STRUCTURES AND CRYSTAL CHEMHSTRY OF WOLLASTONITE AND PECTOLITE by CHARLES THOMPSON PREWITT S.B., Massachusetts Institute of Technology (1955) S.M., Massachusetts Institute of Technology (1960) SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September, 1962 Signature of Author . ... .. ... .. ... ... ... - Department of Geology and Geophysics, August 20, 1962 Certified by. .-.-.-. Thesis Supervisor Accepted by..-.-- Chairman, Departmental Committee on Graduate Students Structures and crystal chemistry of wollastonite and pectolLte by Charles T. Prewitt Submitted to the Department of Geology and Geophysics on August 20, 1962, in partial fulfillment of the requirement for the degree of Doctor of Philosophy. ABSTRAC T Wollastonite, CaSi.O3 , and pectolite, Ca 2NaHSi30 9 have similar triclinic cells; because of this and their analogous chemical compositions, they have been regarded as belonging to the same mineral family. An examination of the results of least-squares' refinement of three-dimensional x-ray diffraction data reveals that although the structures contain similar metasilicate chains, .they are not as closely isotypic as had been supposed. The principle differ- ences are in the coordinations of calcium and sodium and in the way these atoms share oxygens with the silicon atoms. The final R-factors for wollastonite and pectolite are, respectively, 0.089 and 0.075. The structures of both wollastonite and pectolite contain pseudomonoclinic subcells which are joined together on (100) to give an overall symmetry different from that of the subcell. The geome- tries of these sabcells and the possibility of their being joined in different ways are important in explaining the types of twinning which occur in wollastonite and pectolite. Twinning which produces an overall crystal symmetry different from some subcell, known as space group twinning, probably occurs in many types of silicate minerals. Programs written for the IBM 7090 digital computer, including full-matrix crystallographic least-squares refinement and diffracto- meter settings programs, are included as part of a system designed for automated crystal structure solution and refinement. Such a system is not available at present but should be ready within two years. Thesis Supervisor: Martin J. Buerger Title: Institute Professor -.--. U - , Preface This thesis is divided into three parts, A, B, and C. Part A consists of four chapters, each of which is intended for publication. Part B contains an account of work which was done during the thesis period and which is not intended for publication in its present form. There is, however, a possibility that some of this material will be used as a base for future publication. Part C contains four appen- dices, the first three of which are descriptions and listings of computer programs written during the period of thesis research. It is hoped that these programs will be of use to 6thers doing crystal structure work, and that they will eventually be incorporated into a complete system for crystal structure investigations. The fourth appendix contains observed and calculated structure factor data on wollastonite and pectolite. Acknowledgements The author gratefully acknowledges the advice and support of Professor M. J. Buerger in this work on wollastonite and pectolite. Crystals of wollastonite, pectolite, and larsenite were kindly provided by Professor Clifford Frondel of Harvard University. Mr. Alden Carpenter of Harvard loaned several specimens of parawollastonite. Pectolite and wollastonite were obtained from Dr. George Switzer and Mr. Roy S. Clarke of the U. S. National Museum. The author would like to especially thank Professor A. Pabst of the University of California for sending oscillation photographs and specimens of Crestmore parawollastonite and for his comments on parawollastonite. Dr. Waldemar Schaller of the U. S. Geological Survey gave valuable advice on the pectolite-schizolite-serandite series. Many useful and informative discussions with Mr. Donald Peacor have contributed greatly to the successful completion of this work, particularly in connection with his investigations of bustamite and rhodonite. Mrs. Hilda Cid-Dresdner, Mr. Bernhardt Wuensch, and Mr. Wayne Dollase are thanked for their interest and help throughout the period of investigation. Many conversations with Dr. Charles Burnham about computing were especially useful. Miss Gay Lorraine and Mrs. Shirley Veale contributed greatly through their typing of the entire thesis. Particular thanks are due Miss Lorraine for proofreading and for her advice on the format of the final draft. My wife, Gretchen, helped greatly through her moral support and through the preparation of many of the illustrations. Finally, the support of the National Science Foundation through part-time Research Ass istantships, and the M. I. T. Computation Center through the use of the IBM 709 and 7090 computers is gratefully acknowledged. Table of Contents Title page i Abstract LL Preface tiL Acknowledgements iv Table of Contents v List of Tables x List of Figures xi Part A Chapter I. Crystal structures of wollastonite and pectolite 1 Attempts to solve the wollastonite structure from Patterson projections 2 New diffractometer data 3 The three-dimensional Patterson function and its solution 3 Refinement of the wollastonite structure 5 Attempt to fit pectolite into a wollastonite pattern 7 Preliminary refinement of the pectolite structure 8 Comparison of the pectolite and wollastonite structures 9 Chapter II. Comparison of the crystal structures of wollastoniteand pectolite 14 Abstract 14 Introduction 15 Confirmation of the structure 16 Comparison of structures 18 Pseudomonoclinic symmetry 27 Distribution of Ca and Na 35 Interatomic distances and interbond angles 40 Twinning 48 Conclusions 56 Acknowledgements 57 ---- 7- - Vi Chapter 111. Drilling coordinates for crystal structure models 58 Abstract 58 Introduction 59 Coordinate systems 59 Calculation of p and < 63 Discussion 66 Acknowledgements 67 References 68 Chapter IV. Refinement of pectolite 69 Introduction 69 Selection of material 69 Unit cell data 71 Space group 73 Intensity collection 73 Refinement 75 Evaluation of the structure 78 Conclusions 87 References 88 Part B Chapter V. Review of the crystallographic investiga- tion of metasilicates 91 Status of structural work 93 Future possibilities for ino-metasilicate investigations 95 References 97 Chapter VI. Twinning in silicate crystallography 99 Structure and space group twinning 99 101 Implications of space group twinning 111 Energy relations in parawollastonite and bustamite 112 Space group twinning in other silicates 115 References Chapter VII. Crystal structures related to wollastonite and pectolite 116 Status of structural information 116 Pseudowollastonite 118 Hydrated calcium silicates 120 References 122 Chapter VIII. Crystal structure of larsenite, PbZnSLO 124 Experimental work 124 Occurrence 124 Unit cell and space group 125 Intensity cellection 125 Solution of the structure 126 Refinement 131 Discussion of results 133 Oxygen packing 133 Substructures and heavy atoms 134 Direct methods 135 References 136 Chapter IX. Automatic crystal structure analysis 137 Present capabilities 137 Future capabilities 138 Expected results of automated crystal structure analysis 140 Part C Appendices 142 Appendix I. SFLSQ3, a structure factor and least- squares refinement program for the IBM 7090 digital computer 143 Introduction 143 Common storage 145 Sense indicators 145 Tape usage 145 Punched output 150 Description of the main program and its subroutines 151 MAIN 151 READI 154 READ2 154 READ3 155 SET 155 LOOKUP 155 WEIGHT 155 SPGRP 156 REJECT 166 STAT 167 PRSF 167 STMAT 169 PRST 169 CHLNK3 169 TEST 172 CARD 173 DIST 173 Running the program 173 Data deck 173 Submitting a run 180 References 181 Program listing 183 Appendix II. Program for computation of drilling coordinates for crystal structure models 209 Directions for running the program DRILL 210 Data cards for DRILL 210 Description of data deck 211 Description of output 212 Program listing 213 Appendix III. Computation of diffractometer settings 215 Program description 215 DFSET 215 INDEXI 216 INDEX2 216 OUTPUT 217 MIFLIP 217 TERM 217 Speed of computation 217 Running the program 218 Data de ck 218 References 222 Program listing 223 Appendix IV. Observed and calculated structure factors for wollastonite and pectolite 235 Wollastonite structure factors 235 Pectolite structure factors 264 Biographical note 290 List of Tables Chapter I 1. Refined coordinates of atoms in wollastonite and pectolite, all referred to pectolite origin 10 Chapter II 1. Unit cells of wollastonite, NaAsO 3 , and pectolite 17 2. Atom coordinates for wollastonite and pectolite 23 3. Atom coordinates of wollastonite and pectolite referred to a pseudomonoclinic cell P2,/n (origin at 1) 33 4. Interatomic distances and Interbond angles in wollastonite and pectolite 41 5. Coordination of oxygens in wollastonite and pectolite 45 Chapter IV 1. Compositions of two pectolites and the hypothetical composition computed from Ca 2NaHSi 0 72 2. Results of least-squares refinement ofpectolite cell constants 74 3. Refined coordinates for pectolite 79 4. Interatomic distances in pectolite 82 5. Oxygen coordination in pectolite 86 Chapter V 1. List of crystallographically interesting metasilicates 92 Chapter VII 1. Classification of compounds with formula ABX3 117 Chapter VIII 1. Comparison