN CD lO> COC^<DCC<OCNCO^CNT-CNJTTCNCNCO^CO^^CNJT-COCNT- T— CO CO CO CO c£)CN^r^r^cj)coa)cDc^cocoCT)r^LOLor^ CNrfCOCMCDlONCOCOCDCDCDCMCO^CM^CM^ T— T— CO CO CO CO Tf NNNNSSSSSNNNNNSSCOeOOOeOODCOODCOCOOOCOOOCOCOCOCnc»a)CftCOC» ^OOTCONCOWTf«CM^OT-CN(O^T-00)cX)N(OU)TtC^ T— T— i I I I III II ^— — t • • i i T • i i ^— ^— i i i ~ • T I I CN CN CD CO CO OJ CO T- T-C>jr^^U^LOCDTfC^COO^a)T— CDLOr^LOr^T-C^ CN^h-M-xr^r^l-COCO^- lO COCN^CMCDr-CMCOT-COT-CNT-CMCMr-T-OlOOiroONLnn T- CM T- •<- CM (MOioro^cninoTrcoi-ocMtDinirjNcnr-tDirjcDOTrLnNOT CM^NTf^^Tt^COr-r-LnT-COCM^rMinr-CMCOT-cO^CN^C^ T- CM T- CM T- T~ OOOOOOOOOOOOOOOOOOOOOOOOOOO^^T-r-T-^T-T-T-T-T-r-T--i-h" 00 00 CO CO 00 OO CO GO O) 0) O) 0) o> o> Oi O O O O O O ^ t~ i- O T- CM CM CM CM CM CM CO CO CO CO CO^TfCOCNr^O^CNCO^C^CNT^ 164 T- CM «- CM CM T- CM CMCMCMCM^CN^CMCMCM'-COTtCMT-CM'-CMCMCOT-CMWCM'^CMCMCOCMCMCVICO T ' VO)(Ni-lD^*(MtonSSS(MnK)10SnO(0(OMDO»OIDS«)'-N <OCMCMT-»-<OCMCOCM'-CM KI I- N n >- ^ CM CM CM CO CO CO CO If NOnOIDCMtni-(\|(0iriT-T-NI0n<0IDI0(0BOON*(00)01IDfl0 COCOCMT-T-COCMCOCOT-CMI-COT-CMCOT-TI- T- CM CM CO *~ CO CO r- CO (O * (D(D(D<D<0(D(D(D<D(D(OCD(D(DCD(D(DtO(0(fl(D(D(0(OSNNNSSSS nn«Tf^**VTt**inioiniou)inmiotD(D(D(D(DOT-T->-tMN(MN CMCO«pW^COCMT^OT-CM<OinTfCOCM^OT-U>^COCMT^Or^OT-COCMTpO COCMT-CMT-COCMCM CM-t-x-CMCMT-CMT-T-CMCMT-CMT-T-x-T-T-T-T-CMCMCMCMCMCMT-CMCMT-T-CM x— 1 T-^COOfOWT-^NCMT-T-Mr-CINT-T-O) f-CMCO-^-CMCOCOCMCMCO 0)CT>0>CMCOI^-0<0 (0(010CMlONOOO^OO(M(O^^S(OlfiSSS(D(DO>lOnS{OSWT-ol o) N (M T- CN lO ^ ~" — — . — —~ — ~ — — " • — — - • — — — - • — • — — • • — COT-T-COCOCOCM'-'M-COCMT-T-CMT-COCM O) T-CMCOTfCMCOCOCMCMCO cocococococococo iflioiniomioifiinwioif)inioioininioifliniflcD(ococococD(D(0(DcocD(o ncNi-o^cvn* (DCD(DSSSSNNNSSSCOeOeOCOOOtOCOOT-T-T-CNCNCNCMCMNCOCO OT-NCpSCD10^CO{N^Or-S(OU)^CO(N^Or-Ot-(1N^Oi-CJIO^ CM T- T- T" T~ CM T- T-T-CMCMt-CMCMCMCMCOT-CM^CMT-x-CMT-CM^-COCMCOCMCMCNJx-COCMT-CMCM lf)COlO^O)lOT-T-O^T-NOOOOOlf)SNT-(<)(O^COO)CMNOCOO)^CM CMcoinu)T-cMn>-r-inn^cMT-cOT-ni-cocMinT-cou) Oi-tNi-n JSJrt^SPS£"rtS2 ^C\IOfOO^CNCMCOCOCONCNO>CMCOCOeOOOWCOCOCOCOCOOJNT-lOT-lOCO COCDCOCOI^TJ-COCO CM n IO ID N CM CO wco^tcM cOf-cOT-cocMin-T-cDm co T- TI- CM CM co CMCMCMCMCMCMCMCM i— i— i— i— i^i— r~-r^ cfin^cocMT-O"-loioioinioinioiniouiiniriioinuiininininioioinioioioinininininifiin cocococowif^^^^^^^^^^^inmiflioioioinioioioiniocotDtD T-0»-CMCOS(DlO^COCMT-O^CJ(O^CON(D10ttO(MT-O^CMCOCONCO 1 I I I I I I I I I I I I I I I III "-CMCMMr-cilT-T- CM CM CM CN CMCMCMNCMCMCOi-nt^CM IOOT-CMCMT-OCO COlOlf)l01f)CDlOCOCO^^Olflir)CMCMi-COCMCMCOT-COT-(OlOCOiOlOCOlOCO CO >- T- T- CM Tt CM CMCOCMCMCOTfCMCMCOCMCMCMT-CO — - — - ~ >~ CO CM CO N N CM CD (D CO COT-T-CMCOT-<3>CM COCDOlOCDS^'NCOCDlOT-incOT-COT-CDCM'JinCMOCMCO^^in^cOtMN O r •*CM'<-CMCOCMCMCOTfCMCMCOCMCMCM CO T- CO CM ^ S MM CD CD CO I-CflOJCfifflOOOO SSNCOCOOOCOCOXCOCOCOCOCOO]0)CI)a)0)0>0]0)OOr-T-T-CMCMrMCMCM T-0^(NOO)COS OT-CMOJCONCOIO I I I CDup^COCMT^O^Cpr^CDU)'>J-COCM^-inO eo CM T- CM CM CM *- *- ^CMCMCMT-T|-T-CMCM*-COCMCMT-CMT-CMT-T-CMT-CMCMCMCMCMT-T-CMCMCMCM 1 i i i - i snctoctinsn niocooococDft<'>*iDT-*^ajinK]CMiMcooococOT-cococMU)o<Mco COOt-COCMVN^ CO <OmCMO)CM**ir>CMCO U) CM >- CO CO CM CM CM U) r- CM CM CO IT- CM CO OXDITlM-OinM'CO CMlDCDOi-CMlONI-CO^tfiOCOlOCOCOirxON^COOOOONCDCMSCOCO^ CDOCMCOCOTfl^t CO niOCMO>CM«AcMCO IO CM »- CO CO CM CM N * fl- U) r- CMCMCO CMCO coconncoftv ^inininioinininiriioininiricoinincDiococDiocDiDcDcDcDiocDcDNSN r-C-CMCOMDIf) ^C3>COr^<DlOTfCOCMT^OT-CMCOTfU7050pt^CDU)^COCMT^O^CMCOOT 165 CM i- CM CM CM r— r— i— i— •— cvi co co co T- CO CM T- O I i I CM CM CO CO CM O S CM O) OO CO TC CO CD CO CO CO CO CO CO CO CO CO CM T- T- CM CM lO IO U) tf] IA CO CO CO CO CO lO Tj- CO CM T|-T- CO CO CM T-IO IO Kl IO ID CM CO CO CO CO CM m CO CM I I I I T- CM i- CM •>-i— I— •— I— •— r— to ira -«^- co OJ APPENDIX D. STRUCTURE FACTOR TABLES FOR CHOLOALITE 167 Nicoo3noioNNo<Danoo<oo>ooai<aaio«NNomoono«iDini\isoo(0« lOffl(DMD^Oe0NCS(D'-IC00r-IO T-olittOOTfW'tNi-CONNintOVT-OinCSnr-MOl ooconosen(Dffln*ooiooi(0(DCONCsmO(>is^oi^«nnNONooiD(,iOT-Tfn't* UJiOSSlO'-OOSIOSlONSOlNNNnN^OCJVONNCJOOT-T-TflOnoaiMOlNWNCIl . V T— . .— T— 1 . 1— 1— . T *— T— 1— OOOOOOOOOOOOOOOOOOOOOOOT-T-T-T-r-*-T-T-T-T-T-T-T-,--r-T-»-T-marocoffiffloimrocflfflOioooooooooooT-rNNNcvinnnnfon^^^^^t NT-OT-N(0^m03N<0C«O'-NnVin<0N03fflOOi-i-O^(\IMt-O^<\C0C0Nr-O'-M II ^— i i i III U)OC0O^(0Cn^(0T-C001^ffiinSnNWNOOT-N^OnMl0C\IC0N0)**O^N<0N0) 0>lO^T-0)U)OC\l(OOO^r-0003COCD^fOnO>tO^O)^(Dr-^0(ODOCOSr-[SICOT-(QT-00> T~ T~ T" CM T- T- CM N N T- T- T- CM CM T— T— "(— T— 1— T— T i co o co co * CNJ oj CNJ ^i* og o . co co CD wo c*} og ^J* * CM co oo co r - CM o5 crj cz3 c^ co r °i T-" . CSJ T-CMCMCMTfT-r-T-T- CMT- T- T- T- T-0>0>OC»C3>C»0>C»0>0>C»C7)00000000000000000000000000000 NOOT-Nn^in<Dsco<io^^o»-CM«^0'-Ncin«^o^cMn*^ncMr-o^c^ 0)^oo(0^lD^*^^CN^»eoc^lm^^)ocDlncnco*^^co^»ln*cDlO<o*lO*^coln lOCM^CM^CMIOOXJlCMCOr- COflOn^CMfOCOCMNCOSncCiMnCMCMv^niO^inNCO^ ^-T-*-r-T- CM m V-T- T- CMT-T-T-T-T-CM^-CMT-CM acsminnTfifiWTfinio^Tf^coinconcoNN^ujTtMnT-cDNOcD^N ^i-rocM'-^nscocNN(siNCMinocN^cN(D^^c\isnsnm<ju)coc\icMcon*n T- T-T-T- CN m r- CMT-T-T-T-^CMT-CMT-CM coocoiiooococoocoococooeococoocococooiaiQara ^^^^^^^^^^^cnfloc3l)3oocococo^^cMNNCMnnnnon'**<^<;v»*^) nCMt-0>-CMCOV10IONOrCMn*U1IONI»O^Y0''c,l(l,,70''Mnc?tv'70'"Nn,'t ininOTcMiococn^o^c»^co^co^co^^cDCD^cocoinco^r^OTcOTr^ior^^cocoi^coioo> 1 t— T— T- T— T— T-I • II U)ffiSIOC»COSO(»SCMO^CI)COCOIO<OCOCOinCM^O)WCOCOCM{DCOT-ir)lOCO^(Nffi»-ffl COSNS^CMWfflNCMCOT-ncON(NCMlOCOIflCM(MC»CDlOCOT-CMNNOlOO>IOlOlflCDP)CO^T-COCM CMCO T-T- Tj- CMT-T-CMCMCM'-'-T-CMCMCM T- T- CM T- r Nrrr-ri-CMr nif)*ioin*s**co*iricocMsooi»CMin(DCMOooT-socM*o)CMT-oiniocM(Di-OD CDCDCMS10C0U0mc0CMC0T-C0OC0CMCM^0)^CMT-CflCD«)03OCMCDSC0CD0)IO(DinD COCM CM CO *- 1- CM'-CMCMCMCM'^'r-r-CMCMCM rrNrr T-T-T-T-T-T-CMT- T-CO(OCO(OCOCO^V^^^^^TtU)WWU)in«5WlfiiniOCD(OCOCOCOCOCDCDCD(DCDCOSNNNN CMT^OT-CNCOCOCNT^OT-CMCO^TfCOCMT^OT-CMCO^U5up ' T-'T-T-CMT- T-T- T- T- T— -I— • i II i T-nNNP)COCMT-^T-010inO)(DT-CONSCMCOrONO©OT-COSO(D(OCOCOO CMO)fflin^5-CO^©ir)0(OiniOWCDCONIO^^O>CONWCOOC010lf)S(ONCMTI-CD "sf CM CD T- ^r-r-CMT-CMT-^ T-t-v-CM T- IfiT-T-COCMCOT-T-CM SCftCfl(ONniNncOt-COCDCOT-Ot-t^COCMCJ10)(NfflC»CDCOC»LONCOlOCM^N coocjiconT-cDTtoiwcocowmconcOT-ioniooosin^Tti-^ioiocoscococo CO in CM CD T- TJ-T-^-T-T-CMT-TJ- T- T- CM T~ T- ICt-T-COCMCOT-T-CM r-c\iNiN«nnnn<t-^*^*^*v^^^^u)inininininininincnioioinm T-T-T-CMCMT-CMCOCOT-mcOCOeOCOCO^^TfTf-<tT-T-CMCMCMCMCOmc^ T-Oi-OCM^CMOnO«r-OT-CNnOr(Mn*Oi-r-O^CMCMrO^NnO(MrOrCMCO< O CO CM N CD CO CO T- S O lO I. U/ W HI CM T- m C  <f C D CO CO O) CO O) CM m co u)  co T- * M-168 to t0(D(0S*-(0S0)(0OM0t0(0mMf)(DNt-10i'C0Cnffllf)C0SOO^fflO0JrSO(,)0lT-r0 T-T- CM T- T-T-T-T- T- T- T~ T" T-T- T~ T~ T~ CM T- T- T- CM T~ T~ T- CM T-II II II I I I I I I I I I I III I u_ co ini-nNT-scJoinmuj^^^usioo^ntDn^voiomcsLnoi-cDONMT-NNN T- T- CM T- T- CM T- r- T- T- CM T- T-T- T- T- T- T-O CNNNU)NiniOQNNCOT-t-WCD^OCN^lOU5COQO)WCDO)COO)T-N^CvlNCOG^COO^S LL. CONNr-U)NT-*NO*10ncOCD'-SSUinNn*^ONC»lC)T-C»CO(JlNlDNNOCOT-100 T- i- CM T-T-CMT-T-T-T-T-CM x- T- T-^*U)ininU)OiniOU)ininOCOIOCDIDCOCOtDIOIDCDtDNSSNNNNNSNSNNNCDOCO x: n*^nc^r-or'Nn*ln,9tl?cll'70*"N<,*inlD<?'?t,?(ilT0,"Nn*10ID|vfi'(9'? CM c CO o o J= o I o t3 0) I D O 3 "O O u5^r^rococor^co^rooou5oocMcou5Tfcoa)T-cnooOT-T-ocoeooou5roco<Dcooou5^cD NO^iD*cooo)*iO'-QC»i-nfflT-conCB^*rcsni-coiocoinn«*mio<-<'M»ii)N NCO^NCNO)^COIDCONCO^COCNO^*^^M'^lOCOiniflO)CI)NlOt<OCOIftT-i-(ONOOO SQWCO^NOOlCNNNfflCOT-lOT-CNCNCOfflT-OICVfCnWOCftCNCftClT-incOSCOCOM-ffl^^CO T~ CM T" 7-T- T" T" 1- T-T-T-T-T- T~ T~ ^ T~ T~ ooooooooooooooooooooooooooooooooooooooooo lOCOCDCDCOCOCOCOCOCDCOCOCDNSSSNNNNNNNSSSaOCOCOCOCOCOCOCOCOCOCOCOCOCO inin^ncv^o^NcovinocDifi^ciN^OT-NcovuicDNSipin^nN^o^N Q^CS^COiSTTNCOOCOCOinNCB^COSinNO^CO'-COCONfflNNCONCDT-CBOlONlD* ^OnOCOCncDCOmCBOlCOnffi^SNnCOUlNIOOllfllO'-COCOIOCDCDOi-T-SCBtM-nCON ffl(OM'N^COOCO*CClT-U)l£IOri|i-10«)OOII)0€r'r-fflncONBOOIflO»SI01Dll)nN CNT- r- CM T- CM T- CM CM CM T— CM CM CM T— T- T-T- T- T- T-T- T- T- T- T-n*o«iSi-r-\fiorif)ON»nnoNoici!r-«)s«irosnii>«i'-ooi>-n>-i()U)n«)ro co^nMnc)lO»nlor^llOlO^-c^ln^<•cocs^T-NT-T•<•o^o^I-co<•Olnolln^lONr-CM r- T-CMT-CMT- CMCM CM T- CM CM r- T- T-T- T- T- T- T- T- T- T-minmioioiominincocococDCDcococDcocococoNSNSSNNSNSNSSNoocococococo COCMT^OT-CMCOTtlOlrt^COCMT^OT-CMCOTfinCDCDlOT^COCMT^OT-CMCOTtlOC^ "O c CO "D a> £ a> CO JD o LO^<OTT<3^a>c£>OC^ rC»COO)0)0)OCOfflO)(00)lOOn(NO)rNCO<DT-lOT-loro ooT-CNcoTfLOCNLOr^Lor^r^coocoo^c^ T- CMCO CO T- T- CM T- CMCM CM CM T-CM^-T-^-CMT-CM T- CM T- -t-^^T-0<DCfiCSC\lin^tOSfO(WCOS(0(OCNNfONCN^COOT NCN(NCOlO(OT-lfiO>NCOlfi^QCSJQCOinS(NN^ t- CM CO (O r- T~ CM CMCM CM CM V-CM*-^-*-T-*-CM T- CXJ ^ SNNcocococococoaocooooooocooooocon f^- h-- f*-- O T~~ CM CM CM CM CO CO CO CO CO CO "M"^"^"^"^"^"'*!'^ LO LO LO uo to LO LO LO LO LO CD CO CD CO CC CD CD LO(DI^OOT-T^OT-CNJCMT^OT^ r^CNjTtOI^CO^T-COCNOO^COLOC^ - i'- V ^ T V *~ V *7 V T— r^a>^05r^cxDu^LocDco^a^cxr^ O) CO TT LO CO O CO COCOOOCNlOT-CNT-SCNCDNTrcOCNJCONWCNI(D(NOin© CMCO <0-»- C\l CN Tj- CN CO CO CN T- r- CN CN CN T- CO CO CN CN CO *- T-0)OSNs^T-Qcoio^Ot-Noo^»-0)Sco^^ininro(Or^(ons^co^cNcoro CTICN^LOCOT-O^T-OINQCOCDT-CNCNINC^ CMCO CO r- CN T- CN TJ" CN CO CO CN CN CN CN CN T— CO CO CN CN CO T- T- t- T-LOLOLOl/5LOLOCDCDCDCDCDCDCDCDCDc^COCD lOLOlOinLOlTjT-r-CNCNCNCNCOncOCOCOrOTr^ Ot-CN|(OtinOT-r-OT-CNCNr-OT-C>ICOCOWr-OT-CN|CO^^rtW 169 Or-I^O) O(DC0C0NtNONNfflT-nON01OinS(\INn0)M«*C000'tSnNID y-y- CM rNNT-i-T-i-CM^CMr>-ri-m-(Ni-T-T-i-r^T-r-i-T-II ill I i I i I I I i i i II I i (DOCO(O^WrOT-OCOO)(DCOlOCO^(0(D^lfl^S(0^^<N^S^^tOO o «3 B « n oj m ^ m v«(i)«jtocninoioiS(0^ociiN(D«30ino)CNC\ioainu)OSOO)oiN li- NNIOONrUlr COCMCMCMCOr^r-CMCM0OTfr-'*CMCOCMCMCMCOCMCDCOCMO0-»-inCOCOVr--CO J£ 0OCOCOCO0OCO0OCO roOJQfflffiCfiOlCOOOOOOOOT-i-NNNtvlOnnncOrt^^^t^ ^ ^ntjir-c-tMn N^OT-Nn*innN^OT-Nno^^OT-NN^oi-Nnnc\ir-or-O^-COCOIOCOOOCO ^NOCO^T-COS^T-T-COCOCOtltOlflSCOnOCMSfflT-lfltDSOCON^ h-CDCOC0COCO'»-CO lOSCO^ONWP)OlOINT-T-^T-lolD^tN(D^iniOlOO«){DT-SOOIOT-CN CO c (0 o o JZ o ca I o to •s S> t> 2 CO T3 a> o COMDT-CM*NO fflT-cscnoocooo)co(D'-»^ona^i-iNaisiOT-eo(DNoi(D<oci)T-^ uiNNcnninoi^ io^<DMO^NiNo^nnnci>oc\i(»^inn«ncou)oioiD«in oooooooo nnnnnnnnnnonnconnTf*^»Ti-«»^^Tt*if«*** cocoaiaooicoai oooooooT-T-rrr-i-^T-T-^rNNNivnnnnnn^Tr** r^OOOphj.CO'O'^'CO OT-WCO^W©^nN^OT-NCO^OT-YO^CN|CM^OT-NCOCONr-0 cocNOTcor^cOT-^T-incoi^GowiniocDr^u7r^CNicor^GoocDr^^OicDO)cD «!^*l(l»0)00)»N*N(»^C»nOO!'rOO)<0»ll)l»»IIl>-iriS^< ocococor^cnr^coo>cNcDi^ocDCDcoir>Troi~-05coocoocO'*^-Ttr--cD't T- r-T-T-T-CM-I-T-CM T-O) (D O) COCOCOCOCOCOGOCO T-oi-CMco^tmco MOO)SfflfflNWNU)0(ono)^intc\iiNnT-o)<oiflinincocDiO(D^T-01Nlfiril(DCBNCNI0)(NlOST-^00Nl0OOl0O0DT-inOnNNWSWC0 connnnnnnnnconnnnnnnnconnnnnnonnn NCyN(0C0C0COCOC0^^^^^^^^WlfiU)UlU)IOlOWIfllO(0(D03(D(D OT-CMCMT^O-r-CMCOCOCMT^OT-CMCOTtTfCOCMT^O^CMCO^lOin^m c CO TJ CD £ CD ca o O) 1^ CO CO CO CO o CD m CO O) in in ir) CM m CO •* o co o CM in in CM CO CD CO CO CO CO T- a> co -st o> O) o o CD MNO*MfM() lOCMCOCMOCMCMI^ ococococococoincoT-ocDincMincocMcocMininor-c\ii^-ocr>cocMT-inin •*TtT-CMC0CMCMC0l^00CMOOCnTfCMCMr^CDT-C0C0C0C00>inoCMOa)T)-0) COCOCOCOCOCOGOCO ID(0(0(OIONSN c cMcOTi-incDCDin'<j-CMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCM (D(D(O(DNSNSNSSNSNSNSN00COe0C0«(OC0C0COacOlOCO00 co^incocpin-^cocMT^OT-cMcOTrincDr^t^cpinT^cocMT^O'-CMcO'* ftco^ineoiDco in^-0)cocDOO>oi^r^r^^-momT-oincDCMomcocMCDCM05cocoinoim CMT-T-T-T-COT-COT-T-T-T-T-T-T-T-CMCMCMT-CMT-T-CMCMCMCMT-T-T-T-T-o CO CO 1^ CM CO o CO CM ^_ CD m CO O CO 1^ m m LL CO m CO CM CO o> CM CM CM CM m CO co O) 00 CO CO CO co CO CM CM *~ O 1^ o> CO O) a> m CM CO ,_ CO m CO CO LL CM CO CO CO CM co CM CO CM CM CM CD T— CD o> CO o CM CM CO CO CM CM 1— — CO co 1^ 1^ CD(DT-T-(NCM(NCM LOCDOT-T-OT-CNJ COCOCOCOCOCDOT ^lO(DSCO(OS(DU)^(OCNr-OT-Nn^U)(DN» 170 (OTfOOT-(DT-(jTf<OT-on(00'INN«tOCDOC»C»fflTfNNCO(001inU)CDnONOO)ro W'fcn«T-coonc\0)u5u)o)TfT-c\i'fTfin<DCOT-u)o<DT-u)'/,<o<DonouiONNT-^ nctiooffluiocooinBscnm'-iDONON'-ifirtno^fflr-ninNinni-cotT-icinso r^cMC\icoococ\iincMOC»oOT-T»coi^cococ\ir^ooiT-c\i* T^TfTflnlou)lfllnlnlnlnlnln^O(B^O(OlD(DlD^otDlD(D<D^^^^^^^^^^^^^ffleotoo onr-N«Ncoi»sooNi-T-troiio«)r-r-(D(DOC(«)i»ir)Oi>toNS«)(,)ii)'tT-oi«)«)s^ OOOJOOCOCOCNICO (O'-cOTfwsN^ostoNNiDT-^NNeo'l-inTfO'tco^csTi'ioneocooin N(000)NS<OCOS<OCO(Oa)CONOSSO>fOaOindOa>NCO(I)CON(DOCOOSMD01COr-COOO)CM cocnTfNiDNiDniONONN'fNTfT-NffiNioioco^NniotDanronN ^MlM•^lnlOlOlOlOlf)OlOln^)tD{DtotDcDCD(D{O^D^D<Dffl^^^^^^^^^^^^^Ncoco *lno)0«)T-oco(DC8co«)^oolOO)^(»>cD^O(oo>cDco<otDcolnT•eocoffi(DcOT-^o^^o(^M• II iii i iii iii i i i i i i i i i i i i i i i i i i i i i 00^<Dr^C0<0<DCNT-O<0in'J-roin<flt^OT-CNT-in<DCMCNU5(D<0*Tt<Dl0 T-oom<o<OT-t»o>a> tDtDNifltDnro^N^^-cDoo^toowoiacocoNtonssn^M-stotDNT-^cocofflffloxoro COCNl(DU3CNCOTj-0\ICNO(OC>10vlOCNincOT-C\lT-CJCOa>*^ CO<OtDCDtOCD(DNNSSNNNNNNNSNSCOa>OOOO(OOOCOCOOOCOncOCOCOCOCOO)C&O)C0a) 0>-Nn*U)(D<Dm^CONT|-OT-Nt0^10(OSNCDlD^CONYOT-(\in*miONCONlD (OC0TtcOTlT-<DC\ICDC0O>05C0T-0DT-COC0C0CO0}a>COC©0> TTTC!,T7T7'~R7T~R7 T^T^^VV^TT^!' '7T7T'-VT~T7C!,C^T"C!,T7C)'T~,7rl'R!,T7 N*nUC«CDrO(>IO«T-^NNt<INCOU)«WU)SN^(OST-i-<OOi-(D(D^OtOinCBOn<flf) o<OT-»v*^«rollO^I-o^^lCS^^-o^<D<ou)^cD*^c)n[<)^'-ooo^u)c^l<^^lnln^c^lcl) coco<ococoa>c\ic>4cotf>o>in<omc>icoromcou)t^<omM<or^ T— T-T— T— T— T-T— T~ Neo<of^<pu>Tj-nNr-OT-NnTfincoN«c»<ON(0«Tj-nNT^ TfCOTfcOCOCOT-T]-cOnNCOCDCOCD(DWCV|CO(OU)Tj-inu)ulcOCOT|T-COCO(DNT-SONT-(NtDfflin 2nt^!Iw®5w^www^nW^WC0T-NCaOC»SOOWTj-N0)NC0Tt0)Tfc0T-*S#O) cou3coi^cou5eocoiniocoiOT-r^cDT-(OT-cor^cotf5coco<D ^^S^S?^2^m2mN^mffi^NmN°*"«NNlOTJ•oc^llnT-toT-T^(D^TfT^o^^l(D su)tDN(Diniotonsnu)NiDNCNicoNC»n<»c\iinc\inncocscDwooNT|Nin T-T-T-T-T-T-T-cMCMCNC\ic\ir>icMC\jc\icNCNC^CMCMC\(r>irgc^ T-T-T-T-T-T-T-OT-r-CMOJNtNfOCOtOCOOOfl-TfTfTtTfTfTtTflolo oooooooooo 171 COCDI^O)^ir>0)C£)COCOCNLOlf)0)CN|lf> WCMIO^COCDCMCNT-T-CD QCOCNC»NCl)CjC003^a)CNlNNCOO3 COfMO)lfl(MtOO>lf)CONCM CNcor--CM<ococMir>Lna>co^-cocor*-co sncMOrnoroM-NO) 00 00 C0COC0O>0>O)0>O>OT-T-CNCVICNI COCOCOfOCOCOTr^Tj-^^ OT-CMCO'tMrOrCMOO'-rOr CMT-OT-CMCOCM^-OT-CM OT-0)MDMSCO(DINNNNO>00) SOr0T-OtDS0MC0O)(0 CMCMi- CM T-CM-»-T-T-'»-CN^- T- T- 1- T- CNJ T— CM T— T— LO CO CN CO WCOCONCDIDCOCDT-S CMO)SO)COO)0)iniOmT-r^CO^inCDC0lO'^-C0CM'sJ-O)CJ)CDCDCM 0)(OM-NO)SCMT-TrT-CO COSCO^COCOCDCOCNCOCOCNCNI^COCO CNOSO^OJSN^CW CO00COG0C0CO00 00 00 00COC0C0CJ)O)C7> W^CONr-O^CNCO^WCDNlO^CO CM TJ- O CM O -r- O T- CM CDCDCDCDCDSSNNSN SC0^CO^(D0)CI>O(NC0^00NUO OO)^O)O0OOOO)Mn lf>-»-00CO00^J-lOCM'«-CO'^-CO00r^C,OCD CDNrgCOT-OOlOCMCMr-lOCOOOCO^OroS^CDCONO^SN O) 00 CD CO Tf ID T- CO IOT-^-CMCOOOIOCM^-CMOOJOOO CBCNS^OOCOCSICNCOOIN LONC^COCOCOOCDCOIONCINNCOCO a>COC0^^C\|CJ>CDCOCNC0 COCOCOCOCOCOCOCOCOCOCOCOCOCOCOCO cococococococococococo 0>C7>0>0>0)0)0>0)a>0>000000 miOCOCOCDCDCOCDCOCOCO N^Or-NCO^lOOSCDU)^COCN|r- 1flO^COCVJr-OT-NCO^ COSCMCfi(DCO(DOOOra)OrOO C0'"C1OCDOO)T-(000S ^NCOro(0(0C0T-C0C0O00^0)OC0 OOCMOT-COCMCDCOOOOtO OCMOJCDTj-COOOr^T-CM xj- CO CN CO CMLOT-OT-CMT-CMT-CMT-COOOCO^-OOOOCOCDCMIOT-COCOCOCM 001OCD00C0O5T-000OI-O> CM • CTi Tj-CMCO(X)Tj-TrC0T-C0TfC0-*-O) CNCOCNOCNTrCOCNCMCOCN CMCMCNCMCMCNCNCNCMCNCNCNCMCOCOCO COCOCOCOCOCOCOCOCOCOCO T-T-^-Y-T-T-T-T-CMCMCMCMCMT-T-CM Tj-Tj-^LOLOLOLOtOlOLOLO r-OT-MCO,<tmCDOT-CNCO^O'-r- CNCO^^COCNr-OT-(NCO OT-OINCOCOCDCD^OCNIOOOIO^N COCNOCNT-OCOCMCOOM-CD NONCDCOin(00)0>^CONOlf)OW OOOOCM^IOCOCOCOCOT-O) CDCMT-^TTO>0)COCOCMCDcgOT-00>0) COOC0CNIOT-O)WCNCMCMCO cft(D^NQT-T-^io(ocoif)cNO)CNU) scoit^corooiocoi-mco Nr<OT-COWO)CONrCO(00(MON CNT-StOLnONCDCOCO^CM CMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCM COCOCOCDCOCOCOCOCOCOCOCO inioioioinu)in»(0(Ococ£>(0(0(D(D CNCOCOCOCOCOCOTJ-^1^^^' N^O^CNCO^IOlO^COCVJr-OT-CN CMCMT^O^CNCOCOCNT^-OT-172 APPENDIX E. STRUCTURE FACTOR TABLES FOR RODALQUILARITE 173 Q. CD 3 CD T3 O <0 OOOOOOOT-T-CNICMOT-OOT-T-OOOT-OOOT-T-OT^-OT-T-T-T-OT^-T^OOOT-O o osoN«*coo<jT-^inoo)soNT-oiconi-<ji-saooosif)r-nT-Nr<<viO(0'fU) LL CMTj-COT-COmCMCOTl-' ' CMIDnCMtOlO'-Wintm^f T- CM CM ' CD CM r^- TJ- ' TJ- TJ- TJ- CO CO o i-ot'-ncocDnT-sntn^ocooonT-orinfoovsoi-t'-ssnifiNNinnsstoiti LL CMTJ-COT-COIOCMCOTJ- WOONlDmi-niO^lOlM* T- CM CM CD (M N i- T- T- T- CD CO — i-rrrrm-rri-^rrrm-rri-rrrrT-i-T-rrrrrrrrNNNNN ^ ^^^^^^M'^IOIOWWlDAiniOIOIOIOlOniDnUl^COCOfDCDOCOCDCOCDOCDSSNSN J: n^incoscocnoN^io^coN^o^wn«u)(DNcoo^ncM^o^Nco*incDu)^n CO OT-O'-'-OOOOOYT-T-r-OT-OT-OT-T-OT-T-OT-T-T-T-^OT-O^-t-O'-'-T-T-T-o cOT-OJ01^u)ocDT-co^^^c^l^coconoN«^-0)l0^o^ln^leoc^lcDc^^cJJO)CDcDC»^ocD LL CM CO fl" N T" Cv| N Cv| N 'COCMr-^COlOCMinCDOCOr^COCOtOCJlCOCOCO'CO'CO'Tj-CM CO T* CO ' TJ- I"III. I III , 111 o scoST-Ncoocor-«)ncomo)ONnncDTfcOT-TfoionoinNflOTfcoTfcoinir)oicocoTfT-LL CMT- CO S CM CV N N CDCOCOCOmCNCOCOOTtr^-h-COCOOaOCOCO CO TJ-IOCM CO T* CO T-T- M J£ OOOOOOOOOOOT-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-CMCMCMCMCMCMCM .C T-CMCOT^lOCONCOOlOT-T-OOlCOSCOlOtWNT-OT-CMfOTl-inCDNCOCnOT-i-OOlCONIDB) T-T-T7T7 7 1 1 1 OOT-T-T-T-T-OOT-OT-T-T-T-OOOT-T-T-OOT-OOCOT-T-OOT-OOOOOT-T-CM CO I o o •& p O TfcOOSNCOCMCDOJNT-SttTfT-cOCOSNST-lOT-ffiTtoOOST-TteOCftOCOM-CMCONT-TlcO LL. 1 T- CO CD CO Tf (O ^ V 05U>r-j.Tj-T-Tj-r^iTtT-CO T-CMCOCOIOT|- 'lOCOC^T-CMCOCMCDCM O CDT|T-SN(OONO»NCMCOCO(OCMT-lf)cOCOCOCMCMCOCMCDCDO)COOCDO)0)COOOT-T-OT-COO)ir) LL T-T4-COCOTJ-CO CMCO T- O) If) CO T- t- T- CO If) T- TJ- T- T- CO CO IT) T4- TJ-COCOT-COSCMCOCO o 3 L_ .«-» co T> CD 3 o T-CMCOT;U)(OSCOCMT-orocOS{OIOT|-cOCMTjOT-c»ICOT^incDSeOO)CMT-00)« c CO T3 CD £ CD co JD o W ^OO^OOOOOOOT— «i— TT-T-OO^T— T-CNT-T— OO'f— ^— OT-OO'T- oooo-»— OT— O1^-O 10WlOin(DC\|00)WNCOOCOMWCNWtNOJT-00 1 lfiOlOU)rOOOO)(D(DO^^T-CNlO)CO{Nin U- h- CM 1 (D N CO CM CM T- CO CO CO N CM r- (O Tf N If) CM r- ' CD^^COCOCDCNT— T— CNCOCNCDCOCD It II II III — I I || III II O CJ>C£>COr^OCjDTfOCOO}C LL l^^-CM N N CO CO CM T- CM CO CO S CM T- CD ^ CO LO CN T- CD COCOCJOCMT-T-CNCOCONCOCO — OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO ^ ^J- ^ M" LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO CD CD CO CD CD CD CD CD CO CD CO CD r----C Or-Cs|COTfLOCDr^00050r^CO 0) O^-OO^-T-O^-T-^-T-OT-OOO^-OCOT-CMCMOOOT-r-OO^-OOOOOOOOOr-CO O CMCOCflCMC0CMffl0)OOOC0^NCMO00l00)T-n»-(00)^ U_ CN CN • Co CO CO ^CMWCMCDCO 'NCO^Ol^CO^-^COCOlO ^T-Tf-T-00T|-cO^cO^ CD CM CO CN LO ^— r~- O T- CO CD h- LO LO CM CD CD CM CO O — ^~ M" CM T— O CX> CO CO CM CD CM CM M" CO CD (J) _ ^ ^. ^ ™ T-CMLOCMCDCOT-NCO^O)Tj-Tj-CM'-Tr'NTCD TTT-^-T-COT-COT-CO'^- CO IS- CM CN CD CD CO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOT-T-T-T-T-T-T-T-^r-T-T-T-T-T-r-T-T-T-T-T-x-r-T-CMCMCMCMCM T-CMCO^incDSCOOJOT-CM^OCpcONCjpifi 174 m T- o o T^OT-OOOOOOT-T-OOOT-T-OT-T-OT-T^-OOT^T-T-OO upcMCM03^u5T-coc\i(OT-i>» ^- ^^s^vnin^^uoNinuinn^w 1 1 T- co 1 O m T- CO S in<OT-o-*cvic\ioooocor^Tf<o<Dcocn<oo^cMCNic^ cNN(D«iiot-ncM(OT-s T- Tfns»- + cocDin^<ocMinio^f0^v T- co o w T— CMCMCMCMCMCMCMCMCMCMCMCMCMCMCNCSICMCMCMCMCMCMCMCMCMCMCMCNJCNCMCM™ r^<OODCOCDQpCOCO(OCpG3<OCD ocostDin^nN^ot-cNinTfocfcostoin^ T-T-OOOT-OT-OT-OT-T-OOOOT-T-T-CNOOOOOCMOOT-OT-T-T-T-0-<-OT-OCN| co(DOTnoS'-noNinNNT-*iNNcOT-ioi>i(\i • h> r>- m 'IN CO CO m CO *J- 1 T- ' T- r~-• i i r^00C0C0II}C0C0C7>OinOY-l0CMCDC0C0C0OCMI^OOOC0C000CD00TtC0Tt CO lO CO CMCOCOT-COOCOrnCMr^T-T*CMCMCJ>T-^CMCMT-|-~r^Lt2 CM co co co cn ^ T- T-CO 0. c 3 cr CD •a 2 £ o o 45 2 3 "G 3 "a CD 3 O CMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCO ^(ONr-OT-NfOT|lO(DNCOCnOT-OCI)CDNCOin^CONTj-0^ T-OOT-T-OCMT-T-OT-T-OOOOOOT-OOT-CMOOOT-OT-OT-OT-OOOOT-OOO WCOCONCO(OT-*0)COUlT-CNINCO(OCOOCOCOCOCDNT-COCOSCOCOCOCOOOSCDCOSONtniOT-(scOTfCDOicooi'co ' TfNtor|-i-nNNcomcor)iO'-vrin«T|-Tf • iocoio<fcoNNSNincN ONi-ONioincoc))i-iT)iocoos»cooco*'tN»NO>nocov(»insco O <t MI CO CO COT-TrNCOi-T-CONNCOIOSCMv-r-*innT-f mcOCOlOCOCOCMCOCMlOCM NCVNNNNNNNINNNr-r-^r'r-^Y^YTVTVVVVTTTVT T^OT-CMCOTtincOI^COC7>OCMT-OCncOrYCDU>T^COCMT^OT-CMCOTt T3 c CO TJ CD £ CD CO o « T— T— OT-T-T~OOOOU0OCN^OO^OT~T-T— OOOOOOOOCNOOCNIOT— O O i- o OOr^lO^-h- 1 O) Ifi O N CO N CO ' CO T- CD CO O CO 1 NlOOJCOCOCOi-fOOCOCO 1 OCOTfcOT-crjON LT) T-- 1 ' ^ CO TfCNCO^COCO'CMLO ^CsJCO^CMr^CO^COOpCMCO^j.^ CO ' CO O O^OCOWNCDQNCNCONO)^C\JLnCNCOC^C^NC\IN CO T- CO T- Tf N CN O) COCO CM CMCDIOCNSTrr-COCOCMS LO CO CO O) i^r^r^r^r^r^cocDcocococipco • I < « O^^T-OOOT-OOOT-OOOOOOOT-T-O^T-T-^T-OO'T- OOX-OOOO^-T-T-T-O ^NOLOONO)CO»ON(DO)TfT-0)WCNU)COC\ltWNCOQ U- CMTj-T-OCOLOTt-CO 1 CN^COCONNrOT-CNICOCO 'T- CM O) N ^ CO CO CO ' LO -NT LO CM CO r-- 1 CO i i i I ^— II i i i » i IT i O ^CDCN<flt^OO)CNT-OOOlf)^OincO(OCOWCOCOiflOCOW LL CN^T-OrtffilOCOT-(\WO)^NS^t-C\JCOCO T- CMO)S^COt-COC0 CO LO CO CM 1"-- T- CO T— f— T— ~~ ooooooooooooooooooooooooooooooooooooooooo CMCNCMCMCMCNCMCMCMCMCMCMCNCMCNCMCMCNCNCOCOC^ JZ CDU)T|-COCN^OT-C\JCOTfLOCDNCOCn 175 T-OT- OOTJ-OT^- T-OT^OT^O-i-T-^T-CM-t^T-T-OOT-OCMOOOOOT-OT-'r-T-CNIO'*-ocom^^-T-cNO ^scoiOT-inificoinificorNroncNicoinocoiOTrin^Tfnnioffi If) CM o Y CO 'CO in CD CM 1 T- CD CO CM CD 1 o CO CO COCOCOCM-I-CM^J-CM^IO^-IOT-I COCOONNCMCM^- ^SC\|inM-fflOr^COlDCOOOO)tf50lDCOOSlOIO(OW(Ot©WCOOU) CD CM O T- CO CO LOCO CM T- CN LO O *- 1^ OO OOCOCOCMr-CM^CM^W^lOr-CNCMCMCNCNCMCMCN COCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOW 'l''T'T^"'l"'T"^f'l' ^T-T-T-T-C\IC\ICMCMCMCNCNICNINCVNCMCMCMNNW r-OT-Mco^-mco cxJr^cxJO^o^oc^cor^cDu^ ^— OTJ-T— OT-OT- OOOT— T— OOOOOOT— T— T-OCN^-j-"f- OCNOOOT— T—r— OOCNOT-O CD ' LO CD CN ^ r-t^T-COlOT-LOWCOWTj-CDCpOCOr- 1 CDCNICVICOCOT-COr- i (\| r 'T-COCM lOOCMCNooco^-co t^a>^ocot^f^t^<D^co^ooiinc>i^t^^co^cAc^oc^c^a)<oc^tococi> LO M" LO CD CN r- T-CDLO^LOTfCOLOTj-CDC7>OCOT- (DCMr-COCD^CO'-r-T-T- r- CO CM T-T-T-T-T-T-I-T- COCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOC^ ^•TTTf^TfTf'^'N' COCOCOCOCOCMCMCMCNCMCMCMCNCMCM LO^-COCMT-OT-CNJ ^IflCONOONT-OCOCONCOUp^CONr-OT-wn i i i III ^•'^'-'-^-Or-O CNOT-T^CMT-T-T-OOOOT-OT-T^^OT-T-OOT-CNOOOOOT-OO CMIOT-COO>T-COO TTOr^OCNr-OCNCOCNCNCO^TfCNTf^CNM-a>^CO 1 N CM O) LO CM CD CM CO CT)r-CD^COCO^COCVJC^Tr CM CM Lf) T- LO 1 r- CD IN CM T- CO N ^•COCMCMCOCMCMO) rOS^CMLOT-COO)CM^S^»-CMLOT-^CD^COO)cDiOcDO^OCO(ONCM N CM O LO CM CD CN CO CD'-CD^COCO'tCOCSICDTf CM CN CD T- LO T- CO CM CM T- CO h-*-^--«-T-T-T-*-T- CMCNCNCNCNCMCMCMCNCMCMCNCNCNCNCNCNCMCN^ OOOOOOOO LDLOLOLOLOLOLOLOLOLOLOCDCOCOCDCDCDCDCOCO NtOlO^COCMr-O rOCM^OT-CNCOM-LOCONCOCM^Or-CMn^LOi^ OCMOOr CMMO 0^*-00T-000CM*-0000CM0T-000T-0000T-000-<-C\| LO 1 CO lO T- S ^ O CO ' ^T-CMOCMtOcOONCOCD-rCMO^CNIOOO)^ 1 T- CO If) O) ' O CO ^ O CO — ~» -~ — ^in7^9^^Vmo^®^a^m^^^NCSJ^Tf^T7'*c»)(7 cocohj. ^LOLOTfio^LocoooM-Lor^ococoa>r^coa>c^ CM ^^COLOCOT-cOCOCDCOCOCOCMCOCOCM'i-h-CM T}- f^. T— LO CO CD CO CD CNCNCNCMCMCMCNCNCNCNCMCNCMCNCMCNCNCNCNCNC^ OOO^^^T-^T-r-r-^T-^T-T-T-T-T-T-'t-'r-T-'i-T-T-CMCMCMCMCMCM NCDin^COCM^O 0)O^T-OOTCOr^CDUp^COCNT^O^CMC^ CNT-I-T-CNOT-O ^-OOOT-OOOO^- 0-*-T-OCMT-OT-00 O O T- o O T-LOO)CMNOT-T-CM CD(D^CXl^CM^LDCMCOCOCMNCX)^inCOCDCT)CO(0^ LO ^ ' CO CN CO COrOCOCMO)T-CMCOtM^O)00^ WT-rocOSCMCMT-CMCDCMr- '(D^OTr LOCONNLO^CDM" COLO^CDOiCNM-U^CMO^LOCOOCDI^CNI^C^ LO CO CO CN CO COCOCOCMCOT-CMCOCMLOOOT-LO lOT-0>C0r^CMCM-*-CSICDCMt- CD CO CO M-OOOOOOOO CNCNCNCMCNCMCNCNCNCNCNCNCNCNCNCNCNCNCNCN M"M-M-^M-M-M-M- Tf-^COCOOCOCOCOCOCOCOCOCOCOCOrt OON(Olf)^COCMr- NOOCM^OCftopN(DlO^COCMr-OT-CMCO^W 176 CO T- T- O T-OT-OT-OOOT- OOCMT-T-OOT-OOT-OOT-OCMO t^Oroc^JT^•()^^cftC^lCO'ICI)C^lT-^OCO^T-^CDOOCDCOCOCOOCOO^COT-COT-CIl^r-fflCOCO CM OO r~ CO CD CM CM 1 CNlOCNT-T-TtCMCOT-CMT-lfl cocor^r^o^o}c^o?iocoincN^T-Ttcoc7>cococoT-o^r^c\iT4-c^ COr-LONlOr-T-CO CO CM IT) T- CO CD 1" PJ CO N CO CD CM T- CMCDNT-i-COCNCD'-CV'-in cocococococococococococococococococococococococococococococococococoeocom COCOCOCOCOCOCOCOCOCOCOCOCOCOTfTtTfTf^Tt^TfTTTfTfTrTfTfT4-Tt '^COCMT^OT-CMCOTtU5COI^CDC»COI^CDin'<J-COCM in CMT-T-OOOT- O r- o o T-T-OOOOOOOOT-T-T-T-OOOOTJ-OT-T-OT-OO ^COCD^OCONNCOCOT-CNICOC)lCJ)CN|COST-T-^WfflCOC))LO*NO^OSCOCOT-WCNICOBlO T-LOfflCNCD^inOOIOCDNCOTj-CNNCOTj-COLOWCOr-MTj-CJlCpn ' CO(OCNvrT-incDNC)10CDT-COWCONCOCOWLOOOO)C»T-T-NlO^UO^NSCOt-CO^COCDlO^ OlfifflCNCD^lOOCTJIOLONlOTrNCDCOT-COinCDCOT-CNICNffiCDCOlOCNT-T-CO Tf 3 *y CO J3 o £ o o o l_ co T3 (U 3 o — cococoncococococococoncocococococococococococococococococococococococoococococo T^T^T^-^-r^YT^-T^YT^-T^T--T^-T^-T^T^-T-T-00000000000000000000000 JZ I^CDUp^cOCMT^OT-CMCO^inCDI^COCTJOCMT-OOTCpl^COW in OOOT|-T^-T-OOOOOOOOOOT-OOOOT-OOOOT-OOOOOOOOOOOT-Ot-O COCOCJllOCOSCllCOOT-CDlOlOCDlOT-CJlCOr-COCOCOCNLOT-CDCNCO^COLOlOCOffl LL If) CO CM ' ' 1 CMCMCDTj-CpT^-^CvllO 1 CD^U)T-t^C\WIOTfNTj-Tj-~T-CONCOCOCNCOCO 1 C7> T-O LOOT-CDLOCONIOGCOCDIDLDCOCO^OT-T|T-COCOCO^NNNSTr(OLON^NLOIOCOCON'IN LL U01-CO C\lT-ct)T-COT-TflNCOT-STtCDr-T-c\|CN'«'*CD'-T- T-CON00COCMCOC0 CJ)T-— cocococococococococococococococococoeococococococococococococoeococococom a cDcococpcpcDinupir)tnu>u)U|)u>inu>upini^ -C Ni|-OT-NCOOC))CONCDinTfcONr-Or-c\ICO'tinCDT-OC» •o c (0 TJ CD £ CD CO J3 o T-OOT-CMOT-OOO OT-OT-T-CNOCOT-OT-OOT-OOOOOT-OOOT-T-O O 1 ONOO)*fCDCOniOK)TtnU)CNON 1 'CD^CNT-CDCpcacOONCOCDtmO^SCNCMCOCO LL ' 1 ONCOCOMOinSCMSCMCOT-CO '.lOT-CNC\INTC\C\ICMCOCOT-CM'-'fTtincNTj1COT-^ II i II i T^-r--it_ii II^—I i II i O TTC»C7>C7>CMr^ir>COCOlOC7>COCOCMCDCOT*OOCDCDCOWinCNU^ LL OJCOCDCOSCOlONCVNCMCOr-CO Tj-t-t-CMCM COCOCMCOCONNT-^^CDCM^COr-CNCNCNNCN«C\ICNNNNCNNNCNCNCNCNC\NNCNCNCNCNCN«N CMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOW U)^CONT|-Oi-NCOTfincDNCOroOO(»COS(Din^cON I T~ t-OT-T-T-T-T-OOT-T-T-T-OOOOOT-OOT-T-T-OT-T-OT-OT-r^-OT-OOOT-Or-O l0ONST-T-0)^N0)ffiC0C0OT-rC0NT-T-Tfc0OC0O0)OOC0NL0NT-TtCM«'CVC0 O CO CD Tj-lDCONMYNinTj-COCNT-COincONCNCNIOOSlOinCDOCNCO 1 It) T- CO <- ID T CM CD I I I coT-incoT-T4-cT>'**oio^cT>cDCMT-incor^T-ocoTroT-cococ7>T-T-OCO<DT-TfinCDCMCMTfNTf*CO«r-cOlOCOCMC\ICMlJ)T-SlDlOCOOCMN <f T- n t- ll) CM CD CNCMCMCMCMCNCMCMCMCMCNCMCMCMCMCNCMCMCMCMCMCMCMCMCMCMCMCNN CMCMCMCMCMCMCMCMCMCMCMCMCMCMCMT^T^T^T^T^T^T^T^T-^ ^ CO CM r- O T-'CM CO^Ii)CDNCOC))OCNlT-OC))COSCDlO^COCN^OC\CO^U)CDNCOO)OCMT-00) 177 OT-OOOT-T-OOOT-T-T-T-T-OT- T-OT-OOOOT-OT-T-OOOO *00)tO(MOCD*(Oin(Mr-»OS(MCO CM cp 1 infiOT-r'P'-N'iP'* io(0(\iio<oNioinoo'fvoo)T-insii)U)iniDsn 'r-iv-^coivir) rji ^j- i- r- co T- CM co CO CD T- co 10 r-r^Tj-COr-lf) IN •» * r I- CO T- CM CO cocorococoroco^Tj-Ti-Tj-Tj'^'vi'Tr^^ inLoioinu>ioioioininioioinu)iniOLnu)iOLOiOLOin lOlOIOCOCOCOCOi^l^^COCpCpCOCOCpcp CMCMCMCMCMCMCMCMCMCOCOCOCOCOCOCOCOCOCOCOCOCOCO Trioco^oT-cM^fcocMcorYCDupTj-cocNi ^Ov-MOTfin(DNcoi^(DcOTfncv^or-rAinTtin OT-T-T-T-CMT-OT-CVIT-OT-OOOO OOOOT-OOT-OT-OT-T-T-OOT-OOOOT-O TtCT)COO>T-0)CDlf>CJ)OCDCDCDCOir>lf)tJ- 0)CON(01N00300'flOOO(DCI)^CO^tJ)OCOSin(D T-cOT^{XJC\icpup^cpooocj)Cj) co cviTtT^i-.T-T-T^-t^CNiCJj'fi^ T-T-CBCOTJ-COCMCO'CM TfcM'^Ttc\iT-o'st-cor-r^LO'sftDr^r^Tt T-Tti^ocMO)0>r^cocDcsic\ir^OTj-r^c\jr^cocNiT-T-TJ-T-SN(0OTC0CD030)0) CO CO T}- T— f— T— T- S (M OJ T| N CMT-CJJCOTJ-CMCMTJ- CM 0. CO 3 CO •a o COCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCO inLOinuOIX)LOLOObOnU)IOIAIAbObOt01010IOIOLOIO T-T-T-T-T-r-r-T-r-r-T-T-T-T-T-T-T- CMCMCMCMCMCMCMCMCMCMCMCMCMCNCMCMCMCMCMCMT^^-T^-T-OCncOr^COU|)T^COC\|T^-OT-C\JCOTtlf) Nr-OCpeOS.(DIO^CON^Or-Nn>flO<DN(NT-0 OOT-OOT-T-T-OOOOOCMOOO OOOO OT-OOT-OOT-T-OOT-T-T-T-OO (0 I o o •2 a> L_ 3 o 3 •a CD cDuocMcoajT-cMT-csitcncoi^f-cocoo) OTCOCOCOCMT-^-OCO CO CO S 'O^^niNCpTfNNC)! CM CO CO T- T-t O CM ^ CD -CMOOM*OWT-CDO>a>COT-Tj- CM CM hp Tj- T|- -r- CM CM OinnT-OlMMONtOltSNMiOO) 030)inionNCI)<fCM'-StMOOll)01CMiri(DOfMO LL T-CO CO CO 0>T-'0-COCMCO'<*CMr--CM CM CO CO T- T- S<flDT-lfi-INNN f CM CM CM COCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCO Tf^Tr^TfTfTfTfTj-Tj-Tj-TfTfTjTj-Tj-rJ-TfTI-Tj-Tj-^Tr ^cocococococococococococococococo nnnnxf»jTfTt*<Ti-Tffl^Tf>tTj-rr^inioit)in NCMT-OW00N(DL0T|(0(Nr|-Ot-CM[0 lO(OSt»N(D«^(OCMTj-OT-CMCOTj-IOCDN^rOCMTj-T3 c CD •o CD £ CD (0 JD o OT-T-CMT-T-OOT-OT-OOOOT-T- T-000T-00T-T-000T-0T-*-0T-0T-0OO *LO*CMr-T-lOT-0)CDIl)(D^OlOO) 1 CO *f Cp CO 'CMT-cpiOI^CMCM-r-^-^^ *CMCOO)OCOCMO^CMiniOCMO 1 1 rrOT-COCOr 'CO 1 IDlOCjT-i-T-^Nnn'fO)LONCM 'CM niOfOCMCMLOLOr-T-OJSCOSO^N^ OCDr^T-OCOOmcOCM^Tj-oCMTj-CMCMCDOI^OCOCO ere CD oo f CMT-MOSNCMI- * 1 s T- co comcoT-T-T-TfcM t o> in r- co CM CMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCM •^•vt'sf'Nr'^'Nf'^^TtTt^TrTtTf-^Tt'^-^'^Tl-TtT^Tf TfnN^or-cNin'fincoNcocscoin^ oooooooooo coNT-OT-CMntmcosoooirMT-ocDooscocot" III T— Y— I I I I I I I OCMT-T-OT-CMCMT-CMT-OOOOOT- OOOOOOOOOOOT-T-OT-OOT-OOOT-T-NOOT-T-MjncMooi-oicoo)T-sn oicMsoocoTroioconinooi^frMNCDT-T-i-in CMnT-CDCNTfNnNTj-LO ' CO CO CO T- CO CO 'l-COlOCOCOCMCOmcOCMCpCMT- CDT-lOr-OCOr-T-OJT-TfT-TfcOOJNCOlDNlOr- 0)in00OT-T-C0^N^CMCM0)COC0itCMC0CDCMT-T-l0 CMCOT-COT-LOCOCOSn^ CO W SCO T-COCOr-^-CO'tCOCMCMCOlOinCMCDCMr- COT-IOT-CMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCM ^TtTtTtT^TfTt-sr-vt'^T}-Tf^T^Tl-TtT^Tj-Tt-sfTI--st-Tr ooooooooooooooooo cDNCDin^nwr-OT-cMco^incoNoo cpcpcpcpcpininininipinininininipinininw ^Oi-NCOOC»CDN(DIO^COCMT-OT-CMCO'tc()T-o 178 OOOOOOOT-'r-T-'r-T-OOT-OOT-T-OOOT-T-O-'-OO OCNOT-T-T-QOOO ^CONO^COlOO^CNIlOlOO^lO^CNJinCNISffi^CONNOO© COIOT-T|-^CNTJ-T-CD(DCN T-T-inT-CNNCMCNCNi-CM^^NCNr- ' IOT-COCOIOCNCOT-CNICMCOS LL. CO LO ^- CO CO CN r- LO LO CM T-WT-CMCOCMCMCM^-CM^-T-COCM LOT-COCOlOCMCOT-CMCNCOr--lOLOifllOLOLOLOlOlOLOlOLOlOU)LOLnciO(DCD(D(OOCO© CO M" ^J- M" Tj" TJ" M" M" LO LO LO CO CO CO CO CO CD CO CO LO LO LO LO LO LO LO LT) LO LO LO LO Tj" CDCOLO^COCNVJ-OT-CNCO^LOT^O t/i OOT-OT-OOOOOT— OT— T-T— O^T— OOOOOOOT— OOOOOOCNIx—O O OO^COOCNOT-COCNO^T-LO^CD^LOCOO^O^ LL T^COCOCOCO^CNLOr^LOCNTf ' -rj- CD ' T-LOT^COT^T^COCN CO T-J- 1 CO M" CD CO r-O O t- CM ONCDCO(OncO(DCDM,<DCOlOlOLnLOr-0)T-COO^LOTfS^ T-COCDCOCDT-CMLONLOCM^ M- T- CD CMCOT-COT-TtCOCO COT-T-TJ-^COOOT- T— CO LO 3 o-CD 9 2. in o 13 .2 a> 3 t> 3 T3 CD 3 o OOOOOOOOOOOOOOOOOOOOT-T-cj>opr^<Din^cocMTj-o-r-cs)co'*4,iocDt^oOT-oc»cpr^ tO T-T-T-T-OOOT-O OOOOT-T-T-OT-T-OOOT-OO OOT-OT-OT-OCN o nlnc»lDn^-^^olnn*Ntoo*ou)no(Dc^l^uInolnoN'-*o^^T-*onc»(o^ LL T«- CO CM Tf- CO CM TJ- TJ- f- Tf- lO TJ- CO CM IT) 1 lfilOCOTj--rj-COCOCOCOIOCM-rjOpTt-T4-Tj-'cOCO 1 O CO o T-T^sM-NCSO)iocotoocOT-inon^oinu)cosNT^(\i[j)iococOT-B(owNOiofflQO)Ttto LL T4-COCMT4-COT-CO T- r^Tj-ioT-cocM & tiflNT-T-foincoroiowT-NT/M-T- CM w o co Tt^TrTtTtinioioioioicioieinioiniaiflininiaiainiouiuiiniooiaioioifliainia ininioininto<otD(0(Dco(D<DiD(Duiif)u|)uiir)u|im JZ Or-«COTi-COS(DlOTj-COWTjOT-OCftCON(pU)T|tONTjOT-Nn^ T3 c co "D 0) CD U) XI o T-T-CMOT-OT-OT-CMOOT-T-OT-OT-OT-OOOOOT-OT-OOOOT-CJT-T-T-OO roTj-rooor^TT'*T-r^cDCDr^Ttooi^cocMcsiTtcsic»T-ocor^-«4-T-Ti-i^(oocsio ' o CM T- CM to * c« cOTfcnio CM n m c» co CM CM w cOT-ooito)cosT- lOcocMiocOTf-T-cMin^cowcDincOTrco Tj-Tj-om CM n m c> co CM CM co cot-i^Ti-cncor-T- KicMCM»inTj-T-(Min n m LO TJ- n T|- co OOOOOOOOOOOOT-T-T--r-T-T-T-T-T-T-T-T-T-T--r-T-T-T-T-T-T-CMCMCMCMCMCMCMCM CMTj-OT-CMCOT<-incDr^COO>T-Ocnopl^CDUpT|-cOCMTj-OT-CMCO » OOOT-OOT-OO OOT-OOOT-OOOT-T-OOT-OOOT-OT-OOT-T-OO 10CMT/0)Trc0100iniOOCOCONOeMCMT|T-T-TfTfcOTfcOOO ' co co ^ in 10 tn t- 1 1 o M- o co'cOTyT-T7co' T^TJ- to COT^^C»T|CO^COON«>COT-CM(DT-ir)CnOOCOCJ)TtlOTJCOlOCOT-COT-M-tOOCMU>CMWlf)CMCO CO T- CD CM U) CO T- CD CO CO CO T- CO CO Tf CO If) t CJJTtO COT-COT-OT-CO T-T* Tt T^ Tj* -^f CJ)opr^eOU>T|-COCM-r^O-T-CMCO-TrcOCDCMT-OOTCOr^(DU^ 179 OOT-OCMT-CMOT-OOOOOT-OO O O T- T" T-OT-OT-OOOT-T-OOOT-o tocj>r^T4-T-cT>T-T-cT>c©cocMcNcocO'<*inT-c7>'^cor--oo>coir> ooce^T-T-OT-cMNCBoiinojcsi LL I^T-T- LO CO CO CM tDCjlTfr-Tf 'IDMOT-'iKO CO CD CO LO T- ^ 11) T-T-CMTj-ttTrCMT-CM CDCOCDCDCDCDCDCDCDCOCDCDCDCDCDCOCDCOCOCOCOCOCOCDCOCO COCOOOOOCOCOOOOOCOCOCOCOCOCO TfTj-Tj-TfTfT^^Tf^TfCOCOCOCOCOCOCOCOCOCOCOCO CMCMCM-^-T^T^T^-T^T^-T^-T^-r-T-LOTfCOC\T|-OT-CNCO^T-0(JlcpSCDinTfCONT|-0'-NCOTr or-cvicncpi^cpip'fcocsi^-o OOOT-T-T-OOT-OT-T-T-CNO O O O T- O O T- ooooor-T-T-000000 o ocjicocNOCNNcocnT-cocDcoNcooNincococniNcocoinTr ir)i^otmcT)c»coior>-'<i-coxj-o LL lO CO LO CO 1 C7> 1- LO 1 LO Tl-'I^T-C0,0>4T-COlm'*l~- NfrtCM* 1 S t- IJ1 T- I- f) f i I r ll II i ll I'll ll II CO»COCNlT-Ttl^T-TfCVllOCDCDCOC»T-t^eOT-COCOlOlOI^T>-CSI OOlOMOfOCOCDCOTrLOLOOl . _ _ _ . CM *cT CM O T- • LO CO ID CO cj) TJ- LO LO r^T-co co r- co in f s CO T- T- CO iDLOLOioiOLOiDLOLOiOLOLOLOiOLOioiOLOiOLOiOLOLoioioio r^r-~i^t1*-r^r^r*-r'*-h-r~h-r*-r^-r--T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-CMCMCMCMCMCMCMCMCM l-T-T-T-T-v-T-T-T-T-I-T-T-IN 3 CO •a 2 % CD i 3 O 3 CU -4—» m 3 O CO o •a c CO T3 CD £ CD CO .a O J= Cpl^cpUO^fCOCMT^OT-CMCO^rUlCDt^COOrocptYCpin^C^ Cp^cpul'|-COCMT^OT-CMCO'*|v-OT-OOOT-OT-OOOOOOT-CMT-T-OO OOOOT-OOOOOOOT-T-O COCO»NCO(»0)N*C\ILOlO<!)IOCOLOLOO'J-r-COCOC\|T-COCO SCOCOOOCOMDOBlCOrirO CM LO O) Ol tf r-LOrr-TCTOCM^T-T^CMTI-CnCOTfr^CM^-rl CM CM CO CD ID f ' CN CD CM hp O COL010CMCDO)ONLOT-T-lOCDCOCOIOCDOinOM;COCMCMCDCJ) COCOSOOOJCOCONCOr-CMSCM LL CM TJ-T-LOT-CMCM T-rtOCMI-T-T-CM'O-CnCD'M-T-CMT-Tl- CM CM CO CD IT) -"J- CM T- N CM S IOIOLOLOLOUOID1DLOLOIOU)IOLOU)LOLOLOL01DLOLOL010LOLO r^r^h-l*~r^.N.|*-h-r*-l*~r*.h-r*-h-T|-^T|-T^^T|-COCOCOCOCpCOCOCOCOCOCOCOCOCOCOCOCOCOCOCO T|-COCOCOCOCOCOCOCOCOCOCOCOCO .C Or-CMCOTfincMT-OCJCONCDinTfcOCMr-OT-CMCO^lOCDN COOC»COSCOLDTj-COCMr-Oi-N III I OOT-T-T-OOOOOO O O T- CN T- T- T- OOO OOOOT-T-OOT-OT-OOT-CMLOCOMOlf»CNOLOT-T-LOCJ10)COS 'CD 1 r- LO CO CM >- CO LOCOCMOLOCOCONNCMT-TTCOCO TfT-CM^CMCMir>COC0T-U>T-T- t CO ^ CO „ CN CO CO CJ> CM COCMCOCDCDLOr-r-nr-NCOCM 1 T-^COCDI-1-COr-O^-CMOI^T-OCOT-TrcOCOOCOCOOCOCO COSCMOfCOCMOlCOCOCMLOMO fr-T-fCMCMIDCOCOT-LOT-r-i-T-COCO CD CN CO CD CO CN COCMCOCOCOLOT-T-COV-I--COCM ^•Nf'sf'vt'sf'sf'xI-'vf-'xf'Nr-st^Tr^TtTtTtTrTTTfTf CMCMCMCMCMCMCMCMCMCMCMCMCOCOCOCOCOCOCOCOCOCOCOCOCOCO CDCDCDCDCDCDCDCDCDCDCDCDCDCD T-T-T-T-T-T-T-T-CNCMCMCMCMCM CMTj-Or-CMCO^LOCONCOfflOJCOSCOLOTJ'COCMTj-OT-CMCO^ ^O*-CMC0TtlOC0CD00r^cpLpT|-in OOOT-OOT-CMOT-CMT-T-T-T-T-T-OOOOT-OOOO T-T-T-OT-OOT-T-OOT-OO O inCM'-01COCOCOTf'-tO)CMLOTfNT-COT-NCDO>CMLOitTt LL T-|v.'«(-h.C0^-l~.O)'i(-(^l^'|-T- 'cDLD^fCMLOCMLOTfTi-CMS lOLOOCOS^NCOOvJ-CONCOCO CD * CMCDTJ-CONCOCMCOCOCOCD ^TtCDT-*COMOCM*COi-LOCM'-COO')-T-COO)0*T-T-in CDCD(DCMO)xfNCMLOCDOT-OS T-CDCONCOT-SOlTfSNTfr- CDTfM-CMCDCMLOTrt-lNNT- CD CMCDfCOCOCOCM<fO)'»CD — 1-^^Tf^^Tj-TfTfTf^TJ-^^^TtVffTfTf^Tf^TJ-Tt CDCOCDCDCDCDCDCDCOCDCDCDCOCD CMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCM COCMCMCMCMCMCMCMCMCMCMCMCMCM cp'YCpup'^COCMT^OT-CMCOTtlOCDI^COCNT-orocp^cpin'^ LOr-oacONCDBTj-COCM^OT-180 Ul OT-T-T-T-OOOOT-OOOT-OOT-OOOOOOOOT-OOT-OT-OT-OT-OOOOOT-I I III O C0OC0T-T-C0C010T-T*IO<DCN**C000T-OT-C0(0C0C0C0 LL CO T- 1 CDt-Nt-T-fCOr-IOr- CMC0inCOlf)T-C\lTj-(0C>ICNI CO CO If) 1 CO 1 TJ- CO CM ID CM 1 COOC0C0C0C0ffiC0C0C0COC0C0C000C0C0C0C0C0C0C0C0C0C0C0C0C0C00)0)0)0)0)0)0)0)0)0)0)0) Y^oooooooooooOT-rT-rT-r-rT-T-r-NN«NNcjnnnn«N«nNNr NncONCpiOT|-CONTjOT-CN)CONCDlf)T|-CONTjOr-C\^CO(N OOOT-OOT-OOOOT-OOOOT-OOOOT-OT-OT-OT-T-OOO O O T- o o cflM•lnco^nT-coT-^^eococDc^lcocOT-lnT-ocI)cocflOT-cvo)lnoco^Olnco^ocococ^Jcoo^-Tf LL CMTj-COCDfOOjT-Tfr-CD 1 1 CM If) CM CO 'COT-Tt CO CD CM I- ^- X- T- CM TJ- ' CO h- ^- If) TJ- 'T-a. c cu ZJ cr CO TJ o I I o t5 3 TJ =1 TJ a> 3 o SNSNSSSh-NNNSSNSNSflOCOCOCOCOCOCOCOCOCOOOCOOOCOCOCOCOOOCOCOCOCOCOCO CNC\ic\icMC\ic\ic\ic\ic\icNicococococococoinupin-**T^ COin^coCMr-OT-CMCOlOTfCOCMr-OT-lO^COCONCpin^cOCyTjOCflW OT-T-OT-OOOOT-OT-OOOOOCMOOOT-OOOOOT-OOOOT-T-OOOOOOT-I n > TfcosminmNT-ooo)0)CDTtcocDr-cooT-cocvinincO'tTto«oinNi07Sif)coNco[Oco T- TJ- CN If) fNCDTfTJij-CMincOCOTf CM (O r- CO CVI'f'r-W'IY'-CO ' CM r- r- CO CD If) N U)OCOCDCOCO^COCNlCNlT-NSCOSIBCOCNNCOWTfcONtDCDCOincDCOCO^COTj-SMCTjNinif)CD r-T-Ti-cvjif) •*CNCD'Tir)ir)CMcf)ir)cO'<r CM CD i- co •<»• CM -<i- CM o> r^T-r- CM T- T- co ID m N I— i— i— r^i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— i— r~-i— i— r~-i— i— i— i— i— r— ncOCMCNCNCMCMCMCMCNCNCNCNCNCMCMCMTj-Tj-Tj-CO'fOC»COSCDUj)TfCOCMr-OT-CMeOTfOrocONCDlf)'fCOCMYOT-N TJ c CO TJ CD £ CD co XI o OOOOOOOT-T-T-T-OOT-OT-OT-OT-OT-T-OOOOOO O O O T- O T- o ococoo)CDOcorMiocoT-*T-Tfino) 1 o>Tro*-ioco-*rocotf)r^'*c\iu5CNr^r^cj>0)ino)c\icoco in • co 'cotj-CMT-Tj-Tj-Tj-coioiOTj- ^T-incNcipeocviTj-cD cOTj-cNjcsi^upcNj^CNiT-co^csir-pT-rococD'--**cj>mcNiT*a>ocOT-**coOTrroc\iracDcococ\i'*r~co — — — -• — — - - If) T- If) CO CM T- CD — J co •<- co Mi-t'-'-coinif)T-T- COi-CNCMM-lf)CN'<i-CM''-CO'>crCMr^T-CDCDCDCOCDCDCOCOCDCDCDCOCDCOCDCOCDCOCDCDCDCDCDCDCOCDCDCDCDNNNNSNSSNNNN CNCNCNC\IC\IC\!CNCVJC\IC\lCOCOCTCOCOCOCOCOCOCOCOCO'*Tr'*^ cocMTj-OT-cMcO'*incohpCDupTtcocM»j-OT-c\icO'*Tj-cocMTj-OT^ in T-OT-OCMT-T-OOT-OOT-OOOOOOOOT-T-T-OOOOOOO 0*-OOT-000 O COCnCMN^lOO.-eOCMM-CMtONCftCft^CftCOlONfl'TfCOCO^CMM-CO^^T-COOCMOCMOT-rOCO LL TtrpTr 'OCSITJ- cOT|-r-cDr-p Tj-''^-if)cO'<fco,T-Tj-h->f)'*'-'7 IOT-T-CVJCO TjTj-r— O IOi-CMS(OCOCM'-OCOtDCMOi-*CO*OOSCO<-COT-COCOIf)MnT-i-COOi-|DOCMCOCMfM-LL lf)T-TC O) CN CM COT-0Oh-COT-T-'-ir)lf)CO'<J-CO i-T-f-lDTj-T-T- CD i- CM CO r- r-COCOCOCOCDCDCDCDCOCDCDIDCDCDCDCDCDCDCOCOCDCOCOCDCDCDCDCDCDCDCDCDCDCDCDCDCOCDCDCDCD CMNCMCMCMTjr-Tj^TjY^r-Tjr-r-r-r-r-r-r-tjr-OOOOOOOOOOOOOOOOOO (MCO*10CDT-00)CONCDIf)«COCM'-O^CMCO<-lf)CDT-OIJlCONCDin'fCOCMi-0'-CMCOTfincD ^— ^— I I t i I T • I • ^— ^— i i I I I f I I I 181 Tf •<- CM ^ m co TJ-0)0)0)0)0)00)0)0) TTTTT0000 inTfcocMTj-inTj-cocM T-T-OT-CMOOOO (DCOm^l-CMCMCOCOO T^inCMCD ' Cp CM f T-00 CO CO CO CO CO CO 00 co CMCMCMCMCMCMCMCMCM O) cp hj- cp in ^- co OOOOT-OOO niOIMSOONfT-T- 1 CM 1 Cp CO Tf CM •* J^I— r^i— r^i— — h~ OOOOOOOOT-CVI^OT-CMCOtlOO) OT-OOT-OCMT-OCM T- 1 CD O CM O) CM l~- CM ' T- „, CM r- CO CM CO ' T- _ fcoffononn CM T- CO CO CO T- T-NCDlOfCONT-OT-N I I I 7 i i i T-T-T-T-OOOOOO T-OCOCMCOCOCOlOt'-T-CM CM •» T- CO S CM CD K) T-I-MDSCOMDNO CM CM * r- CO N CM CD LO COCOCOCOCOCDCOCDCDCD OT-T-T-I-T-T-T-T-T-r^O0)cphpCpin'*f-cpCM APPENDIX F. STRUCTURE FACTOR TABLES FOR GRAEMITE 183 in 0)CMO0)OS0)C0NC0C0M-CDOC0O00NOT-S^00ST-S(N|T-tfflCflT-Ol0l0C0SC0T-N^ LL T-co*-cOT-a>CNir>T-oinior~T-a> a> co ^>-<-(MO«ro 10 CM T-iniocMn^-cMt-r-CNIr-Cnt-ONCO(OCOT-GlD^^NCftU)OO^COO)CJ)lflNCOr-fflWT-f\|0'^niONN^M-i-lOrO ^cOT-M-NOT-CDni-uiiocoi-cOT-mnT-NNM-cooNnoNiOt-nn^i-ionninNNri ooooooooooooooooooooooooooooooooooooooooo JZ CMCO^IOOT-CMCO^IOT-CMCOTTOT-CNCO'^^CMCO^OT-CMCO'^-T-CMCO'^-OT-CMCOT-CMCOOT-« co(N»*nMNffl«)c»o*nNonwNnT-coonoNcoiONnooi*nno)Ov»^ton TI- i- Tf in s to co o ss<-<-iocOMnincM fcocMNcoeocoit COCOO>COT-T--^CO(^CMCO CN CD C Q. E CD CO CO o o .8 2 o TJ CD ^—' TO 3 O CD O TJ c CO TJ CD £ CD CO •Q o T|-TJOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO SSOOOT-r-T-i-i-T-NNNNNCVIMCOCOCOnncOM-^fl-Tt^^M-lOlOUllOCOIOIOCOIOCO CM CM oi-N*coi-cvco^u)coo^Nco^incoi-<Nco^«)ioo^NcoTrincoT-c\ieOTrincDo^cMco Tftou)NT-NNOcoNO^*^'-wcOTrincococoinoi-coOT-eoi-omcoo>ocn lOIOC01-CO*C»0>010inONtD»SIOC010*0)O^C\iniOCONM(OCOO)lf)NSSCO^NWCO CO«l(00)'-COCO<,CO'-'-0^t-OMD*<-MVlO<,CM^CO*COr- T- CM CO CM T- T- CM CM CO CD M,lf)S*COtOCMCOCDO)COtOCMlOinNCOlOCMNN10CJ)fl-O^CDO)flO^,COCMlOT-»-COOCMT-tOO O) tfl CO O! CM CO CU lO CMT-lOCOT-COCDTfmNi-10(OCMCMCO**CM«vT-NCVT-T-CMT-CMO)N T— T-T— 1— 1— T— .— I I I I I I I I I I I I I I I I I I I I I I I I I I I t I I I t I I I 1 I I I CDCDIOSSSSSNCOCOCOCOCO(IiaC»CBC»0)00000'-T-i-T-T-T-NCVICMCMCMCOP)(OCOCO co*inor-cMco*inT-Nn*inoT-tMnM-iOT-NcoM-inOT-NcoM-u)T-cMnTf«)OT-iMn* in SinSnCOOCOCOCOOIM'NCOCMr-OlTfCOCO'-COM-CIIO'fTlSCO^COCM'fVOION'tlOiniOCO O TfN'-B0)C001C0SC0SCMC!lC0r010CDin01NU)M,'-CMC0T-t0C0OO10C»M-U)C00)M-C0CDNC0 LL COCDO)COU)T-CMOCOT-OTfCDT-COCMlflCMTfit'(MCO(M<-C010COT-flOinT-CO ICOCMT-COltinS O M-lfiCflNO)^T-COincnifiCM^tMOCMWOCOinr-coeOCOinCMM-COO)COM-cOM-[OT-lOCOCI)OM-N LL rOC001CD10T-t-T-SeMOTfN(MCMT-«)COinT-t-10COTfiniflCOTiNTtCMCOT-T-CDnCMCOIOU)N ODCOO)0)0)0)OOOOOt-T--rr-CMCMtMCMCV|COCOCOCOM,M,^T|M'10iniOlOlDCDCOCONSSCO COt'-rMCOTfOi-lMCOM-r-CMnTfOv-NlO^T-CMCO'tOT-CMnM-T-CMCOM-Or-NCOr-IMCOO TfincBinoiniOfflcoininsocMcoo)iococooicooiT-scOT-0)0)cocoN*inTtino) COCOOCOCMrOOCOfflrCONCOC»SNW10T-i-0)^IOCOlOCO^T-(MOOncO^CflCMT|(MT-lOCO NcocOTt(OTfiniocoOTtTfcocou)TfneMT;co*iocosococMNU)cocococoioiocosco<!)cocM 10r-Tfl010COCMO)COOIOCOIOT-0)CO*COCOOin'ICOT-CO<JCOincOT-lOCOCM010NCOCOCMCOCO cocoiOT-T-inincoiocoiOTrconinTfcococos^iosNcoinT-T-insvr-T-^fM-cMcocMcniOT-Or-T-i-r-CMCMCMrOCOIOCO^^M-ininiOincOCOCOSSSSCOCOCOOlOlOlOOT-T-T-CMCMCOCO CNOT-CMCOT-CMCOOT-CMCOT-CMCOOT-CMCOT-CMCOOT-CNCOT-CMCOOT-CMT-CMOT-CMT-CMOT-184 tD(DS(DLOoooiooicoc))cocMiosTttocowcoT-iooeNOn C\lCOC\ICOCOC\l*crCO CM»f*t0O0)f(0'J O N O CO T-NNCVinincOOCOr-i-lOO)'f(D*Tt LL C\IC0CMI^-UOCMIOCOCMT-CMTJ-00O>CO (DTfWTf(D07ffiT-T-T-NNL0U)C001WOT-l0C0^CD^Tf oooooooooo •fTtioioioioiONOfflooOT-r-t-T-T-i-T-NNNCitNnnnnn CMCSJCNICMCMCMCNCMCMCM CMCOT-C\JOT-C\lT-Ov-C\iT4-OOOT-CNCOTtLOCOt-C\JCOT*lO CO (DCTCOO^^NCO(DS01eOLOTfcNClCONCnN(D^SCOSNLOfflCI)LO cp •<* CM CO c Q. E 0) £2 o o £ 3 o 3 O COOCNIIflS^COCOSNO^LOCOmOCOCDLOCOCOCDCONOJSO^lONOCOT-OSCOCNCOS^ LL COT-LOCOO)C*)T-COCOCOT-T-Tj-COT-r-ONT-fOSTfCO[NCO^COO ^f'-^COCONCOLOCOSCOlO O 0)COT-CDCOT-T-COU)I^T-TtcOC\iT-COCNOr^T-lOO>OTCOT-l003CNJCM LL >»T-incoco*NSM-c»Nr-*onoocOT-vcOTtcoc\icncocoT-T-TfT-Ncon - ooooooooooooooooooooooooooooooooooooooooo J£ CDCO(DSNSSSSCOCOCOCOCOCOCncnfflfflO)OOOOOOT-T-T-T-T-NCSNNCNirVCOCOCO -C **lOCOT-CNCO^LOCDOT-C\ICOTrLOT-C\ICO^LOOT-C\ICOV w nNconcocxiNTjcOTi-cosnoO'tcniococDinsocDncocon I II I I I I I o ffiT-oincD«nnor-u)oin(r)cor-(oinc»nNinio(Doocom LL CO Ol MO (MlOt-LOnOIO>-'-lDT-*COCDniO TfNCOIMSSTMOniO'C'Or-T-T-COOl'f O >-ONIO(NIOTfCDr-CDNOlOnincO(NI010C»C>|T-CON'-CONLOCOCl)ONNOW LL OC7>t^LOT-C\ICOLOT-iOCOT-t^T-CN|inT-IJ)COLOTrCOT-LOr^C\l •o <u 3 o (0 o T3 c CO T3 CD £ CD co o lO'-«CO*COOr-NCO^'-C\ICO'rOT-MCOTrr-MCO'tOT-Nn*T-C\ICOOT-W CI)C))cnT-01TtT-CSCO'-'-CIlT-C\IO>COlOC\INCONCOONCNT-NCl)OCN|T-Nn r-T-inonniocooiT-roiOT-cor-ooit-'i-ssnswciiT-uiT-nocDOCDconcoffi T-|^CNCJ)T-'<4-COC\I TT COLOCMC\JLO'<tCOOCJ)->tCO'* COr^OOl 1-CNCOCMLOmcDOCOT-T-lO o OT^nol^cocococoocJcncO'-lnQT|•coocOT-T-^lnTJ^^(oc^ltO)co^nI-cD^ooTfT-ln LL CN(^T-COT-TtcOC\|T-Tl-T-T-COCNCM •*OOOCT)T-[^TfCNlTrt^OOT-T-CVIO)COLOCOr^OCOC\lT-CO •T-T-T-T-T-CNCS|CMCMCS|COCOCOCOCOCO^TT^TJ-^ T-c\icOT-c\icooT-c\iT-cNOT-T-oc\jTtcooT-c\icOTtiocoT-cvicOTrir)OT-CN <o cpopiOT-T-T-T-cOLOcocNcpCNjOTtcpOTrcsiincncocjii^i^ LO CO CM I— CO O COL010COT-COOCOU5^fTl-03^CMCDr^OO>T-CDCJ)C»COCOCncOT-10COT-LL CN*COCOTfnTfrfin>Jo«COT-CO«NlOM'CDNCONCN*'-*COiniOT-nm -fl-T-CNtO) CO T- T- T-O COlONSCOrocOOlT-^lOM-Ol'fOlNNCllOCONr-^r-inoSCXIOOCD'fCDVCON LL n»fiO'-'-T-N(ocD*on«'-conc\iion(DT-c)iT-nTfociic)ico^r-ncD« n*iniocosooo»-T-i-T-r-N(NNNWNnnnn(Ot^^*'f*cocoioiou)iD Ni-OrT-OOCi|'trNnTrcOOT-Nn>|inT-c\IO'flOOT-NO*Wr-NnM'fflOT-!Nnit 185 CO CM CO CO CO in CO •3- m o> m m CO t CO CJ> CO a> CO CO cp O co •3- CO 1 0 0 CO m CM CO co CO O GO CO CO CO in •3-CO m o> CO o> 00 0 CO m •3-CM CO CO •3 0 in CM in CD CO O) en 0 m co CD in 0 in CM CO m CM M- CM CO m •3-m CO CO CO •3-m CM CO CM CM CM CO 10 CO CO CO CO O) CO CO CO lO CO t r-CO CO CO 10 •3-co m 00 r-0 CM r-CO •3 CO CM co M" m 00 •3-D) in CM 00 00 CO in CO 0 CO CO 0 m r-co O CO CD CO CO CO in in CO M- CM 0 CM CO •3- 00 CM CO •3 m CM co r-CM O) CM m co CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO co CO CO CO CO CO CO CO CO CO CO ID co co co co co T— CM CM CM CO CO CO CO •* m in m m CD CO CO r~- 00 00 00 0 O) 0 0 m *- CM CO •3 m 0 0 CM CO *- CM CO 0 T— CM CO CM CO 0 CM CO CM CO 0 CM co CM CO 0 CM CN o CO CO CO CM CO CO LO t 0 CO CO CO CM 0 1- O) CO 0 CM CO •* 0 •3- 0 00 00 in CM CO CO •3-r-CN O) 00 CM •3-CO CM CO 0 CO CM CO 1^ 0 ? o> CO 10 CM CO CM m m CO CM O) •3- CM CO CO CM CM co in m CO 00 O 00 O m m CO CD m -3 in co 00 CM m CO CO CO •3- CO m t~- CM CO o> CM o> 01 CO 00 m m O •* CO 0 CO CM •3-00 CJ> CO CO CO CO CO O) - CO LO CO O m CO •3 10 CM CO m CM CD CM m 1-•3- 0 CD CO •3-m r-co CM O CO m •3-•3-0 CD m m CD O 0 0 0 O 0 O O CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CO •3- •3- •3- 1- •3- 10 0 CM CM CM CM CM CO CO CO CO •o- M- M- •3- m m m CO CD CO CO CO CO 00 m 0 CM CO m •3- CM CO O <" CM CO Tf CM CO Tf O CM 00 CM CO 0 <" CM CO <- CM CO 0 CM O) m cp CO 0 CO •3- CM 0 CM CO r— in CM O op o> CO 00 in O 1 0 M- •3- CO op cp •3 CM cp CO 0 CD CO r-CO CM 0 CO r~ CM O) m CM m 00 CO a> CO 00 CM T— CM o> m co CO 0 O) O CO CO CM M" 0 CM m CO m O) CM 00 CM CO co m m 0 CM CM •3 CO 00 CM 3 00 O) CO CM •3 0) •3 CO CO in CM CO co CO CM in CM •3- in CO O CM a> CM CO m m CM m 0 CO 1^ CO CM m co CD CO O co CO CO m CO M" O O) m CO in CO CO ^— CM CM 0 CO CM O) CM CO O) •3-T— CO CO 0 cn CM 1 • CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CO CM CO CM •9-CM •3 CM m CM m CM m CM CO CM CM CM CM CM CM CM CO CO CO CO CO •<»• •* •<»• m m m m m CO co CO CO CO CO CM CO CM 0 CM IO 0 T- CM CO m *- CM CO m O CM CO m CM CO •3 in O *- CM CO •3- m CM CO CM CO CM CO •3 "3 CM CM CO r-CO O) CO CO in m m m CO op 0 CO m CO •3- •3- o> CO CO •3- co CO CM r- cp CO O) CM •3-m CO CO •3- •3-m CO O m CO a> CM in CO m •3 CO CM CO CO in m CD 1^ CD CM CO CO CM CO m r- T- CM in CO CO •3 in CO •3- CO o> O •3-CO O) CO 0 •3- CM 0 CD CM f~ O) 0 CO CO co CO m c-•3-O) co 00 a> co CO CO CM CO r~ •3-m m 00 •3- 00 •3 CO 0 •3-m in CM CM 0 in •o-CD r~-T- CO •* t CO m 00 CM CD •3- CM in m CO •3-•3 lO O r-co CO CO •3-•3- O CO r--•3- CM m 10 m w m m CO CO CO CO CO 1^ r— 1^ 00 CO OO CO O) 0 OJ o> O CM 0 CM 0 CM CM CM CM CM CM CM CM CM CM CM CO CM CO CM CO CM CO CM •3-CM o T— CM CO •3- m CM CM CO "4- 0 .— CM CO •3- T- CM CO 0 T" CM CO *" CM CO O T— CM CO T— CM CO 0 T- CM CO o CD CO co op CM 0 in CO 1- •3- CO • CO 1 CO m 00 1 m CM M" 1- m CO t-p CO 1- Op cp CM co CO CD cp cp r— O O) en CM a> CO m o> M" 00 CM o> 0 s 00 00 O m O) CO CO in 1— 0 0 CO •3- m •3-0 CO r- m co CO TT m "J- o> CM .— CD CM •* CM •3- in 00 m •3 CD CO CM co O) CO CM m co CM r— h- CM Tf CM •* co O 1- CM in "*r O a> *» CO m CM 00 m o> CO CM CM 0 m CM CO 0 m h- co CO Tf M-•<f a> CO M" CM •* CO CM CD r--0 •3 CO a> CM CM O •3-co CM CM •3- co CM T— CM CM CM CM CM CM CM CM CO 1^ 1^ CO 00 CO 1^ 1^ 00 CO 00 CO CO a> a> O 0 O) 0 O O O O CM CM CM CM CM CO CO T— CM CO 1- O ,- CM CM CO •3- in CM CO M- m 0 CM CO m CM CO •3- m 0 CM CO •3 m ,- CM CO •3- in 0 186 oiniNO't'toinioiocjtoiDO tci'-co'-oior-nfint-r-n nnnnnnnnntonnnn OT-T-i-cjc«inir)n*ioioiDN CMOT-CMT-CMOT-CMT-OT-T-O T-eoffiCfttONT-cocnT-cococnco •<roiocor~<DOT-or^cN<oouo CMroT-Tj-cOCNT-Ttv-COLOCMCMI^ CD^COnu0O>(OlOC0(0(0(0C0(0 T-0DT-TJ-CX)COT-COT-C\1'TJ-T-T-T-CMCMCMCMCMCMCMCMCMCMCMCMCMCO COT-CMCOOT-CMT-CMOT-T-OCM ro*nsinc\icscoos(00)ci)co T-T4-CD rOCDCOtOtOT-CMOtOT-OOOCOSP)CO»J:OIT-C))NS<DO C0*rc0T-r-l0C0C0C0CMOOC0C0 CMCMCMCMCMCMCNCMCMCMCMCMCMCM MSCOCOCOCOOtOIOlCDOOOO COCOlOI^CNCOCQCM'»JrTl-'»l-COCDO LO CM (OT-TtT-TfTJ-mTfOMrl CO T-T-COCDT-COCOIOI^OJI^COCMOT-CDT-COCDT-TlrCOOCOlOCOCJJ^J-T-co CM CM CM CM CM CM (SI CMOT-CMT-Or-OCMI-T-CMCOTf MJOSCOC0100COCOCOCOM3) nnnnTi-^^^TjioioininincD CNCOTti-CMCO'l-lOOT-CMCOTt-


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items