.fi—v ABSTRACT STRUCTURAL AND PHASE INVESTIGATIONS I. CRYSTAL AND MOLECULAR STRUCTURE OF w-CYCLOPENTADIENYLBIS(ACETYLACETONATO)CHLOROZIRCONIUM(IV) II. NONSTOICHIOMETRY IN Sm(II)-Sm(III) FLUORIDES BY John Joseph Stezowski The crystal structure of w-cyclopentadienylbi§(acetyl- acetonatoj)chlorozirconium(IV), w—C5H5(C5H7oz)22rc1, which crystallizes with the symmetry of the monoclinic Space group P21/c, has been determined by equi—inclination Weissenberg single crystal X—ray diffraction techniques. The theoretical density (1.553 g cm-a) calculated for four molecules per unit cell with the observed lattice parameters (a = 8.42 r 0.01, b = 15.66 i 0.01, c = 15.17 i 0.02 X, a = 123025° i 4') is in agreement with the measured value (1.556 r 0.005 g cm—a). The final discrepency factor, R = 0.092, results from a full matrix least squares refinement of visually estimated relative intensities for 1453 reflections (sin 9/A.i 0.54, CuKa radia- tion). The observed dodecahedral stereochemical configura— tion of the molecule is compatible with w-bonding between the cyclopentadienyl ligand and the zirconium atom and also ap— pears to allow dv—pv interaction between B-oxygen and the zirconium atoms. Intermolecular forces within the lattice, which exhibits distinct layers, appear to be confined to van der Waals interactions. John Joseph Stezowski A nonstoichiometric Sm(II)—Sm(III) system has been pre— pared by reacting varying amounts of samarium metal with samarium trifluoride. The system, SmF2 to SmF2.5, diSplays crystal lattice modifications of the fluorite unit cell exhibited by stoichiometric SmF2.00. A cubic phase which displays a regular decrease in its lattice parameters (a = 5.867 t 0.001 to a =w 5.841 r 0.001 R) as the composition is changed from smF2.00 to smF2.16: a tetragonal phase (a = 4.106 t 0.002 and c = 5.825 i 0.003 R), SmF2.35, and a rhombohedral phase, which also displays variable lattice parameters (a = 7.124 i 0.002 R, o = 33.40 i 0.020 to a = 7.096 i 0.002 R, a = 33.23 i 0.020) as the composition is varied from SmF2.41 to SmF2_46, have been found by Guinier powder X—ray diffraction techniques. The density-composi- tion behavior of the system has been measured; the density increases as the F:Sm atomic ratio is varied from 2.00 to 3.00 and is compatible with an interstitial anion description of the lattice modifications. Several similar- ities between these fluorides and the UOz—an system have been observed. STRUCTURAL AND PHASE INVESTIGATIONS I. CRYSTAL AND MOLECULAR STRUCTURE OF v-CYCLOPENTADIENYLBIS(ACETYLACETONATO)CHLOROZIRCONIUM(IV) II. NONSTOICHIOMETRY IN Sm(II)-Sm(III) FLUORIDES BY John Joseph Stezowski A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of chemistry 1968 ACKNOWLEDGMENT The author wishes to convey his sincere thanks to Dr. Harry A. Eick for his interest, encouragement, and support throughout the pursuit of this work. Appreciation is extended to Dr. Alexander Tulinsky for the use of his equipment and to Dennis E. Shinn for his as- sistance in the early stages of this investigation. The rapport among the members of the High Temperature Research Groups was particularly interesting and frequently a source of inspiration. The author is grateful to the E. I. duPont de Nemours Company for a duPont Teaching Fellowship. Financial assist- ance from the Department of Chemistry and the United States Atomic Energy Commission is also gratefully acknowledged. ii TABLE OF CONTENTS PART I. CRYSTAL AND MOLECULAR STRUCTURE OF w-CYCLOPENTA- DIENYLBIS(ACETYLACETONATO)CHLOROZIRCONIUM(IV) Page I. INTRODUCTION . . . . . . . . . . . . . . . . . 1 II. EXPERIMENTAL . . . . . . . . . . . . . . . . . 6 Crystal Properties . . . . . . . . . . . . 6 Characterization of the Unit Cell . . . . . . 7 Lattice Parameters and Density . . . . . . . 10 Intensity Data Collection . . . . . . . . . . 12 Absorption Correction . . . . . . . . . . . . 14 Computations . . . . . . . . . . . . . . . . 16 III. STRUCTURE DETERMINATION . . . . . . . . . . . 18 Patterson Synthesis . . . . . . . . . . . . . 18 Light Atom Structure . . . . . . . . . . . . 24 Refinement of Structure . . . . . . . . . . . 26 IV. DESCRIPTION OF THE STRUCTURE . . . . . . . . . 33 The Unit Cell . . . . . . . . . . . . . . . . 33 Molecular Geometry . . . . . . . . . . . . . 37 PART II. NONSTOICHIOMETRY IN Sm(II)—Sm(III) FLUORIDES V. INTRODUCTION . . . . . . . . . . . . . . . . . 52 VI. EXPERIMENTAL . . . . . . . . . . . . . . . . . 55 Preparation of Samarium Trifluoride . . . . . 55 Preparation of the Redhced Samarium Fluorides 57 Vapor Transport Experiments . . . . . . . . . 61 Powder X-ray Diffraction Patterns . . . . . . 62 Analysis . . . . . . . . . . . . . . . . . . 65 Density . . . . . . . . . . . . . . . . . . . 67 iii TABLE OF CONTENTS (Cont.) VII. VIII. IX. Page RESULTS . . . . . . . . . . . . . . . . . . . 69 Samarium Trifluoride . . . . . . . . . . . . 69 Physical Appearance of the Reduced Samarium Fluorides . . . . . . . . . . . . . . . . . 69 Vapor Phase Crystal Growth . . . . . . . . . 70 Analytical . . . . . . . . . . . . . . . . . 71 Density . . . . . . . . . . . . . . . . . . . 73 Unit Cell Symmetry and Lattice Parameters . . 73 -DISCUSSION . . . . . . . . . . . . . . . . . . 80 Fluorite Lattice . . . . . . . . . . . . . . 80 Interstitial Anion Model . . . . . . . . . . 81 A Homologous Series . . . . . . . . . . 89 Comparison with the Uranium Oxide System . . 90 SUGGESTIONS FOR FUTURE RESEARCH . . . . . . . 93 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . 96 APPENDIX I. Description of Computer Program . 100 APPENDIX II. Parameters from the Anisotropic Refinement of the Structure of w-C5H5(C5H702)22rC1 . . . . . . 107 APPENDIX III. Powder X-ray Diffraction Data for the Sm(II)-Sm(III) Fluorides . . . . . . . . . . . 109 iv LIST OF TABLES TABLE PAGE I. PrOpertieS of space group P21/C (No. 14) . . 11 II. Crystal boundary planes and their distance from the origin within the crystal . . . . . . . . 16 IIII. Positions and intensities of principle Patterson peaks . . . . . . . . . . . . . . . 23 IV. Electron density peak heights and assignments to atoms for v-C5H5(C5H7oz)22rcl . . . . . . 25 r. V- Dispersion corrections for zirconium. - - . - 29 v1. Atomic co-ordinates for U—C5H5(C5H702)ZZrCl . 31 VII. Observed and calculated structure factors . . 32 VIII. Selected interatomic bond lengths and angles. 40 IX. -Summary of interatomic parameters for some hexa—co—ordinate transition metal acetyl- acetonate complexes . . . . . . . . . . . . . 41 X. Samarium analysis and stoichiometry . . . . . 72 XI. Oxygen analyses obtained from National Spectro- graph Laboratories (Cleveland, Ohio) . . . . 72 XII. Density of reduced samarium fluorides . . . . 74 XIII. Lattice parameters as a function of composi— tion for a reduced samarium fluoride phase .~ 76 XIV. Rhombohedral unit cell parameters as a function of composition . . . . . . . . . . . 79 XV. Comparison of the stoichiometries generated by Sm12F24+n and those observed for phase boundaries . . . . . . . . . . . . . . . . . 89 LIST OF TABLES (Cont.) TABLE XVI. XVII. XVIII. XIX. PAGE Atomic co-ordinates for w-C5H5(C5H702)2ZrCl from the structure refinement with anisoe tropic.thermal parameters . . . . . . . . . . 107 Anisotropic thermal parameters . . . . . . . 108 Powder X—ray diffraction data for the cubic Sm(II)-Sm(III) fluorides . . . . . . . . . . 109 Powder X-ray diffraction data for the samples in the cubic-tetragonal two-phase region . . 110 Powder X—ray diffraction data for the tetragonal SmF2,35 with the superstructure lines also included . . . . . . . . . . . . . 111 Powder X-ray diffraction data for the rhombo- hedral Sm(II)—Sm(III) fluorides . . . . . . . 112 vi Figure 1. 13. 14. 15. 16. LIST OF FIGURES Crystals of UvC5H5(C5H7OZ)ZZrCl . . . . . Optical extinctions . . . . . . . . Representation of space group P21/c . . . . Symmetry of the Patterson Map . . . . a) Symmetry of the u,1/2,w§ plane b) Symmetry of the 0,1/2,w line Comparison of weighting schemes . . . . . . Stereographic projection of the unit cell . Stereographic projection of the unit cell Projections of the molecule . . . . . . . Square antiprism . . . . . . . . . . . . . . Undecahedron . . . . . . . . . Dodecahedron . . . . . . . . . . . . . . . Projected co-ordinate angles for the octahedral undecahedron . . . . . . . . Projected co-ordinate angles for the general undecahedron . . . . . . . . Projected co-ordinate angles for the W-C5H5(C5H702)zer1 o . . . . . . . . . . . Projected co-ordinate angles for the dodecahedron . . . . . . . . . . . . . . . Schematic representation of the SmF3 prepara- tion line . . . . . . . . . . . . . . . . vii Page 11 21 28 34 34 38 43 43 44 47 47 47 47 56 LIST OF FIGURES (Cont.) Figure 17. 18. 19. 20. 21. 22. 23. 24. 25. Page Schematic of Guinier Camera . . . . . . . . . 63 A typical film cassette-shrinkage correction for Guinier photographs . . . . . . . . . . . 66 Density of CHZBrZ as a function of temperature 74 Estimated relative line intensity from powder pattern obtained from samples in the composition range smF2.17-SmF2.35 o o o o o o o o o o o o 77 Density as a function of composition . . . . . 82 The effect of composition on the lattice parameter on the cubic samarium fluoride phase 83 Samarium co—ordination in the fluorite lattice (four SmF2 units) . . . . . . . . . . . . . . 85 Sm(III) co—ordination a) Interstitial anion model . . . . . . . . . 85 b) Samarium trifluoride . . . . . . . . . . . 85 Fluorite related rhombohedral unit cell . . . 88 viii I. INTRODUCTION The compound U-cyclopentadienylbis(acetylacetonato)- chlorozirconium(IV) presents an interesting Opportunity to examine the properties of three classes of ligands: a mono- dentate chlorine, a bidentate acetylactonate, and a v- bonded cyclopentadienyl ligand. The preparation of this neutral complex, as well as the bromo— and benzoylacetonate analogs, was reported by Brainina and co-workersl'3 who postulated an octahedral molecular configuration for these complexes, and noted the possibility of gig and trans isomer- ism. The infrared absorption Spectrum was cited as support for a w-bonded cyc10pentadienyl ligand and was not in con— flict with octahedral stereochemistry. An analogous compound, w-C5H5(C5H702)CrBr, has been prepared by Thomas‘, who postulated an apparently tetrahedral molecular configuration. In both of these systems only one stereochemical site has been attributed to the cyclopenta- dienyl ligand, and the acetylacetonate ligand has been de- picted in the keto rather than the enol form even though the latter would allow equivalent metal oxygen bond formation. Considerable attention has been devoted to theoretical treatment of bonding between a central metal atom and a w-bonded cyclopentadienyl ligand. In a review of several of these calculations, Wilkinson and Cotton5 indicated the 1 2 probable formation of three low energy bonding molecular orbitals between the metal and the ligand. In an applica— tion of group theory to some mixed ligand cyclopentadienyl complexes,Cotton6 displayed molecular orbital diagrams (with estimated energy level separations) for (C5H5)N1NO and (C5H5)Mn(CO)3. The cyclopentadienyl ligand portion of the diagram for the manganese complex is depicted with three low energy bonding molecular orbitals and three higher energy orbitals which may be described as nonbonding. The comparable diagram for the nickel complex displays the same general form but the energy level separation between the first and second bonding orbitals is considerably larger than that for the manganese complex. The stereochemistry of complexes containing cyclopentadienyl ligands has been discuSsed by assignment of three coordination sites to the ring7‘9. ~If this interpretation is applied to the com- plexes reported by Brainina and co-workersl"3 and Thomas4 their stereochemistry might be expected to reflect the geometry of six and eight coordination for Chromium and zirconium respectively. Several crystallographic investigations of acetyl- acetonate complexes have been compiled in a review by Lingafelter and Braunlo. These authors establish the equi— valence of the C-0 and C-CH bond distances as would be ex- pected for the enol configuration of the ligand. Further— more the ligand geometry appears to be essentially in- varient with the exception of the 0-0 distance; this 3 distance and the 0M0 and MOC bond angles are determined by the particular metal atom and the stereochemistry of the complex. The selection of U~C5H5(C5H7Oz)2ZrCl as the most suit— able of the mixed ligand complexes was the result of several considerations. The four oxygen atoms from the acetyl— acetonate ligands and the chlorine atom represent five unambiguous stereochemical sites, as compared with only three in the w—C5H5(C5H702)CrBr complex. The rejection of the benzoylacetonate complex was a consequence of the pack- ing requirements of the larger benzene ring relative to the smaller methyl group on the acetylacetonate and the desir- ability of the well characterized nature of this ligand. The chlorine derivative was selected in lieu of the bromine complex also as a result of packing considerations since the chlorine atom more closely approaches the size of the coordinate oxygen atoms. Brainina and co—workersl‘3 have reported several pre— parative techniques for W-Cyclopentadienylbis(acetylacetonato)- chlorozironium(IV). Preparation of the complex from (U-C5H5)2ZrClz resulted in a 95% theoretical yield and the net reaction may be described by equation one: w-C5H5(C5H702)ZZrCl + C5H6 + HCl (1) The (U-C5H5)ZZrC12 was dissolved in a large excess of acetyl— acetone and maintained under reduced pressure at 70 to 800 for two hours. The volatile products, as well as about half 4 of the solvent, were distilled away as a result of the re— duced pressure and the complex was obtained as a precipitate which was subsequently separated from the reaction mixture by filtration. The product was then washed with petroleum ether and dried, and the melting point determined both before and after recrystallization from benzene (188 - 190°). The compound was characterized by an elemental analysis, which agreed with the proposed composition, and by its infrared absorption spectrum. Additional Characterization of the complex has been reported by Pinnavaia et al.11 These authors have investi— gated the solution behavior of the complex with conductance and proton nmr measurements. The conductance measurements, determined for a nitrobenzene solution, indicate a monomeric complex which is probably a weak electrolyte. Proton nmr spectra indicate the presence of non—equivalent environments for the methyl groups and -CH= protons on the chelate rings. Application of variable temperature nmr techniques is being pursued by these authors in an attempt to establish the existence of stereochemical isomers. A structure determination of this complex has been effected by application of single crystal X-ray diffraction techniques in an attempt to clarify the stereochemical properties of the molecule. The results of this investigation should be of value both for the prediction of probable stereochemical isomers of these molecules11 and for interpretation of the geometry 5 of similar mixed ligand complexes,such as the complex ion (F-C5H5)2(C5H702)Ti+ which has been prepared by Doyle and Tobiaslz. They should also contribute to an understanding of the general chemistry of mixed ligand complexes contain— ing one or more v-bonded cyclopentadienyl ligands. II. EXPERIMENTAL The preparation, represented by equation one, and characterization of the crystals of w-C5H5(C5H702)2ZrCl used in this investigation were effected by Dr. T. J. Pinnavaia of this department. The product had been re- crystallized from dry benzene by allowing a saturated solu- tion confined under a dry nitrogen atomsphere to cool slowly with stirring.. Subsequent separation of the precipitate from the solvent was accomplished in the recrystallization vessel and the crystalline product was thoroughly dried in .yagug_at 80°. An infrared absorption spectrum taken of the solid dispersed in a KBr matrix displayed no bands in the -OH stretch region (3400-3500 cm-l); an indication that hydrolysis had not occurred. The observed melting point (189-1900) was in good agreement with that reported by Brainina g£_al,1 (188-190°) and a carbon hydrogen analysis (found 46.0% C, 5.00% O; theoretical 46.2% C, 4.91% O; Galbraith Laboratories, Knoxville, Tenn.) was obtained to establish further the composition. Crystal Properties Crystals of the ccmplex were examined with aBausch and Lomb stereozoom variable power microscope ard photographed with a Bausch 6 7 and Lomb Dynazoom metallograph. The hexagonal prismatic morphology of the transparent crystals, as displayed in Figure 1, is typical of their general form. The fairly soft crystals exhibited several Cleavage planes, the sharp- est of which was later determined to be nearly parallel to the (101) plane. A second cleavage plane, less sharply defined than the first was observed to be nearly parallel to the (011) plane. Several other cleavage planes, which could be reproduced only with difficulty, were not charac- terized. An examination of the crystals with polarized light (Ernst Leitz Weltzer polarizing microscope) revealed dis- tinct optical extinction axes (Figure 2), two of which were coincident with crystal faces, and a unique oblique extinction. These optical extinctions are indicative of a monoclinic unit cell and thus provided the first indication of the space group symmetry. Characterization of the Unit Cell The confirmation of the unit cell and the determination of the space group were accomplished by examination of precession and equi-inclination Weissenberg photographs taken with CuKa radiation. Initial equi-inclination Weissenberg photographs ob- tained for a crystal rotating about the normal to the (110) plane displayed the characteristics of monoclinic symmetry and provided some of the criteria for the selection of the Figure 1. Crystals of W—C5H5(C5H702)2Zrcl. - [E Figure 2. Optical extinctions. 9 space group. The angular repetition period, the angle of rotation necessary to produce the equivalent of any given reflection, was 180°. The zero layer photograph contained two distinct central lattice lines separated by 45 mm (90° angle of rotation), one of which, designated'B1,.dis- played systematic extinctions (OkO, k = 2n + 1), and both of which possessed mirror symmetry. There were no observ- able central lattice lines on the first layer photograph, however, mirror symmetry was observable about an imaginary line overlaying the other central lattice line, A1, of the zero layer photograph. A curved festoon nearly overlaying B1 was noted, and the festoons containing B1 on the zero layer were overlayed by the equivalent set on the first layer. A central lattice layer line overlaying Al was ob— served on the second layer photograph (hog extinct when E = 2n + 1) while an additional shift was observed in the region of B1. A sUbsequent precession photograph taken of the (101) reciprocal lattice plane confirmed the monoclinic unit cell. Additional equi-inclination Weissenberg photographs were taken with a crystal rotating about the b-axis. The zero layer photograph contained a central lattice line, A2, which was identical to A1. The angle measured from the precession photograph (58°) and the separation displayed on a rotation photograph taken for the previous orientation facilitated selection of the remaining crystallographic axis. A comparison of the zero and first layer equi—inclination 10 photographs confirmed the hog extinctions described above while examination of additional layer photographs indicated no other apparent systematic extinctions. The observed systematic extinctions are uniquely described by the extinc- tion requirements for the general positions of space group P21/c, which are displayed together with the general posi- tion coordinates in Table I. A schematic representation of the symmetry elements of the space group may be viewed in Figure 3. Lattice Parameters and Density Lattice parameters for monoclinic v-C5H5(C5H702)ZrCl were obtained from calibrated single crystal X—ray diffrac— tion photographs taken with a Charles Supper non-integrating Weissenberg camera mounted on a Philips X—ray generator and exposed with CuKa radiation (40 kilovolts and 20 milliamperes). A goniometer head containing the single crystal used for intensity data collection (rotation about the b—axis) was mounted firmly on the camera. A single sheet of Ilford Industrial Type G X—ray film was encased in opaque paper and placed in the 57.3 mm diameter cassette. The Cassette cradle on the Weissenberg camera was centered on the X—ray collimator, fixed rigidly in place, and the cassette placed on the cradle to its farthest extent. After a rotation photograph had been taken, the cassette and goniometer head were removed, and a second goniometer head containing an aligned recrystallized NaCl crystal was mounted firmly on 11 Table I. Properties of space group P21/c (No. 14) Posi— Point Co-ordinates of Conditions for tions Symmetry Equivalent Positions Extinction 4e 1 x,y,z; §,§,E; hkz: no extinctions x,1/2+y,1/2—z; x,1/2-y,1/2+z. hOfl: £=2n + 1 OkO: k=2n + 1 2d I 1/2,0,1/2; 1/2,1/2,0. _ as for 4e, 2c 1 0,0,1/2; 0,1/2,0. plus hkz; 2b I 1/2,0,0; 1/2, 1/2, 1/2. k + g = 2n + 1 2a i 0,0,0; 0,1/2,1/2. 1/4 <®—-c> j— 0 1T, o-—> 1/4 1/4 4—— f E o g o ——> 1/4 1/4 4—- o : o ‘: ——o ——> 1/4 Figure 3. Representation of space group P21/C. 12 the camera after which the cassette was returned to its former position and a second rotation photograph was taken. An analogous procedure was followed to obtain a calibrated zero layer Weissenberg photograph for the same crystal ori— entation. The spot separation was determined to the nearest 0.01 mm with a Picker X-ray film reader, and correction factors were determined from a comparison of the observed NaCl lattice parameters with the known cubic value13 (a = 5.6387 R), Thecflflique monoclinic angle, 6, was determined from the corrected a and c parameters and corrected d— values obtained for hOE reflections. The lattice parameters, together with their standard deviations and expressed in coincidence with Space group P21/c, are: a = 8.42 i 0.01, b = 15.66 i 0.01, c = 15.17 i 0.02 R, and B 123°25' 1 4'. The density of w-C5H5(C5H7Oa)2ZrCl,as determined by the flotation technique with a solution of A.C.S. Reagent 3, 24°) and Grade carbon tetrachloride (p14 = 1.5863 g cm- chloroform (p14 = 1.4816 g cm_3, 24°) employed as the im— mersion medium,was found to be 1.556 r 0.005 g cm“3 at 24°. This value is in agreement with that calculated for the measured lattice parameters on the basis of four molecules per unit cell, 1.553 g cm_3. Intensity Data Collection Intensity data were collected with Ni filtered Cu radiation on a 0.12 x 0.03 x 0.07 mm crystal by application of the multiple film equi—inclination Weissenberg technique. 13 A non-integrating Charles Supper Co. Weissenberg camera mounted on a General Electric X—ray generator equipped with a high intensity Cu tube was used to obtain data for levels hOfl through h8£ (sine/$23154 3-1) Three sheets of Ilford Industrial Type G X-ray film were sandwiched between two pieces of opaque paper and placed in a cassette. Two twelve hour exposures (40 kilovolts at 38 milliamperes) were made for each layer; the first employed rotation from 0 to 190° and the second from 180 to 370°. The film was processed by placing the exposed sheets in a light tight (5 x 7 in capacity) processing cassette and transferring this cassette to the appropriate solution tanks. All processing operations were carefully timed with a Gra Lab Universal Timer Model 168 viewed with the aid of a safe light used only after the film had been inserted into the processing cassette. The film was systematically agitated by raising and lowering the processing cassette at the following time intervals: development, every 30 seconds for five minutes; stop, every 15 seconds for one minute; and fix, every minute for fifteen minutes. The films were subsequently washed with a slow flow of distilled water for a minimum of one and one half hours, and allowed to dry thoroughly after which they were labeled and stored in clear cellophane envelopes. An intensity calibration strip, for which two sheets of film were exposed, was prepared by incremented (I = n+1 1.15 In) exposure of the (002) reflection. The relative 14 intensities were estimated visually by comparison of spots on the half of the film containing the reflections for which spot area is compacted with this calibration strip. An esti- mation of Spot area as well as density was made and the intensities determined from each film were correlated and scaled to the inner—most film of the series. Scaling between adjacent sheets was accomplished by an increase of six in the calibration spot number obtained for the weaker film; this scale factor was determined from an examination of the two sheets of film exposed for the calibration strip and was found to account for changes in spot area as well as density. Reflections with an intensity less than the five cycle cali— bration spot were not recorded. Agreement between the esti— mated intensities from the first film and the scaled intensi- ties was generally within 10% with apparently random devia— tions. A small number of reflections were duplicated on the two exposures made for each layer and agreement comparable with the inter-film estimated intensity deviation was ob— tained for these reflections. A total of 1453 different reflections (including the average intensity for duplicated reflections) from half the sphere of reflection was measured. Absorption Correction . . —1 The linear absorption coeff1c1ent, u = 74.7 cm , for N-C5H5(C5H7OZ)QZrCl was calculated from tabulated15 mass absorption coefficients and the experimental density. The Shape of the crystal used for the intensity data collection 15 and its orientation (a flat plate mounted with the rotation axis perpendicular to its broadest face) were such that ap— plication of the available absorption intensity correction program seemed desirable. This program, written by Coppens, Leiserowitz, and Rabinovich16, is an extension of one written by Busing and Levy17. The correction factor, A = f(1/V)exp[—u(ri + rd)]dV where V is the volume of the crystal, and r1 and rd are the incident and diffracted beam path lengths, respec- tively, is evaluated numerically by the method of Gauss. The crystal, bounded by n plane surfaces, is described by a set of n inequalities which may be satisfied only if points which define the co—ordinate variables are inside of or on the surface of the crystal; these inequalities are used to determine the limits of integration necessary for the Gaussian approximation. As a consequence of this de- scription of the crystal boundaries, no re—entrant angles between boundary planes may be included. These limits are used to establish a grid (dimensions mX, my, and mz) of points each of which is used to determine a value of r. 1 and r The net absorption correction for each reflection d' is determined as a weighted average over all points. The crystal on which the intensity data were gathered was bounded by the eight plane surfaces tabulated in Table II. and was represented by a 16 x 6 x 10 (960 points) grid which resulted in the ratio Icor:Iobs = 1.84 i 0.23 (extreme values: 2.81 and 1.47). 16 Table II. Crystal boundary planes and their distance from the origin within the crystal. (hkfi) of boundary Distance from the planes origin (cm) 0.0022 0.0022 0.0034 0.0034 0.0040 0.0040 0.0062 0.0062 HI H H HI HI HI 0 O O 0 HI HI H H H H O 0 MI NI N NI O O Computations The calculations associated with the absorption cor- rection described above and most of the remaining calcula- tions were accomplished on a CDC—3600 computer (64K memory). A number of prOgrams, which had been either written or modified by Zalkin and obtained through his courtesy, were used throughout the solution of this structure. A descrip— tion of the program used for intensity data reduction and Fourier's series calculations, as well as the full matrix least squares program used in this solution has been given by Shinnls. Intensity data, collected by equi—inclination Weissenberg techniques, are treated with two correction factors, the reciprocal of the Lorentz-polarization factor, 1/L—p = 2 sinecose/(l + c0520), and a velocity correction 17 factor V = [1 - (h7\/2asin9)2]1/2 /sin9 where a and h are the rotation axis parameter and the corresponding Miller index, respectively. The full matrix least squares program minimizes Z w(|FoI -IFC|)2 (w = weighting factor, F0 and Fc are the observed and calculated structure factors, re- spectively), by varying the scale factor, x, y, z co—ordinates and, the thermal parameters, either isotropically or aniso— tropically. This program also calculates the standard devi- ations associated with the position co-ordinates and the thermal parameters. Distances and angles, with their stand- ard deviations which result from the standard deviations of the position and lattice parameters, were calculated with program Distan described in Appendix I. Planarity calculations were made with a program ob- tained from Dr. A. Tulinsky of this department. This program, which is also described in Appendix I, fits a least squares plane of the form ‘AX + BY + CZ — D = 0 to a specified set of atoms and calculates the standard devia— tion of the plane, but does not include the standard devia- tions of either the position co-ordinates or the lattice parameters. The stereographic projections of w-C5H5(C5H702)2ZrCl and its unit cell were drawn on a CDC—6600 computer equipped with a cathode ray plotter with a program written by A. C. Larson. III. STRUCTURE DETERMINATION Patterson Synthesis The Patterson function: A = 1/V 2 cos 2W(hw + kv + 3w) h (uvw) E i IFhkzI2 where A(uvw) is the peak height in terms of relative elec- tron density at the ends of the real space vector u + v + w, V is the volume of the unit cell, and Fhkfl is the struc- ture factor for reflection hkz, affords an opportunity to obtain valuable information from phase independent data and consequently represents the starting point for intensity data analysis in most crystallographic solutions. This function exhibits certain symmetry relationships which are useful in the examination of a Patterson map (a two or three dimensional array of A( displayed as uvw) a function of u, v, and w). That the Patterson function (an even function) is centrosymmetric can be examined by con— sidering two points A1 and A2. The vector from A1 to A2 may be expressed as (uvw) while the vector from A2 to A1 would be (66%), and since any point in space may be viewed as the origin in a Patterson synthesis both of these vectors would be produced. 18 19 Consider now a diad screw axis parallel to the y—axis. This screw axis produces the following set of equivalent positions: x, y, z and —x, 1/2 + y, -z. A consideration of the three symmetry related points Bl, (x1,y1,z1), B2, (—x1,1/2 + y1,-z1), and B3, (x1,1 + yl, 21), will illustrate a second symmetry property of the Patterson map. The vec— tor from B1 to B2 may be expressed as (u,1/2,w) and similarly that from B2 to B3 as (—u,1/2,—w). These vec- tors are related to each other by a simple diad axis. Thus any space group containing a two fold screw axis should produce vectors of the form (u,1/2,w) in the Patterson map. Furthermore, these vectors are generated twice for every unique atom since the centrosymmetric nature of the Patterson synthesis generates the additional vectors (—u,—1/2,—w) and (u,—1/2,w) and the v = 1/2 and v = -1/2 planes are coin— cident. It may also be shown in a similar manner that the vectors generated between two nonsymmetry related atoms of a space group with a two fold screw axis display the higher symmetry of a two fold axis through the origin of the Pat— terson map. The investigation of one more important symmetry opera- tion, the glide plane, remains. This plane produces the general transformation (with the glide taken in the direction of the c-axis) x,y,z to x,-y,1/2 + 2. If points C1, C2, and C3 are generated as were B1, B2, and B3 the points (x1,y1,zl), (x1,—y1,1/2 + 21) and (x1,y1,1 + 21) are produced for which the vectors between adjacent points are 20 of the form (0,v,1/2). Application of the center of sym— metry in the manner described above produces a second vector of this type. These coincident peaks are generally referred to as Harker peaks and are useful for determination of atomic co—ordinates. The set of vectors produced from non- symmetry related atoms in a unit cell containing a glide plane display mirror symmetry about the origin perpendicular to the y-axis. The Patterson map for space group P21/c, which contains a center of symmetry, a diad screw axis parallel to the y-axis, and a glide plane with the glide direction along the z-axis and reflection perpendicular to the y-axis, should display a two fold axis parallel to and a mirror plane perpendicular to the y-axis. The symmetry of the Patterson map obtained for this solution may be viewed in Figures 4a and 4b. The Patterson map for this space group should also contain Harker peaks of the form (u,1/2,w) and (0,v,1/2). The relationship between these Harker peaks and the atomic coordinates may be determined from the transformation equa- tions of the space group: x,y,z; —x,-y,-z; —x,1/2 + y, 1/2 — z; and x,1/2 - y, 1/2 + z. The peak (u,1/2,w) may be Shown to correspond to (-2x,1/2,1/2 - 22) from which a solution for the x and z co-ordinates of the atom may be obtained. The second Harker peak (0,v,1/2) corresponds to (0,1/2 i 2y, 1/2) and consequently may be solved for the y co-ordinate of the appropriate atom. 21 Zr—Zr Zr-Zr '+' Locating (0,1/2,0) a) Symmetry of the u,1/2,w plane. Cl-Cl Zr—Zr Zr—Zr Cl—Cl -+ Locating (0,0,1/2) b) Symmetry of the (0,v,1/2) line. Figure 4. Symmetry of the Patterson map. 22 As I have indicated, these peaks are generated twice for each unique atom in the unit cell and consequently have a peak intensity of twice that of the general vectors (u,v,w). Since every unique atom in the unit cell will produce a set of Harker peaks, their major application is found in the solution of crystal structures by the heavy atom technique. This structure investigation was well suited for solution by this technique. The ratio of Zgr : 2 niZ: = 1.45 is nearly the generally accepted op— timum talue and thus calculations based on the phase con- tributions of the zirconium atom should produce a reasonably sensitive electron density map. A Patterson summation, effected for half the unit cell with the absorption corrected data, produced the peaks and their corresponding co—ordinates displayed in Table III. Harker peaks corresponding to the zirconium atom were ap— parent and produced the co—ordinates: X = 0.04, Y = 0.160, and Z = 0.140. Only the (0,v,1/2) Harker peak for the Chlorine atom was included within the limits of the summa- tion and was used to determine its Y co—ordinate. The remaining co-ordinates for the chlorine atom (X = 0.300, Z = 0.140) were determined by adding a general vector of the appropriate magnitude (2.52 R) to the zirconium atom co-ordinates, and additional Zr-Cl peak assignments are contained in Table III. 23 Table III. Positions and intensities of principal Patterson peaks. Relative X Y Z Intensity (999) 0.00 0.00 0.00 999 0.08 0.50 0.22 435 Zr—Zr 0.00 0.18 0.50 413 Zr-Zr 0.00 0.82 0.50 413 Zr-Zr 0.80 0.66 0.72 235 Zr-Zr 0.80 0.34 0.72 216 Zr—Zr 0.00 0.50 0.76 187 Zr-Zr 0.28 0.24 0.48 151 Zr-Cl 0.00 0.68 0.50 145 Cl-Cl 0.00 0.32 0.50 145 Cl—Cl 0.12 0.00 0.84 144 0.04 0.50 0.62 140 0.28 0.08 0.98 140 Zr—Cl 0.36 0.72 0.70 134 Zr-Cl 0.16 0.04 0.48 125 0.00 0.34 0.26 117 Zr—Zr 0.00 0.50 0.38 116 0.36 0.58 0.20 114 Zr—Cl 0.28 0.92 0.98 114 Zr—Cl 0.02 0.38 0.98 114 0.00 0.38 0.00 113 0.00 0.62 0.00 113 0.20 0.88 0.96 113 0.28 0.76 0.48 107 Zr-Cl 0.16 0.86 0.98 106 0.02 0.82 0.74 106 0.00 0.18 0.26 105 0.26 0.08 0.00 105 Zr-Cl 24 A subsequent least squares calculation with the atomic scattering factors for Zr and Cl- calculated by Thomas and Umeda19 and Berghuis et al.2°, respectively, of these param- eters produced the following values: X Y Z B zirconium 0.0437 0.1649 0.1424 2.963 chlorine 0.3392 0.0986 0.1656 4.292 and a discrepancy factor R = 0.308 (R = (wlFol-[FC|)/wIFo[). Light Atom Structure The light atom structure was determined by application of the phase signs determined by the zirconium and chlorine atom positions in a Fourier's summation: exp[-2Ui(hx + ky + 32)], where = l/V i th p ZZF (xyz) k E nyz) is the electron density at point (xyz). The similar magnitudes of the atomic scattering factors for carbon and oxygen made assignment of their co—ordinates by peak height alone unreliable and consequently a three dimensional model of the electron density map was constructed. Subsequent comparison of the electron density model with the known geometrical configuration of the cyclopentadienyl and acetyl- acetonate ligands resulted in assignment of the peaks con— tained in Table IV. A least squares calculation on these parameters with carbon and oxygen atomic scattering factors calculated by Berghuis et al.2° produced R = 0.155. 25 Table IV. Electron density peak heights and assignments to atoms for w«C5H5(C5H702)22rC1 Peak x Y z Height Atom 0.06 0.16 0.14 999 Zr 0.34 0.10 0.16 347 Cl -0.34 -0.10 -0.16 347 Cl 0.18 0.28 -0.20 162 04 0.18 0.22 0.30 162 04 —0.18 0.28 0.08 138 01 0.18 0.28 0.12 136 O3 -0.10 0.16 -0.04 128 02 -0.10 0.34 0.46 128 02 0.02 —0.02 -0.12 112 Cl -0.02 0.02 0.12 112 C1 0.22 0.34 0.16 107 C12 0.22 —0.04 -0.08 102 C2 -0.22 0.04 0.08 102 C2 0.26 0.36 0.28 102 C13 0.06 0.50 0.38 99 C1 0.06 0.02 0.24 94 C4 -0.26 0.28 -0.08 94 ca -0.26 0.22 0.42 94 C8 0.26 0.30 0.34 93 C14 0.26 0.20 -0.16 93 C14 —0.22 0.28 0.40 91 C7 -0.22 0.22 -0.10 91 C7 0.30 0.32 0.44 788 C15 0.30 0.18 -0.06 88 C15 -0.26 0.30 0.02 83 C9 -0.06 0.08 0.26 83 C4 0.22 —0.08 -0.16 79 C5 -0.22 0.08 0.16 79 C5 —0.26 0.20 0.50 75 C9 —0.10 0.50 0.26 73 C4 0.26 0.44 0.12 73 C11 -0.26 -0.06 0.38 73 C11 0.26 0.16 —0.20 71 C6 -0.26 0.30 0.30 69 C6 -0.26 0.20 0.20 69 C5 -0.02 0.46 -0.14 60 Cl —0.02 0.04 0.36 60 Cl -0.34 0.38 0.02 60 C10 0.34 -O.10 0.48 58 C10 26 Refinement of the Structure The refinement proceeded in two phases: a) application of a weighting scheme and b) averaging of equivalent re— flections. Visual estimation of intensity data, accomplished as described previously, presents the probability of reading errors in addition to the errors associated with film Col— lection of data. Reading errors would be expected to vary with both spot area and density and be of greatest magnitude for high intensity reflections. They would also be signi— ficant, particularly on a relative basis, for very weak spots. The intensity of very dense spots is determined by visual estimation of Spot density on successive sheets of the multiple sheet film package exposed simultaneously and, with the exception of very strong reflection, may be averaged for two or more adjacent sheets of film. The intensity of weak reflections is obtainable from only the first sheet of film and thus may be averaged only by repeated reading of the same spot. A weighting scheme is generally applied in order to let the most accurately obtained data have the greatest ef— fect on the final refinement of the structure. This scheme should in some way represent the standard deviation in the data. Obtaining a direct estimate of the standard deviation of a series of reflections requires multiple determination of the intensity of each Spot and is not practical for visual 27 estimation. The weighting schemes frequently applied to intensity data are those of Hughes21 and Cruickshank which weight the data as the reciprocal of a function of [F0|2. A modification of these weighting schemes has been applied to the data in this solution. The modified scheme, the inverse of a parabola, is described by the following equation: w = (A + IFOIZ — 2B|F0| + B2)/C)—1 where A, B, and C are adjustable constants which deter- mine the shape and minimum point of the parabola. A graphical display of this weighting scheme along with typi- cal examples of the schemes of Hughes and Cruickshank may be examined in Figure 5. This scheme allows selection of a minimum value of [F0] which is believed to display favor— able relative accuracy (A = 10 for this solution). Simultan- eously it decreases the relative importance of weak reflec— tions in the least squares refinement. This selection was made from an estimation of the intensity range most readily compared with the calibration strip (120 to 150 cycles for this investigation). The remaining Constants, B and C, were determined by a trial and error procedure for which the minimization of R was the criterion. An examination of |Fo| and IFCI produced by a least squares treatment of the weighted data indicated random deviations for the intense reflections. Thus it would ap— pear that the effects of extinction are smaller than the scatter in the estimated intensity data. The R factor 28 nement ) for least squares refi Weight 0 Stezowski 0.10.. [J Cruickshank Hughes 1 l l l L l l I I I I I I I 10 2O 30 40 50 60 70 IFobsI Figure 5. Comparison of weighting schemes. 29 obtained with the weighted data was 0.105. Anamolous dispersion effects are significant for zir- conium when CuKa radiation is used (Table V), however, the centrosymmetric character of space group P21/c and the optical activity of the molecule eliminate these effects. The Laue symmetry, the symmetry of the intensity weighted reciprocal lattice, for monoclinic space groups is 2/m and results in the intensity relationship Ihkfl = Ith' The intensity data set for this solution was collected over half the sphere of reflection and contained a number of equivalent reflections of this type. A portion of these reflections, 15kg = Ith (only this symmetry requirement was initially recognized) were averaged in an effort to reduce the effects of random errors and this reduced data set was employed for the final refinement. Table V. Dispersion corrections for zirconium. f = £0 + Af' + iAf" Sin e/x Af' Af" 0.0 -0.6 2.5 0.6 -0.7 2.2 The parameters which had been obtained from least squares refinement with the entire data set were subjected to further 30 refinement by least squares treatment with the 1131 reflec— tions. The refinement was continued (no zero weighted data) with isotropic thermal factors until the Shift in all the parameters was less than 0.001 times their reSpec— tive standard deviations. This refinement was effected with the atomic scattering factors for Zr, Cl, 0, and C reported by Cromer and Waber23, and produced a final R factor of 0.093. The parameters obtained from the final isotropic least squares refinement, with their standard deviations are displayed in Table VI, and the calculated and observed structure factors for each reflection are pre— sented in Table VII. A subsequent refinement of the parameters with aniso— tropic temperature factors for all atoms (no Special posi— tions) produced an R of 0.083. This small change in R compared to the isotropic case would appear to reflect fairly high random deviations in the intensity data and consequently all subsequent calculations were based on the parameters obtained from the isotropic refinement. The atomic co- ordinates and the anisotropic thermal parameters are tabu— lated in Appendix II. 31 Table VI. Atomic co—ordinates for v-C5H5(C5H702)2ZrCl. Symbol Atom in X Y Z Figures Zr Z 0.0439 3)* 0.1657 2) 0.1414 2) 4.23 Cl P 0.3356 9) 0.1006 5) 0.1655 5) 5.20 Cyclopentadienyl ligand C1 c —0.0550 39) 0.0038 19) 0.1186 22) 6.49 C2 C -0.2174 36) 0.0534 19) 0.0761 20) 5.30 C3 c —0.2217 40) 0.0997 20) 0.1525 22) 6.19 C4 C —0.0421 36) 0.0837 10) 0.2541 20) 5.59 C5 C 0.0660 35) 0.0298 20) 0.2331 20) 5.47 Acetylacetonate ligands 01 0 —0.1708 20) 0.2661 11 0.0950 12) 4.40 02 0 -0.0901 20 0.1614 12 —0.0238 11) 4.44 C6 A -0.2580 32 0.1918 17 -0.1073 18 4.86 C7 A —0.2108 33) 0.2196 18 —0.0982 19) 4.65 C8 A -0.2920 34) 0.2880 17) -0.0858 20) 4.15 C9 A -0.2694 31) 0.3082 17) 0.0074 18) 5.15 010 A -0.3694 38 0.3895 20) 0.0151(22) 6.50 03 N 0.1680 20) 0.2782 12) 0.1193 12) 4.86 04 N 0.1867 21) 0.2232 13) 0.2928 12) 4.82 C11 B 0.2526 38 0.4264 20 0.1173 22 6.52 C12 B 0.2238 31) 0.3497 18) 0.1685 17 4.36 C13 B 0.2659 33 0.3638 17) 0.2682 19, 4.60 C14 B 0.2510 32) 0.3027 19) 0.3267 18) 4.44 C15 B 0.3072 31 0.3167 18) 0.4386 17) 4.99 * Numbers enclosed by parentheses are standard deviations multiplied by 104. *x Standard deviations Table VII. 111111 ‘I‘IIC-‘Q‘Oi«IOIIOCIOIICIII‘lllll'bb ODIiUIiUIIUIl-Ilblbhllvli-I-U'O II III II ii~ld~iii 11111111111111111111111111111 I ??oooo??oao:7ooooocoooooooooooooooozaoooaooooaoaaaaaaooo:213:)' -??CH33??I“.OO??THDOO??¢HDOO?€MDOO3 r I0 ~OOCIHI -- 0). DIIIIOIIIDDID'I. .lDIIOIUQIIIDOII 3 ~ 3 II. Ulla 3:~&11331111‘ - 111331111 ' "1113311113; woo-030u~o3:oocou:3acooo~00~ ::szssz::::s=ezzszes 0‘5 ..~‘..il~“°I.—‘...".H..~"° 1111 a:::a§::::::e:x 1*. c... O 5 III I 1"DledieideOOOOOOOOGIDJDIOOOD0.0.0.5000ooonuuuouuuuuuuu---------—-_--_—__——ucacao—nu— 111 L Inns I O 59 I I 61 I P 12‘ | 3 1‘ I 0 0* I 1 6. I A so 1 I 1‘ I l3 1‘ I ll ‘0 I II J! I -I I91 I 0 II‘ I I IO‘ I I IO” | 0 6| I q 15 I A ‘26 I 1 IOI I 9 OH | o 6‘ I I0 II' I II I I! 61 | 0 IO! | 1 no I I I." | 0 on I I! 1° I-l! 1" I'II ‘9 I-In I“ | -1 06 I -O ’9 I '7 IV] I -O )0. I 0‘ 16 In. 61 I '1 II! I -! .66 I -I I“! I Q l“ l O F‘ I-lfl 7° l -9 66 I -8 6‘ I -1 68 I -O 10 I -5 32 | -. 2% I .1 an I -' PC? I -| 0‘ I D II” I 3 OI I 0 I1, I S .0 I H QR I’ll 56 l-lo 00 I -0 38 I -7 no I -. 50 I -5 Q) I c. In I -1 I00 I -’ ”I I -I It? I I 7) I O I?! I‘ll 5? l-ll 1o I-Io I60 I -0 90 I -l 38 I-1 1G I -. I00 I -5 II' I -O I.‘ I -3 I) I -1 I -I I“ I I .I I 3 I. I 0 l0. I°l3 ‘1 I-IO 91 I .1 00 I -I 3! I -. 0‘ I -' 66 I .0 I91 I -! 35 I O 1? I’lO )1 I'll 50 IOIO 53 I -. J! I» M I -9 )0 I O. 7I I O 0‘ I’ll .6 none .6 I -1 11 I -. 13 I -0 9! I -§ 90 I -0 I. I o 60 I-u n I -l 1‘ I -I 0' I l 9! D I II? I l 0| p 1 on 2 O 93 I 1 05 I O 33 l 1 .9 I l 9? 1 II IOC I It as 2 -I II‘ p n in I I I‘0 I I 3! P 1 ‘0' I 0 I9 I 1 ISO 0 1 II. 2 II 0‘ l I) 92 i 6 A" v | n- ! P IIO P 1 ffl? ’ 0 fl 1 1 II’ ’ ’ ID? 232 Observed and calculated structure factors. 0(Ag fifl .- ?.5 6| I“ 10 6? v1 51 W. - ~ D .0 I)! P?“ OI [.0 II I III Dada!aq¢0000000000.¢.loodliboODDO.0.0.00599bauuu0bu“”V-------—----_---°°°°°°°-~ 11111151 4JJJU'OIJUJJJJJBUUUO‘UJJUJ cut—.- -'.~'.~"II~‘I-"V‘D~V .OJ’UVUOOiIOUD-Ju-JOIJDJ-3 -1 'I“I~l.~'.~li"lfi'b?'.~'D~‘U~'I~IUQ'IV"~ J "O'I"I~'."I~|i~ OIDU IO... 11 11111' -~u--u--~7 n O l- ~01003~ -ID-NI§~II- 6.1111111 22 P-II ?“I‘. 'II I -~.O‘O I...— D a n - o - aI-c I 3 l O a..- JI‘UIIU UI‘UH‘UI‘UI‘OI‘U f JIOIIUIUIOO u 31‘ 0131!“ a U u u a a a aura a d 0 J are a a J 3 u a a a u U a J J a a 3 a a a a J a u a 4 a J ‘fUI‘UIIUIIUI‘U JU YIIUUIIUUIIJOIDU fYIIUIIUI'UIOdIIU £1 "'J 4,1 a) d. I. JV-) I - i-i.’.J--’Dfldild~ 54“:m:d.ln~‘:I‘L‘N$O-"COIDU~ 3.311111 111131:.~111111$113 - ‘IIOI! 11.11111111 151 .910! O. 0.1.01.I»DOD.IDOIDDC>OIIOIIOIDOIDOC II ii. - .IIU‘.-"dll. J‘ ‘3 d. DJ-'J ICaL - )Qa .1 I i ‘1 1} -Q 160 -‘ 1. 0" ‘ -‘ I“ OJ 2" -V 1:6 -3 7‘ -3 :9 -1 w‘ a m -3 IDi -3 or -3 a. -3 I?» .( ur a! as a to) -0 POA o! )7 -I 96 -l a. -l '1‘ cl 3| -8 as 4 on -I Ila -I It" -I so -1 m '1 so -I w -I to, 0' you 0| 5| ° 10a 0 n1 ° Ho 0 Ian 0 OI 0 0o 0 ll 0 II 0 a I l1! I I. I .0 I 90 I on I I1 I 1! I IOI I on I I31 I .1 I If I 00 3 3| 1 I" l .. D I ‘I a an 3 NJ I u? I g. 3 .01 3 .00 3 Co 3 a. 3 I” ’ g. 3 .01 3 3. 3 n 3 nu 3 l1: 3 to 3 It! 3 1. 0 I00 0 1' 1 IN I Do- Q .I O I. O .1 . I31 0 III 0 3! O h 0 .3 Q I)! I 43 . 10 1 I61 ' 3‘ I 11 O I. I I. I OI I 1“ 0 10 0 n . .‘ O .. 3 9| . 0| ' .0 1 .‘ 1 SI , u " 00 d o: “ .. 00 ca ’1 o1 ‘1 to :: 3‘ o! “ u " .9 -9 ’. -3 -! 13 .q 11 02 :3 IO. IO “ be '9 In -. 60 _. a, .. 9' -0 .? O. l7I .0 )3 -Q 114 .3 II. -3 0.... 0.1.01. .IDOIIOIIOIIOIIOII.IDOIDOD OIDDCIOII. O. 001-. D. D n ‘1‘. ’OII~ID.1...H..IJ~ '— - OI'a-HI.:d’ I. J~ 3) v v- I UGDC. C4 c3 126.3(2.0) 02 c2 1 .36(2) 02 c2 c3 127.5(1.7) C3 C4 1. M( ) c4 c3 c2 123.8(1.9) c2 c3 1. 34(3) c5 c4 01 113.0(1.7) c4 c5 1. 56(3) c1 c2 02 109.9(1.7) 01 c2 1. 53(3) Zr 03 2. M( ) 03 Zr 04 77.8(0.5) Zr 04 2.13(1) C7 03 Zr 132.2(1.1) 03 o4 2. M( ) c9 04 Zr 132.4(1.2) 03 c7 1. M( ) 03 c7 c8 125.0(2.o) 04 c9 1. m( ) 04 c9 c8 125.5(1.8) C7 c8 1 .38(3) c7 08 c9 122.5(2.1) c8 c9 1. M( ) c6 c7 03 120.1(1.7) c9 c10 1. 52(3) C10 c9 04 111.8(1.8) c6 c7 1. 51(3) Zr—Cl 2. 50(1) Zr—Cyclopentadienyl ligand plane 2 2.24(2) *- The values listed in parentheses are the standard deviations of the last digit(s). 41 The Zr—O mean bond length obtained in this solution (2.15 i 0.04 X) is also in reasonable agreement with those reported for Zr(C5H702)4 (2.198 t 0.009 R) and for the Zr(C204)44_ complex ion25 (2.199 i 0.009 X), In addition, the intraligand O—O separation (2.73 i 0.04 R) falls midway between the mean value reported for tetrakisacetylacetonatozirconium(IV) (2.67 R) and that for the octahedral complexes (2.80 2), Table IX. Summary of interatomic parameters for some hexa— Co—ordinate transition metal* acetylacetonate complexes. Dist Atom 1—Atom(s) 2 R Atom 1 Atom 2 Group 3 Angle deg C o 2.80(4)** o M o 93.2(4.7) C o 1.27(2) M o C 125.3(3.3) C CH 1.38(2) o C CH 125.6(1.4) C CH3 1.53(3) o C CH3 124.4(2.8) C CH C 114.0(1.2) * Metals considered are Mn, Cr, Co, and Fe. * The values contained in the parentheses are the standard deviations in the last digit for the averaged values. Adapted from Lingafelter and Braun10 Zirconium compounds demonstrate a marked tendency to adopt lattice arrangements that produce stereochemical con— figurations which are related to the geometry of eight co— ordination. A number of these compounds have been tabulated by Nyholm et al.9 For example, the ZrF4 lattice27 is ar- ranged in a square antiprismatic configuration and the 2— . . . . ZrF6 ion28 has been found to crystallize as a chain-like 42 polymer with dodecahedral links, while the Zr(C5H702)4 and Zr(C204)44‘ complexes are examples of discrete square anti- prismatic and dodecahedral arrangements, reSpectively. In an analysis of eight co-ordination Hoard and Silver— ton29 discuss three configurations of possible stereochemical merit: the square antiprism, the undecahedron, and the dodecahedron. The undecahedron has not been reported as a suitable model for any discrete eight co-ordinate species, but has been invoked by Zachariasen to explain the co-ordina- tion of Th78123° and PuBr331, and several compounds iso— structural with PuBr3 have been tabulated by Nyholm et al.9 The equations for the dodecahedral and square antiprismatic valence bond orbitals have been proposed by Duffey33:33 and Racah34, and extensive calculations for the ligand-ligand repulsion energies for these models have been reported both by Kepert35 and by Parish and Perkins36. The presence of different ligands in w-C5H5(C5H702)ZZrCl eliminates the possibility for a close approximation to the symmetry of any of the ideal stereochemical models and there- fore reduces application of a model to a general description of the overall geometry of the complex. The ambiguity as- sociated with the co—ordination of the cyclopentadienyl ligand further confines application of the model to a descrip— tion of the orientation of the plane of this ligand rather than the designation of positions for specific carbon atoms. Schematic representations of the square antiprism (Figure 9), the undecahedron (Figure 10), and the dodecahedron (Figure 11) 43 Figure 9. Square antiprism. Figure 10. Undecahedron. 44 Figure 11. Dodecahedron 45 have been constructed with the positions of the chlorine and oxygen atoms chosen to most closely approximate the geometry of the molecule. On the basis of ligand—ligand repulsion calculations the most stable configuration for eight co-ordination is the square antiprism (approximately 1 kcal/mole more stable than the dodecahedron)36. The symmetry of the ideal square antiprism (D4d-82m) gives rise to two sets of eight sym- metry related edges designated 2 and s by Hoard and Silverton29. The ratio of the z and s edges for a number of zirconium complexeslsv33l34 averages to 1.05, and 9, the angle between the 8 axis and a co-ordinate bond, is approximately 57.50. An examination of Figure 9 indi— cates the lack of compatibility of this model with the geometry of w—C5H5(C5H702)2ZrCl. One O-Cl distance would have to be approximately-J2 times the other (observed ratio 0.95) and the angle 26, CerO, is 90.2 i 0.30 and not 115°. There is considerable merit for consideration of the undecahedron (C —mm2) as a model for this compound. For 2v example, if a special case of this model is considered it closely resembles an octahedron with the zirconium diSplaced from the four co-ordinate plane. A mirror symmetry plane perpendicular to the four co—ordinate plane requires opposite edges of this plane to be equal. This model may be con— sidered the equivalent of an octahedron if all four sides are equal; an acceptable condition for this structure, if the larger size of the Chlorine atom relative to the oxygen 46 atom is taken into consideration. Placement of the zirconium atom on the mirror plane and on the two fold axis (at the origin of the polyhedron) displaces it from the four co— ordinate plane. The resultant orientation of the cyclo— pentadienyl ring with respect to the four co—ordinate.plane is also compatible with the observed structure. If the molecule is describable in terms of the octa— hedral case of the undecahedral model the angles formed by the four co-ordinate.positions and an origin defined by projecting the zirconium atom onto the plane should be right angles (Figure 12) or for the more general case the adjacent angles should be supplementary (Figure 13). The extension of one corner due to the larger size of the chlorine atom would not effect these angles beyond the possible pack— ing effects. The appropriate angles are displayed in Figure 14 and clearly do not fit either criterion for this model. They do, however, more closely approximate the expected results for a similar operation carried out for dodecahedral symmetry (Figure 15). The dodecahedral polyhedron contains two sets of sym- metry related positions which may be designated as the A and B sites in the manner of Hoard and Silverton29. This configuration may be constructed for this mixed ligand molecule by placing the chlorine atom and one oxygen atom from each acetylacetonate ligand in B positions and the remaining oxygen atoms in A positions (Figure 11). The observed oxygen-chlorine plane consists of an A and three 47 180-9 90 Figure 12. Projected co-ordin- Figure 13. Projected co- ate angleszfiX'the octhedral ordinate angles for the undecahedron. general undecahedron. 82.3 87.70 92.40 7.60 Figure 14. Projected co-ordin— Figure 15. Projected co- ate angles for the ordinate angles for the w-C5H5(C5H7OZ)2ZrCl. dodecahedron 48 B sites, in which case centering the zirconium atom on the S4 axis of an ideal dodecahedron results in its displace- ment above this plane in the manner observed. Dodecahedral.molecular geometry is generally character— ized by two sets of angles, 9A and 9B, and the ratio of the bond lengths. Appropriate parameters for this molecule are: 6A = 37.80 (no meaningful deviation, only one measure— ment), SE = 77.8 i 0.30, Zr-O Similar parameters calculated by Silverton and Hoard24 for A : Zr-OB = 1.03 i 0.02. the ideal D2 -42m model (9 = 35.20, GB = 73.50, M-AzM-B = d A 1.03) and for a hard sphere model (9 = 36.90, 9 = 69.50, A B MrA:M-B = 1.00) are in reasonable agreement with the values observed for this structure. Additional characterization of a dodecahedron is obtained from a comparison of the four symmetry related edge lengths, or more appropriately, their ratios. The values for this structure (m/a = 1.03, g/a = 1.05, and b/a = 1.25) may be compared with the analogous ratios for both the Dzd-42m (m/a = 1.00, g/a = 1.06, and b/a = 1.27) and the hard sphere models (m/a = g/a = 1.00, and b/a = 1.25). The large m/a ratio found for this mole— cule arises from the larger size of the chlorine atom which occupies one of the sites determining the only unambiguous m edge. As a further check on the dodecahedral molecular con— figuration a series of calculations were made based on the 9 and 6 angles of the -42m dodecahedron and the A B Dzd mean bond distance for the observed Zr—O bonds (2.15 R). 49 The co—ordinates of three B and four A positions were generated by defining the z axis coincident with the S4 axis of the dodecahedron and by assigning the first A and B sites to the xz and yz planes, respectively, and operating on them with the S4 symmetry operations. The remaining site was determined by extending the fourth B site, generated from the above operations, to a length of 2.50 X (the Zr—Cl bond length). Calculations based on this model produced a four co-ordinate least squares plane (one A and three B sites, 0 = i 0.04 X), which is comparable to the oxygen—chlorine plane of the observed molecule, and indicated that the origin (zirconium) was 0.64 X from this plane. Similar calculations on three of the remaining do— decahedral sites, which may be assigned to the cyclopenta- dienyl ligand, established a 5.40 angle of intersection between the two planes. For this complex the standard deviation of the oxygen-chlorine plane is i 0.06 A, and the angle of intersection between the cyclopentadienyl ligand and the four co—ordinate plane is 3.00. The agreement between the observed structure and this model is considered reasonably good since distortion due to both repulsion and packing effects was not considered. It must be emphasized that the use of the three co-ordination sites for the cyclo— pentadienyl ligand in no way implies the occupation of these sites by specific carbon atoms, but is intended only to cor— relate the effect of the three molecular bonding orbitals with the molecular geometry of the complex. This interpretation 50 is supported by these calculations which indicate that only the nearly parallel nature of the two planes may be predicted, since consideration of three sigma bonds produced a ligand plane to metal distance of 1.56 8 while the observed distance is 2.24 R. The possibility of dW-pv interaction between the oxygen atoms located at the B sites and the zirconium atom has been discussed by Hoard and Silverton29 for Zr(C204)44-. Due to the high net charge on the central atom and the ap« parently small orbital overlap these authors postulate only a small net contribution to the Zr—O bond stability. The B mean bond ratio, Zr-OA:Zr-OB ? 1.03, reported for the oxalate complex is identical to that obtained in this solution. The C-O bond distances in the acetylacetonate ligands, which have less geometrical constraint than the oxalate ligands (C—OB/C-OA = 1.00), would be expected to show the effect of delocalization of electrons about the oxygens atoms. The observed bond length ratio, C-OBzc-OA = 1.03 i 0.01, is in agreement with these expectations and indicates sufficient dv-pv interaction to produce a geometric effect. The con— tribution of the dw-pv interaction to the bond stability of the Zr-OB bond is probably minor since the fold observed for the acetylacetonate-metal bond would be expected to de- crease the effective overlap of these orbitals. The molecular configuration of w-C5H5(C5H7O2)2ZrCl may be correlated reasonably well to the dodecahedral model frequently associated with the stereochemistry of eight 51 dywxdination. This assignment has been based upon the geome— try characterized by the five unambiguously defined co-ordina- tion sites, by the position of the zirconium atom with re- spect to these sites, and by the orientation of the plane of the cyclopentadienyl ring. No attempt has been made to associate specific carbon atoms of the ligand with the three co—ordination sites assigned to the ring. The dodecahedral description of the geometry of this complex presents some interesting possibilities for stereo— isomerism and has contributed to the initiation of an in- vestigation of these possibilities.11 V. INTRODUCTION The preparation and characterization of nonstoichio- metric systems are currently topics of considerable interest. Nonstoichiometric systems result from substitution within the crystal lattice of either mixed cationic oxidation numbers or different valent anions exhibiting similar crys- tal radii. Examples of both types of nonstoichiometric phases may be found in the chemistry of the lanthanide ele— ments, some of which have been studied extensively. Perhaps the most thoroughly investigated nonstoichio- metric oxide system is that of praseodymium. The phase dia- gram for this system, which has been reported by Hyde et al.§7 displays several discrete ordered phases in the composition range Pr01_7 to PrOl,8. The nonstoichiometrically re— lated phases appear to reflect the flexibility of the parent fluorite lattice displayed by PrOZ. This praseodymium sys— tem may be described by an anion vacancy model which com— pensates for substitution of Pr3+ ions for Pr4+ions by creation of an appropriate number of anion vacancies. Eyring and co-workers38r39 have indicated that the symmetry of the parent lattice varies from triclinic to rhombohedral as a result of slight shifts in the metal ion positions. 52 53 Nonstoichiometry has been reported in ternary systems possessing anions of unequal valence, for example, the lanthanide oxide fluorides.40 These compounds also exhibit a fluorite related structure. For example, stoichiometric samarium oxide fluoride crystallizes with rhombohedral sym- metry41 which Zachariasen42 has related to the fluorite lattice. Brauer and Roether43 have recently reported the existence of a number of complex phases which may be de- scribed by the formulation: SmOnF3_2n where n = 0.80 to 0.84. They reported that these phases, which have not been completely characterized, apparently exhibit one lat- tice parameter of three to seven times the nominal fluorite value. Mechanistically, the oxide fluorides may be described in terms of an interstitial anion model with a constant valent cation lattice. The preparation of SmF2.29 by reduction of SmF3 with hydrogen has been reported by Asprey et al.44, and the existence of a cubic mixed fluoride phase of variable compo- sition was postulated. It seemed probable that a system exhibiting a considerable range of nonstoichiometry might be obtained by further reduction of SmF3 and that this system should comply with a still third mechanism for mod- ification of the fluorite lattice. This mechanism may be considered most easily by starting with the fluorite SmF2 lattice. ~For each Sm2+ ion replaced by a Sm3+ ion an inter— stitial fluoride ion should be added to the lattice, and thus this SmCU}(IDQ fluoride system should resemble the variable 54 cationic lattice of the oxides and also display the inter- stitial anion behavior of the oxide fluorides. The uranium—oxygen system has Characteristics which indicate some similarities with this fluoride system. Uranium dioxide displays fluorite symmetry and a considerable range of nonstoichiometry has been reported for the uranium oxygen system.45 In particular, the UOZ-an portion of the system may be expected to comply with a similar interstitial anion model.46 Both the higher ionic charges of these ions, which may produce more ordering in the defect lattice, and the greater difference in their crystal radii, may make the uranium oxide system more complex than the samarium fluoride analog, however, the expected similarities should permit a meaningful comparison between these systems. The reduction of SmF3 with graphite, molybdenum, or tungsten was investigated by Kirshenbaum and Cahill47, but in each case the reducing agent was found to be less effec- tive than hydrogen. These observations indicate the need for a more active reducing agent than hydrogen; consequently, the reaction between elemental samarium and SmF3 was in— vestigated. VI . EXPERIMENTAL Preparation of Samarium Trifluoride Samarium trifluoride, one of the reactants for prepara— tion of the reduced fluorides, was prepared by reaction of Sm203 (99.9% theoretical samarium content, Michigan Chemical Corp.) with gaseous anhydrous HF (99.9% minimum purity, The Matheson Company, Inc.) diluted with nitrogen. The sesqui- oxide, contained in a platinum boat and calcined at 800— 850°, was inserted into a nickel tube lined with platinum foil in the center of the heat zone (Figure 16). The sys- tem was flushed with nitrogen for one half hour before the HF flow was initiated. After the mixed HF/N2 atmosphere was established,the nickel tube was heated: first to 2500 for two to three hours, and then to 5000 for approximately ten hours. The sample was cooled to room temperature under the mixed gas atmosphere, after which the HF flow was term— inated and the system flushed with nitrogen for at least one hour. The product was weighed, recycled to check for constant weight, and subsequently stored in platinum in a vacuum desiccator. The samarium trifluoride was analyzed for samarium and a powder X-ray diffraction pattern (here— after called powder pattern) was obtained. 55 j - —*—:—-j-—r-::—-“"; 56 HF and N2 Gas inlets (polyeth lene) Tube furnace T N2 outlet Ni reaction tube Pt fOll liner __1 L—’—" L.— ‘____1 C__'——T_____—1 r__—__—' *‘t—‘—“ NaOH Gas mixing bottle r———n—j/’(aq) (polyethylene) Pt sample boat CHzBrz Figure 16. Schematic representation of the SmF3 preparation line. 57 Preparation of the Reduced Samarium Fluorides Two closely related techniques were employed for prepara— tion of the reduced fluorides: a) direct reaction of the metal with the trifluoride and b) subsequent reaction of the product from (a) with either elemental samarium or the trifluoride. Due to the high vapor pressure of samarium and the desirability of obtaining fused samples, the reac— tions were effected in tantalum bombs. Tantalum tubes (6.2 or 9.0 mm irL, 0.4 mm wall), from which the reaction bombs were constructed were outgassed by induction heating under vacuum (approximately 10-6 torr) to a minimum temperature of 21000 (optical pyrometry, emis— sivity corrected but no transmittance correction) for at least three hours. After heating, the inner surface of the water cooled Vycor jacket of the vacuum line was examined for a metal deposit. The presence of such a deposit was considered as an indication that the tantalum had been sufficiently outgassed. One end of the outgassed tantalum tube was crimped and sealed by arc welding in an argon atmosphere. Because of the susceptibility of tantalum to reaction with oxygen at high temperatures, considerable effort was expended to purge the welding apparatus of air. A mechanical vacuum pump (Cenco Hyvac 2, Central Scientific Co.) evacuated the system to about 0.01 torr after which it was flushed with argon three times, and then filled to a positive pressure with this gas. A zirconium button (which served as an 58 oxygen getter) was first arced and then the tantalum tube welded under this positive argon pressure. A very clean, shiny weld was generally obtained by this technique. How- ever, if any sign of discoloration was detected after weld- ing, the tube was subjected to further outgassing. The tantalum tubes were charged with the appropriate reaction mixture in a controlled-atmosphere glove box. The argon atmosphere of this glove box was recirculated over activated alumina to remove water and over BASF Catalyst R3-11 (Badische Anilin-& Soda-Fabrik A.G.) to remove oxygen. Samarium metal (99.6% lot analysis, Michigan Chemical Corp.), which was stored under xylene when not in the glove box, was chipped from an ingot with a carbon steel cold chisel (the fragments were subsequently checked for steel particles with a permanent magnet), rinsed with trichloroethane and stored in the glove box until needed (less than one week). The procedure employed in charging reaction vessels with sample depended on the preparative technique used. When reaction between the trifluoride and the metal was employed the trifluoride powder was first weighed into the open bomb. The powder was inserted through a small funnel whose delivery tip was at least two centimeters below the top of the tube and was subsequently packed tightly so that it was in the lower portion of the bomb. The tantalum tube was crimped tightly against the sample after it had been Charged with the appropriate quantity of samarium. The charged bomb was then transferred to the arc welder via an argon 59 filled desiccator. A slightly different procedure was employed when one of the reactants was a reduced samarium fluoride. The reduced fluoride was first weighed into the bomb (generally the smaller diameter tube) and the stoichi— ometry of the mixture was adjusted with the appropriate quantity of either the trifluoride or the metal. The charged tantalum tubes were then sealed by arc welding as described previously and the welds were examined for discoloration or obvious faults. If a weld appeared unsatisfactory (usually indicated by discoloration) the sample was discarded. The bombs were heated under vacuum to 1600—19000 de- pending on the composition of the reaction mixture. In the initial stages of this investigation samples were maintained at temperature for about five minutes and quenched, however, since the powder patterns were diffuse, sample annealing was initiated. Two annealing techniques were employed in the course of this investigation. A group of four samples was heated to 19000 until the bombs expanded, after which the tempera- ture was lowered to 12000 over a period of four hours, and then to room temperature over a two-hour interval. These samples were then transferred to a quartz tube (lined with tantalum foil in the sample region) for further annealing. The quartz tube was evacuated (10-6 torr) and heated sub— squently to 12000 (Pt—10% Rh thermocouple, Honeywell Potentio— meter) in a Marshall platinum—40% rhodium wound tube furnace 60 (National Research Corp). After the temperature had been maintained at 12000 for eight hours, it was lowered to room temperature over an interval of approximately one hundred hours. Since minor golden discoloration was observed on the tantalum bombs annealed in this manner, subsequent an— nealing was effected in the vacuum system used for prepara— tion of samples. After samples had been heated to 19000 as part of the initial preparation, they were cooled to 12000, maintained there for about eight hours, and then brought to room temperature with stepwise cooling over a period of about fifty hours. The temperature control was considerably less rigorous when samples were annealed in this manner but there was no detectable discoloration. All bombs were opened with a tubing cutter under the argon atomOSphere of the glove box and the product removed by fracturing the solidified melt. The product was generally powdered in the glove box with an agate mortar and pestle and placed in dried glass vials which were sealed with paraffin wax upon removal from the box. One sample was placed in an outgassed tantalum tube and the top was crimped tightly but not welded. This sample was heated to 11500 for five minutes, quenched, removed from the vacuum line after thorough cooling, and immediately placed in the glove box. The water cooled jacket of the vacuum line was washed with 6§_HC1 to determine the reactivity of the condensed effusate. 61 Vapor Transport Experiments A portion of one of the initial products was placed in an outgassed tungsten effusion crucible to examine its vapori- zation behavior. After the sample had been heated for about two hours at 11000 (black body temperature measured with an optical pyrometer, no transmittance correction), it was cooled thoroughly and examined. A deposit which was identi- cal in appearance to the residue had condensed on the lid. The above observations led to a decision to attempt crystal growth by a vapor phase transport technique. Con- sequently, a sample was placed in an outgassed tantalum tube and a bomb prepared in the usual manner. This bomb was placed in the vacuum line and the induction heating coil was positioned so that the lower end of the bomb was centered in the coil. The sample was then heated for about five hours with the furnace power adjusted to produce a tempera— ture of approximately 12000 over the sample region of the bomb. The temperature of the upper portion of the bomb was estimated by Optical pyrometry to be 900-10000. The product, removed from the walls of the bomb by scraping the surface with a needle, was examined subsequently with a microscope by placing the material under paraffin oil and using reflected light. 62 Powder X—Ray Diffraction Patterns A Guinier focusing powder X—ray diffraction camera equipped with a fine focus copper X—ray tube (Figure 17), acquired during the course of this investigation, was used to obtain powder patterns of the various products. This camera has an effective radius of 80 mm, which when combined with its focusing character results in better resolution than that obtainable from the previously available 114.7 mm Debye Scherrer cameras. Even greater resolution is pos- sible by extremely precise adjustment of the monochromator (a quartz crystal cut at 3° to the (1011) plane and ground to a radius of 500 mm) and the primary beam slits for elim- ination of the Kaz radiation. This precise alignment (very difficult due to lack of reproducibility in the necessary adjustments of the camera) has not yet been accomplished successfully. In order to obtain the maximum accuracy in the lattice parameters obtained from the Guinier films, an internal standard is used to calibrate the film cassette and compen- sate for film shrinkage. Potassium chloride (a == 6.29300 i 0.00009 X48, 25°), which had been annealed at 600° after pulverizing, was used as the internal standard in this investigation. Both the sample and a small amount of KCl were secured to the planchet with amorphous plastic adhesive tape and, in the case of long exposures, were covered with a thin Monochromator Targetg/Primo aperture I . 63 FoCusing circle 05\ Diffracted film “ beam iii, Prim. beam focus Figure 17. Schematic of the Guinier camera. 64 coat of paraffin oil to minimize hydrolysis, which occurred upon prolonged exposure to air. The planchet (a steel disc with 5mm hole in the center) was placed in the holder, a slowly revolving magnet, with the back side of the tape against the magnet. The film cassetua which contained a 20 x 140 mm strip of Illford Type G Industrial X-ray film encased in two sheets of paper to prevent light exposure, was placed on the pin point triangular support of the camera box. With the incident beam stop on the film cassette open, the camera box was closed for safety purposes, and the shutter on the X—ray tube was opened to expose the film to the incident beam. After this exposure (about one second) the beam stop on the cassette was closed and the camera box was evacuated with a mechanical pump (Hyvac 7). The films were exposed four to twelve hours (35 kilovolts at 20 milliamperes, Picker Nuclear X—Ray Generator). The pro— cedure used to process the Guinier photographs differs from that normally employed. Due to the sharp lines obtained and angle of intersection of the diffracted beam with the film, two noncoincident images are recorded, one on the inner layer of the emulsion and the other on the outer layer. Consequently one layer of emulsion must be removed (usually the outer layer), and this was accomplished with a tooth brush after the film had been desensitized by the fixing solution and before it had cleared. Determination of the lattice parameters for the samarium fluoride samples required precise reading of these powder 65 patterns. The recommended procedure utilizes a scale cali- brated to the nearest 0.1 mm photographically printed directly on the film and read by projection on a screen. Unavailability of the scale necessary for the photographic reproduction resulted in use of a Picker X—ray film reader calibrated for direct reading to the nearest 0.01 mm. Un- fortunately this apparatus is subject to parallax errors. The film shrinkage — cassette calibration was obtained graphically from a plot of AS XE: S for the KCl powder pat- tern, where S is the observed distance from the index (the incident beam image) to the diffraction line and AS is the difference between the observed and theoretical distances. The linearity of this correction (Figure 18) was very re- producible, however, its magnitude varied from film to film. Sin2 9 values corresponding to the corrected S values were obtained from an appropriate table, and refined lattice parameters were obtained from the indexed sin2 9 values by application of a least squares linear regression program written byIJndqvist and Wengelin49. Analysis Each reaction product, including SmF3, was analyzed for samarium by steam hydrolysis to the sesquioxide. Three 0.2 g samples (two samples were used when only small quanti— ties were available) were weighed into platinum boats and placed in a 25 mm Vycor reaction tube. Heating was initiated after a steam generator had been connected to this tube. (H1111) 66 1.20 ~— m <1 H o 4.) 80.80 -- m C. o H 4.) 80.60 -— H H o O 0.20 -b 1 1 l l l I r r I l *7 l 30 50 70 90 110 130 Index—line separation S(mm) Figure 18. A typical film cassette-shrinkage correc- tion for Guinier photographs. 67 The steam flow rate was such that one to one and one-half liters of water evaporated in a twelve-hour period. In about two hours the temperature of the reaction tube attained 1000° where it was maintained for at least six hours. The samples were cooled in air and subsequently placed in a 900° muffle furnace to drive off any absorbed carbon dioxide, recooled in a vacuum desiccator, and weighed. Several samples were Checked for constant weight by recycling them through the preheated hydrolysis line for two hours. In an effort to determine the magnitude of oxygen con- tamination in the reduced samarium fluorides several samples were sent to National Spectroscopic Laboratories (Cleveland, Ohio). Their oxygen analysis was effected by the platinum- carbon fusion technique. The presence of fluorine generally produces erroneous results due to the formation of fluoro- carbons, however, the procedure employed at thflr laboratory was modified in an attempt to obtain satisfactory results. Density The density of the reduced samarium fluorides was deter— mined pycnometrically with CHzBrz as the solvent. The volume of the pycnometer, which was equipped with a thermometer for monitoring solvent temperature, was calibrated with boiled distilled water and the density of the methylene bromide was determined subsequently as a function of temperature. Only a small volume of product was available, thus all weighings were made to the nearest 0.01 mg on an automatic Mettler (Medfler Instrument Corp.) semi-micro balance. 68 A well—powdered sample was poured into the pycnometer through a funnel to avoid contact of the powder with the ground glass joint. The sample and pycnometer were weighed quickly and solvent was introduced in an effort to minimize exposure of the sample to air. The pycnometer, containing the sample and about half filled with solvent, was placed in a vacuum desiccator and subjected to reduced pressure. Approximately one cubic centimeter of solvent was pumped off in an attempt to remove adsorbed gases from the powder surface. After the pycnometer had equilibrated to room tempera— ture, it was filled with solvent. The temperature of the pycnometer generally increased by a couple of degrees when it was wiped to remove excess solvent, and thus several measurements were effected as a function of temperature while it cooled. Weighings were made on a dynamic system, since solvent was evaporating continually. Formation of a men- iscus on the side arm was taken as the reference point for all weighings and the temperature was read immediately after the weight was obtained. At least ten weight-temperature measurements were obtained for each density determination. VII. RESULTS Samarium Trifluoride Several samples of samarium trifluoride were prepared during this investigation and in each preparation the pro- duct was a fine white powder. The weight changes during the reaction (99.9 i 0.1% theoretical) as well as the samar- ium analyses (99.9 i 0.2% theoretical) were indicative of complete conversion to the trifluoride. The Guinier photo- graphs obtained from these samples displayed lines corre- sponding to both the hexagonal and orthorhombic crystal forms.5°:51 Physical Appearance of the Reduced Samarium Fluorides The physical appearance of the reduced samarium fluorides varied as the composition was adjusted from SmF2 to Sszos. The color of the opaque fragments obtained by fracturing the fused product was purple when the composition was near Ssz, but became progressively more red as the fluoride content increased and was a dull burgundy red at the com- position SmF2.5. The samples displayed a minor color change upon powdering, which required a considerably greater ef- fort for material whose composition was near SmFZ than for more fluoride rich samples. The purple fragments gave a 69 70 deep blue to blue-green powder while the burgundy colored samples simply appeared lighter when powdered. When viewed with transmitted light under a microscope, the powder re- mained opaque and subsequent examination of both fragments and powder with reflected light revealed an apparently regular change in color as a function of composition. Microscopic examination of the fragments confirmed the pres- ence of sharp faces, but recurrent morphology was not de- tected. A number of powdered samples were exposed to 6N HCl solutions and a definite increase in the rate of gas evolu- tion was noted as the fluorine to samarium.mmmic ratio was decreased to two. The rate of evolution was moderate for Ssz, but was considerably more vigorous when the relative samarium content was increased. Similar gas evolution was noted when 6N_HC1 was added to the coating deposited on the Vycor jacket of the vacuum line during heating of the sample in the open tantalum tube. Vapor Phase Crystal Growth The appearance of the material on the walls of the tantalum bombs used for vapor phase transport indicated the probabkaexistence of single crystals. When light was di- rected into the top portion of the tantalum tubes bright reflections were noted as the tubes were rotated. The material, when observed under a microscope, was found to consist mainly of fine powder; however, a couple 71 of small crystals were detected. One crystal in particular displayed very sharp faces and was selected for examination with single crystal techniques. A considerable number of oscillation photographs taken of this crystal failed to allow selection of any rotation axis with the expected cubic lat- tice parameters. A number of equi-inclination Weissenberg photographs, taken with rotation about an axis believed to be a face diagonal of the fluorite cell, produced a set of indices which could not be transformed to the desired cubic set nor correlated with any of the crystallographic Space groups. As a result the crystal was thought to be a twin and further identification was not attempted. Analytical The composition of the samples is displayed in terms of per cent samarium (average deviation) and stoichiometry in Table X. The fluoride content of the samples was deter— mined by difference and consequently the precision indicated in the stoichiometry reflects only that of the metal analysis. The analytical results were consistent with the composition of the starting mixtures, and thus are believed to be re— liable. Each of two different sets of samples sent to National Spectroscopic Laboratories contained a portion of "Sm20F4" taken from the same preparative sample. A sample of CaF2 (A.G.S. Reagent Grade) was also sent with the second set of samples. The analytical results are tabulated in Table XI. 72 Table X. Samarium analysis and stoichiometry 222?;iiz Stoichiometry iiegiig Stoichiometry 81.22(25)* SmF1 83(3) 77.74(03) smF2,26(1) 79.83(06) SmF2 00(1) 77.50(0 8) SmF2.29(1) 79.78(17) SmF2 01(2) 77.31(13) SmF2.32(2) 79.78(05) Ssz 01(1) 77.09(0 6) SmF2.35(1) 79.58(05) Ssz 03(1) 76 99(10) SmF2.3e(1) 79.26(05) Ssz 07(1) 76. 77(04) SmF2.39(1) 79 01(07) Ssz 10(1) 76 68(0 9) SmF2.41(1) 78.71(04) SmF2 14(1) 76. 67(09) SmF2.41(2) 78.52(07) Ssz 17(1) 76.45(0 9) SmF2,44(i) 78.31(06) SmF2 19(1) 76. 25(0 5) SmF2.46(1) 77.89(13) SmF2.24(2) 75. 73(03) SmF2.54(1) * The numbers enclosed in parentheses are the average deviations. Table XI. Oxygen analyses obtained from National Spectro- scopic Laboratories (Cleveland, Ohio) % 0 (wt) Set I % 0 (wt) Set II "Sm20F4" (Pt)* 4.26 4.69 "Sm20F4" (Ni) - 3.82 Can - 3.09 SmFX 0.24(04)** 0.38(00)** * A portion of the sample prepared in the platinum boat was sent with both sets of samples. *- The values included in the parentheses are average devia— tions. 73 and it is apparent from the inconsistency in the “Sm20F4" analyses and the high results obtained for CaFZ that the procedure used was inadequate. The oxygen content has not been adequately analyzed; however, the precautions taken to avoid oxygen contamination were extensive and therefore the samples are believed to contain considerably less oxygen than these results indicate. Density The volume of the pycnometer, as determined from the tabulated52 absolute density of water, was found to be 9.7990 i 0.0001 cm3 at 24°. The measured density of the A.C.S. Reagent Grade methylene bromide used as the solvent is displayed graphically as a function of temperature in Figure 19. The small volume of fluoride samples available for these measurements limited the precision of the density determina— tion. For example, a deviation in sample volume of 0.0004 cm3, a typical value, produced as much as 0.02 g cm—3 devia- tion in the measured density. The measured densities and their standard deviations are contained in Table XII. Unit Cell Symmetry and Lattice Parameters Guinier powder patterns taken of samples throughout the composition range displayed considerable similarity to the pattern obtained for the face centered cubic Ssz. The sin2 9 values obtained from these photographs are listed in 74 23.6-e O O O a 23.2- 13 0 g _ a °9> 04 _ E 22.5 0 B 22.4— O ##l!.!!: 2.484 2.485 2.486 2.487 Density (9 cm'3) Figure 19. Density of CHzBrZ as a function of temperature. Table XII. ~Density of reduced samarium fluorides -3) Composition Density (9 cm smF2.01 6 16(5 ) SmF2.10 6. 22(2) SmF2_24 6. 37(2 ) SmF2.32 6. 55(5) SmF2036 6. 57(2) SmF2.39 6. 57(2) SmF2,41 6. 658(4) 5mF2.44 m( ) *- Values given in parentheses are the standard deviations based on a minimum of ten measurements. 75 Appendix III. Powder patterns obtained from the quenched and annealed samples displayed few significant differences. The most pronounced change, as was expected, was the sharp- ness of the lines. Lines obtained from annealed products were sharper than those obtained from quenched samples; these sharper powder patterns were used in the analysis of the unit cell symmetry and for lattice parameter determinations. The powder patterns obtained for samples with an atomic ratio F:Sm of less than 2.00 were generally rather diffuse; however, they were identical in appearance to those of SmF2 and the lattice parameters obtained from the sharpest of these photographs are the same as those of the stoichio— metric compound. A cubic phase, as determined from the Guinier photographs, was found for the composition range SmF2,00 to SmF2,14. The cubic lattice parameters for this phase were observed to decrease as a function of composition and are listed in Table XIII. The Guinier photograph obtained from a sample with com— position SmF2.17 contained the first indication of deviation from the cubic symmetry of the parent lattice. This powder pattern (the first one displayed schematically in Figure 20) contained doublets for each of the lines normally produced by the cubic samples. As is indicated in the figure similar powder patterns were obtained for samples throughout the region of stoichiometry: Sszol7 to SmF2_32; but a trend in the relative intensities of the lines was noted (Figure 20). The powder patterns obtained from two samples, SmF2.35 and 76 Table XIII. Lattice parameters as a function of composition for a reduced samarium fluoride phase Lattice Parameter Composition a cubic (X, 240) SmF1,83 5.876(1)* SmF2.00 5.868(1) SmF2.01 5.867(1) Ssz 01 5.870(2) SmF2.04 5.865(1) SmF2.O7 5.855(2) SmF2.10 5.853(2) SmF2.14 5.845(2) X- Values given in parentheses are the standard deviations determined from application of a least squares linear regression program.4a 77 smF2.17 II S F m2.19 L II VI JJ II II I 1. Il J H II Estimated relative intensity smF2.32 1] l I, , ll ll Line position, 0.04 jsin2 9 2.0.15 Figure 20. Estimated relative line intensity from powder patterns obtained from samples in the composition range SmF2.17—SmF2.35. 78 SmF2.36, contained lines with the same sin2 9 values as several of those described above and were indexed on the basis of a tetragonal unit cell with lattice parameters of a = 4.106 r 0.002 and c = 5.825 r 0.003 R. A number of very weak lines (indicative of superstructure) were observed in the powder patterns obtained throughout the latter half of the stoichiometry range, but were not assignable to the tetragonal unit cell. Further examination of the strong lines in the Guinier powder patterns obtained from samples in the above composition range allowed identification of a face centered cubic unit cell with a == 5.841 i 0.002 R. The relative intensities of the lines associated with only the cubic phase decreased as the fluoride content increased. When thezfinmic ratio F:Sm was increased from 2.36 an additional change was observed in the Guinier photographs. The new powder pattern was indexable on rhombohedral sym- metry. Only one sample, SmF2.39, produced lines that were assignable uniquely to both the tetragonal and rhombohedral phases. Samples with compositions between SmF2.41 and SmF2.46 produced X-ray powder patterns which were also indexable on the rhombohedral unit cell, but which produced a systematic variation in their lattice parameters (Table XIV), indicative of a continuous decrease in unit cell volume. The powder pattern obtained from a sample of SmF2.54 displayed the lines of the rhombohedral phase and of samar- ium trifluoride. The lattice parameters obtained for the 79 rhombohedral phase in the two phase mixture were the same as those found for SmF2.46. Table XIV. Rhombohedral unit cell parameters as a function of composition Composition a (X) 0 (deg) SmF2.41 7.124(2)* 33.40(2)* Smrz,44 7.122(2) 33.32(2) SmF2.46 7.096(2) 33.23(2) *- Values enclosed in parentheses are the standard deviations in the appropriate parameters. VIII . DISCUSSION The reaction between samarium and samarium trifluoride has produced a reduced Sm(II)-Sm(III) fluoride system which displays a considerable range of nonstoichiometry. The Guinier powder patterns obtained from samples throughout the nonstoichiometric range closely resemble the face centered cubic pattern obtained from Ssz and thus indicate that the structural behavior of this system results from modification of the parent lattice. Fluorite Lattice Cubic compounds possessing AB2 stoichiometry generally display either the rutile or fluorite structure and Pauling53 has determined the minimum univalent radius ratio (0.732) for which the fluorite structure has the greater stability. The univalent radius of samarium may be approximated from the trivalent radius reported by Templeton and Dauben54 and this value, 1.27 2, when combined with that of the fluoride ion, 1.36 853, produced a radius ratio equal to 0.93. Thus the fluorite lattice would appear the likely model for the parent lattice in this nonstoichiometric system. Pauling has also compared the sum of the crystal radii and the observed interionic distances for several crystals with the fluorite structure and has demonstrated their gen- 2+ eral agreement. The crystal radius of Sm , 1.18 X, 80 81 calculated from the observed lattice parameters and the crystal radius of the fluoride ion53 may be compared with 2+ that of Eu , 1.17 X, obtained from the lattice parameters of NaCl-type EuO55. Lee, Muir, and Catalano56 have re- ported lattice parameter a =: 5.836 i 0.005 X for Equ; however, further work by Catalano and Bedford57 has shown the actual composition to be EuF2.06. If the lattice , parameter—composition dependence observed for the samarium system applies to its europium analog, the lattice parameter for the stoichiometric europium difluoride would be a :: 5.842 X, a value which compares very favorably with that calculated from the above crystal radii (a :: 5.843 X), + as 1.12 R, a Pauling lists the crystal radius for Eu2 value somewhat smaller than that obtained from these calcu- lations and possibly indicative of incomplete reduction in the compounds from which it was determined. Interstitial Anion Model Two models based on the fluorite lattice may be pro— posed for a description of this nonstoichiometric system: a) an interstitial anion model described previously, and b) a cation vacancy model with a constant anion lattice. The theoretical densities calculated for each of these models from the observed unit cell volume and the observed density are displayed graphically as a function of composi- tion (Figure 21). It is apparent from an examination of this figure that the cation vacancy model is not applicable to 82 this system and that the interstitial anion model is in agreement with the observed density behavior. 3 m m % 0 Measured 5-6“[] Interstitial A Cation vacancy l 1 p l .1 l 2100 2.10 2.20 2.30 2.40 2.50 Composition SmFX Figure 21. Density as a function of composition. The unit cell volume decreases as the fluoride content increases. The volume—composition behavior of the inter- stitial anion model is governed by two opposing events: a) substitution of a smaller and more highly charged cation with subsequent decrease of the unit cell volume and b) addition of a fluoride ion into an interstitial site with a resultant expansion of the lattice. The observed decrease 83 in the unit cell volume is indicative of the dominance of the substitution step in the mechanism. An indication of the effect of addition of the inter- stitial fluoride ions may be obtained from an application of Vegard's law to a fluorite lattice solid solution be- tween cations with the crystal radii of the Sm2+ and Sm3+ ions. The observed lattice parameters and those calculated from this law are displayed graphically as a function of composition in Figure 22. As is expected, the observed lattice parameters are progressively larger than those pre- dicted. 5.8704- 5 .8603- 03 0 H g 41. O 5.850 m 5 .840w— 1 1 l I A I T l f I 2.00 2.04 2.08 2.12 2.16 Composition SmFX Figure 22. The effect of composition on the lattice parameters of the cubic samarium fluoride phase. 84 The cationic co-ordination for the fluorite lattice is displayed in Figure 23. The interstitial sites, whose ef- fective radius equals the cationic crystal radius, are represented by open cubes. A possible description of cat- ionic substitution and anionic addition for the present system is indicated by the arrows in this figure. The smaller size of the Sm3+ ion allows its displacement from the ideal cationic position of the fluorite lattice. Hard sphere contact between the trivalent samarium ions and the fluorite—type anions would result in an increase in the ef- fective radius of the adjacent interstitial site (1.33 8) and would require less distortion of the adjacent co-ordin— ate polyhedra when a fluoride ion was added to the lattice at this site. The proposed geometry for the co—ordination of the trivalent cation is shown in Figure 24 along with the co-ordination sphere for SmF3 as determined by Zalkin and Templeton.5° The similarity between these co-ordination geometries and the culmination of the nonstoichiometric phase in a two phase region with SmF3 serve as good support- ing evidence for the proposed model. Application of this model to the Sm(II)-Sm(III) fluoride system is based on the assumption that initial deviations from the SmF2 stoichiometry occur by random location of the interstitial defect pairs. The regular decrease in the cubic lattice parameters appears to indicate that this mechanism can operate until the composition approaches Sszola. the phase boundary determined from the cubic lattice 85 \ .\ ‘2‘." ‘ . . ' .5” \(y- 1‘ \. -. - . \ I. :x\ \\\"\ 3‘: C @ F’ Fluorite c Sm(III) replacing Sm(II) '€> Direction of shift Figure 23. Samarium co-ordination in the fluorite lattice (four Ssz units) a) Interstitial anion model b) Samarium trifluoride Figure 24. Sm(III) co—ordination. 86 parameters measured in the two phase region. The appearance of a nominally tetragonal phase with a narrow composition range indicates the operation of some order in the lattice and the two phase region between the cubic and tetragonal systems may represent the region in which the random substi- tution mechanism gives way to an ordered substitution pro— cess. The variation in the relative intensities of the powder pattern hnesci’the cubkzand tetragonal phases in this twoephase region indicates the probable absence of any intermediate phases. Samarium analyses on samples whose Guinier photographs indicated only the pseudo tetragonal powder pattern (apparent superstructure lines) place its composition at SmF2.35i0.02. The description of this phase as tetragonal probably reflects the pseudosymmetry of the samarium ions. since the major contribution to the X-ray scattering factors in this system is from the samarium elec— trons (59 and 60 ys. 10 for the fluoride ions). Consequently, the strong lines in the powder patterns should reflect the symmetry of these ions. The observed superstructure may correspond to the symmetry of the fluoride ions and there— fore more closely reflect the geometry of the unit cell. Unfortunately, attempts to index these superstructure lines have not met with success. A third phase, which also appears to be nonstoichio— metric with variable lattice parameters, has been observed for samples with an atomic F:Sm ratio greater than 2.41 i 0.01. The powder patterns obtained from samples of this 87 phase have been indexed as a rhombohedral modification of the fluorite lattice. One sample, composition SmF2.39, pro- duced a powder pattern that contained lines attributable to both the rhombohedral and tetragonal phases and thus established a narrow two phase region between these two phases. Guinier photographs and samarium analyses indicate that the fluoride rich phase boundary is near SmF2.46, and, as with the nonstoichiometric cubic phase, there is a regular decrease in the unit cell volume in the SmF2.41- SmF2.46 region (Figure 24). Samarium trifluoride is present on the fluoride rich side of this rhombohedral phase and therefore it must be the last phase in the nonstoichiometric samarium fluoride system. The rhombohedral geometry of the lattice at the tri- fluoride phase boundary may indicate the composition to be SmF2.50 rather than the analytically determined SmF2.46. Since no superstructure lines have been observed in the Guinier photographs obtained from these samples, the struc- ture seems to be that of a simple rhombohedral cell. The rhombohedral unit cell (Figure 25) contains only two samarium ions, one of which is located at the body center and the other is shared between adjacent unit cells. The decrease in the rhombohedral angle, a. is consistent with the location of the trivalent ion in the body centered position; however, the interstitial sites, which would be considerably distorted, are not favorably oriented for this symmetry and thus the probable location of the fluoride ion can not be predicted. 88 Samarium positions indicated Figure 25. Fluorite related rhombohedral unit cell. 89 A Homologous Series If the observed phase boundaries are considered as dis- tinct phases, a homologous series may be constructed for this system. The general equation Sm12F24+n, where n has an integal value from 0 to 6 inclusively, will generate atomic ratios, F:Sm, in agreement,within experimental error, with the observed phase boundaries (Table XV). Two of the phases predicted have not been detected in this investiga- tion: Sm12F25, which falls in the center of the nonstoicio— metric cubic region and Sm12F27, which falls in the cubic— tetragonal two phase region. Table XV. Comparison of the stoichiometries generated by Sm12F24+n and those observed for phase boundaries n Sm12F24+n Observed ° smF2.00 smF2.00 1 Ssz .08 ‘- 2 SmF2.17 SmF2.16 3 ssz .25 -" 4 smF2.33 SmF2.35 5 SmF2.42 5mF2.41 6 SmF2.50 5mF2.46 If indeed the system is describable in terms of the proposed homologous series, the basic structural unit might contain twelve samarium positions which undergo substitution in an ordered manner. 90 Comparison with the Uranium Oxide Syptem Considerable similarity exists between the samarium fluoride and uranium oxide systems. A lattice parameter and density study by Lynds et al.58 has produced results similar to those reported here. The lattice parameter for stoichiometric U02 (a =: 5.470 i 0.001 2), when treated with the crystal radius of the oxide ion53 produced a crystal radius for U4+ of 0.97 X, a value identical to that re- ported by Pauling.53 The cubic lattice parameters have been found to decrease as the oxide content of the lattice increases. Lynds et a15.8 present two equations to describe this latttice parameter variaths: one for the composition range UOz-U02.1257 and another for the range U02.17-U02.25- The first equation characterizes this behavior in terms of a nonstoichiometric U02 phase while the second describes a nonstoichiometric U409 phase (U02.25). The region described by the first equa- tion has a clear counterpart in the samarium fluoride sys- tem (Figure 22, page 83), however, the analogy in the second range is not well defined. The region between SmF2.17 and SmF2.25 has been described as a two phase region containing the cubic phase, SmF2_16, and the tetragonal phase, SmF2.35- No significant indication of a phase with the composition ssz-zs has been observed in this work. A single crystal study by Belbeoch et al.59 has demon— strated that the unit cell of U409 consists of sixty-four 91 nominally fluorite unit cells arranged in a 4 x 4 x 4 array. Superstructure observed in the two-phase region and assigned to the tetragonal unit cell may in part correSpond to this type of cell, however, it was not defined well enough for sufficiently accurate measurement to allow assignment. The concurrence of the phase boundary at SmF2.16 and U02.17 pro- vides some support for the existence of a phase at SmF2.25, provided that the analogous nature of the two systems may be substantiated further. Additional comparison between these systems may be effected by considering the homologous series, Un02n+2’ which has been proposed by Makarov.6° This series indicates a second phase, U7016, which should have a samarium analog, Sm 2.23, which also occurs in the cubic-tetragonal two- phase region. The existence of this phase in the uranium system has not been well established, and no evidence of its analog in the samarium fluoride system has been found. The next member in the series, U6014, has an analog in the samarium system, SmF2.35, and the two phases are struc— turally similar. The lattice parameters of the uranium phase generally have been reported in terms of a face centered tetragonal cell. However, Hoekstra et al.61 have indicated they correspond to a body centered tetragonal cell with a = 3.78 and c = 5.55 X. As in the samarium phase, the a parameter is less than one half the face diagonal of a cube with edge c. A modification of the tetragonal cell with a = 3.84 and c = 5.40 R has been 92 observed in the uranium oxides, but no evidence for it has been found in the samarium analog. The next phase in the homologous series U5012 (U02.4o) has been reported to be tetragonal with a = 5.364 and c = 5.531 X, The nearest approximation of this phase observed in this work is SmF2.41, which has been indexed on a rhombo- hedral lattice. The latter indexing is consistent with the Guinier powder pattern and corresponds to a simple modifica- tion of the parent lattice. The samarium analog of U4010, the next phase in the homologous series, is the end of the nonstoichiometric rhombohedral phase. The uranium compound has been examined by single crystal techniques and has been found to be ortho- rhombic. It seems apparent that while the same stoichiome— tries are involved, the lattice modifications are different for the two systems. The uranium system displays at least one more phase, with several crystal modifications, before the lattice collapses to that of U03, and thus appears to be more complicated at the anion rich end of the nonstiochio- metric region. This complexity may be a result of the dif- ferent charges and size of the ions. It is apparent from the above discussion that the non- stiochiometry displayed by these two systems is the result of similar modifications of the fluorite lattice. While the present investigation of the Sm(II)-Sm(III) fluorides has not established the nature of these changes, it may have provided an alternative path to their illucidation. IX. SUGGESTIONS FOR FUTURE RESEARCH The Sm(II)-Sm(III) fluoride system displays a wide range of nonstoichiometry and undergoes a number of lattice modifications. Its similarity with the uranium oxygen system has been discussed. In view of these similarities, an understanding of both of these systems would benefit from a systematic examination of the samarium fluorides by single crystal X-ray diffraction techniques, with a de- tailed structural analysis as the primary goal. The samarium system is better suited to application of the heavy atom technique than the uranium analog since uranium (88 and 86 electrons) would dominate the structure factor more than samarium would. Vapor phase transport experiments conducted during this investigation indicate that single crystals may be obtained by this method. Attempts to apply this technique to crystal growth may be facilitated by a consideration of the following procedure. Place about one gram of sample in an outgassed tan— talum tube and flatten the container to reduce its volume. This flattening will reduce the argon pressure in the bomb and increase the mean free path length. Once the tube has been sealed, it should be heated in vacuo to about 1800°; 93 94 at this temperature the bomb will generally expand to its full size. Subsequently, cool the bomb and reposition the heating coil to adjust the temperature gradient. A ten centimeter long bomb with its bottom end at the center of a twenty to twenty—five centimeter coil appears to produce a reasonable gradient. Heat the sample portion of the vapor transport bomb to 1200-1400° for twelve to twenty-four hours and then cool it in a stepwise manner over about a fourty-eight-hour interval. This heating procedure should produce well annealed single crystals. The bombs may be opened in air (standard tubing cutter applied near the center of the bomb) and the vapor transport product removed by scraping. The product should be maintained under paraffin oil since hydrolysis occurs on prolonged exposure to air. The composition of the bulk sample should be samarium deficient with respect to the desired composition of the crystal. The high samarium content of the condensate found on the vacuum line walls after an open bomb was heated indicates that the vapor contains a higher samarium to fluorine ratio than the residue. A mass spectrometric determination of this ratio as a function of composition would facilitate selection of the composition of the start- ing samples. A series of crystals should be examined to provide an understanding of the structural aspects of this system. These should include: SmF2,16, the nature of which is un- known in both systems; SmF2_25, to establish the existence 95 of a distinct phase and determine its structure; SmF2.53. to determine the true symmetry of the unit cell, SmF2.41. to establish the relationship of this phase to SmF2.50; and SmF2.50 to establish this crystal structure and compare its co—ordination with that in SmF3. The complexity of the oxygen-rich portion of the uranium oxide system may estab- lish merit for additional investigation of the analogous region in the samarium system. Accomplishment of this suggested research represents a considerable eXpenditure of effort but should contribute substantially to an understanding of the anion rich behavior of the fluorite lattice and consequently serve as a model for the description of other related chemical systems. BIBLIOGRAPHY «t- -...LA'\’ . "~— ' 'l‘: 10) 11) 12) 13) 14) BIBLIOGRAPHY E. M. Brainina, R. Kh. Freidlina, and A. N. Nesmeyanov, Dokl. Akad. Nauk SSSR, (Eng. Transl.) 138, 628 (1961). E. M. Brainina, R. Kh. Freidlina, and A. N. Nesmeyanov, ibid., (Eng. Transl.) 154, 143 (1964). E. M. Brainina and R. Kh. Freidlina, Izv. Akad. Nauk SSSR, Ser. Khim., 1964, 1421; Chem. Abstr. Q4, 14214c (1966). J. C. Thomas, Chem. and Ind., 1956, 1388. G. Wilkinson and F. A. Cotton, Progress in Inorganic Chemistry, Vol. I. Interscience Publishers, New York, 1959, pp 1—124. F. A. Cotton, Chemical Applications of Gropp Theory, Interscience Publishers, New York, N.Y., 1963, pp 177- 180. R. J. Doedens and L. F. Dahl, J. Am. Chem. Soc., 81, 2576 (1965). F. A. Cotton and G. Wilkinson, Advanced Inorganic Chemistry, 2nd ed, Interscience Publishers, New York, N.Y., 1966, pp 664-668. R. J. H. Clark, D. L. Fepert, R. S. Nyholm, and J. Lewis, Nature, 199, 559 (1963). E. C. Lingafelter and R. L. Braun, J. Am. Chem. Soc., §§, 2951 (1966). T. J. Pinnavaia, J. J. Howe, and A. D. Butler, ibid., 22, 5288 (1968). G. Doyle and R. S. Tobias, Inorg. Chem., Ex 1111 (1967). M. Straumanis and A. Ievins, Z. Phys., 102, 353 (1936). E. W. Washburn, Ed., International Critical Tables of Numerical Data, Physics, Chemistry, and Technology, Vol. III, McGraw—Hill Book Co., Inc., New York, N.Y., 1928, pp 28. 96 In... .. .__... 'r --. .._.. ”4‘. 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 97 C. H. MacGillavry, G. D. Reick, and K. Lonsdale, Eds., International Tables for X-ray ngstallography, Vol. III, The Kynoch Press, Birmingham, England, 1962, pp 166. P. Coppens, L. Leiserowitz, and Rabinovich, Acta Cryst., 18” 1035 (1965). W. R. Busing and H. A. Levy, ibid., 12, 180 (1957). D. B. Shinn, Ph.D. Thesis, Michigan State University, East Lansing, Mich., 1968, pp 115-119. L. H. Thomas and K. Umeda, J. Chem. Phy§,, 26“ 293 (1957). J. Berghuis, M. Haanapel, M. Potters, E. O. Loopstra, C. H. MacGillavry, and A. L. Veenendaal, Acta Cryst., §, 478 (1955). E. W. Hughes, J. Am. Chem. Soc., 63” 1737 (1941). R. C. Weast, Ed., Handbook of Chemistry and Physics, 45th ed, Chemical Rubber Co., Cleveland, 0., 1964, pp E-72. D. T. Cromer and J. T. Waber, Acta Cryst., 18” 104 (1965). J. V. Silverton and J. L. Hoard, Inorg. Chem., 2, 243 (1963). L. Pauling, The Nature of the Chemical Bond, 3rd ed., Cornell University Press, Ithaca, N.Y., 1960, p 260. G. L. Glen, J. V. Silverton, and J. L. Hoard, Inorg. Chem., 2, 251 (1963). R. D. Burbank and F. N. Bensey, U. S. Atomic Energy Comm., Report No. K—1280, (1956). H. Bode and G. Tuefer, Acta Cryst., 9, 929 (1956). J. L. Hoard and J. V. Silverton, Inorg. Chem., 2, 235 (1963). W. H. Zachariasen, Acta Cryst., 2” 288 (1949). W. H. Zacharaisen, ipid,, l/ 265 (1948). G. Duffey, J. Chem. Phys., 18” 746 (1950). G. Duffey, lhlgf' l§x 1444 (1950). G. Racah, ibid., 11’, 214 (1943). 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) 51) 52) 53) 98 D. L. Kepert, J. Chem. Soc., 1965, 4736. R. V. Parish and P. G. Perkins, J. Chem. Soc., 1967A 345. B. G. Hyde, D. J. M. Bevan, and L. Eyring, Phil. Trans. Roy. Soc., A259, 583 (1966). L. Eyring and N. C. Baenziger, J. Appl. Phys. Spppl., §§, 428 (1962). J. O. Sawyer, B. G. Hyde, and L. Eyring, Bull. Soc. Chim. Fr., 1956, 1190. I l D. B. Shinn, Ph.D. Thesis, Michigan State University, #- East Lansing, Mich., 1968, pp 62-104. l L. R. Batsanova and G. N. Kustova, Russ. J. Inorg. Chem., ( (Eng. Transl.), 2x 181 (1964). ‘ W. H. Zachariasen, Acta Cryst., 4” 231 (1951). G. Brauer and U. Roether, presented in part at the VII Earth Research Conference, Coronado, Calif., Oct. 19 8. L. B. Asprey, F. H. Ellinger, and E. Staritzky, Rare Earth Research 11. K. S. Vorres, Ed., Gordon and Beach, N.Y., 1964, PP 11-20. R. M. Dell, Reactivity of Solids, G. M. Schwab, Ed., Elsevier Publishing Co., N.Y., 1965, pp 202-203. H. Hering and P. Pério, Bull. Soc. Chim. Fr., 1952, 351. A. D. Kirshenbaum and J. A. Cahill, J. Inorg; Nucl. Chem., 14“ 148 (1960). P. G. Hambling, Acta Cryst., 6x 981 (1953). O. Lindqvist and F. Wengelin, Ark. Kemi, 28“ 179 (1967). A. Zalkin and D. H. Templeton, J. Am. Chem. Soc., 22x 2453 (1953). I. Oftedal, z. physik Chem., pg, 272 (1929); 313, 190 (1931). A .33. R. C. Weast, Ed., Handbook of Chemistry and Physics, 45th ed. Chemical Rubber Co., Cleveland, 0., 1964, pp F-4. L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, N.Y., 1960, pp 507-537. 54) 55) 56) 57) 58) 59) 60) 61) 99 D. H. Templeton and C. H. Dauben, J. Am. Chem. Soc., 22, 5237 (1954). H. A. Eick, N. C. Baenziger, and L. Eyring, ibid., Zfix 147 (1956). K. Lee, H. Muir, and E. Catalano, J. Phys. chem. Solids, 26. 523 (1965). E. Catalano and R. Bedford, personal communication, University of California, Livermore, Calif., 1968. L. Lynds, W. A. Young, J. S. Mohl, and G. G. Libowitz, 1963, Advances in Chemistry Series, 22/ 58 (1963). B. Belbeoch, C. Piekarski, and P. Pério, Acta Cryst., 837 (1961). E. S. Makarov, Dokl. Akad. Nauk SSSR, (Eng. Transl.), 139, 720 (1961). H. R. Hoekstra, A. Santoro, and S. Seigel, J. Inorg. Nucl. Chem., 12' 166 (1961). 1:5 APPENDIX I DESCRIPTION OF COMPUTER PROGRAM r‘//’. APPENDIX I DESCRIPTION OF COMPUTER PROGRAM Program Distan Program Distan written by A. Zalkin and modified by Lundgren and Luminga, calculates interatomic distances, bond angles, and their standard deviations. This program also calculates the thermal motion effects associated with the temperature factors. A. Interatomic Distances Interatomic distances are calculated from the posi— tion co-ordinates (X,Y,Z) in an oblique co—ordinate system (A,B,C,d,6,y; iyg;_a triclinic unit cell) by application of the following equation: d = (d: + dy + dz + adydz cos a + 2 dxdy cos 5 + 1 2 d d cos y) 2 X Y where dX = (X2 - X1)A, etc. B. Standard Deviations in Interatomic Bond Distances \ Standard deviations are calculated as the sum of in— dependent components. The contributions due to the standard deviations in the lattice parameters and the position co- ordinates are determined separately and then combined according to the equation: 100 a... Lunmavmn—‘l'aN—ou . ._ 101 1 0= (2 GEM/2 . l l The standard deviation of the interatomic distance due to the variation in the lattice parameters is 4J>9 S 2 (X2 — X1)(dx + dz cos B + dy cos y) standard deviation in the A lattice parameter, and O S = —(d d sin C1)----g . o = standard deviation in angle (1 X2 d a The component resulting from variations in the atomic position co—ordinates + 28 S cos y* o a o X I y O l l 1 1 1 l * *- + 28X Sz cos B + 2Sy Sz cos a ) i i i i where o Xi SXi (dxA dy A cos y dz A cos B) d an 0x = standard deviation in the xi position co—ordinate. i Space group translations and symmetry elements also govern the manner in which the standard deviation in the position parameters effect the variation in the bond dis— tances. Translation Related Elements: 3' = 25 and s' = 0 X2 X2 X1 102 142, Atom (1) is considered to be a stationary point and its standard deviation is added to that of the second atom. For high symmetry space groups, (hexagonal, rhombohedral, tetragonal, and cubic) the translation equations result in an exchange of co-ordinates ($43. X = Y). These transla— tions produce the following equations 5' = 25 and s' = 0, X. X. y l l and for symmetry such that yi = 2xi s' = 33 and s' = 0. X. X. . l l y]. Cubic and rhombohedral space groups impose similar re— quirements on S2 and they are also related to SX . i 1 Therefore, standard deviations in the bond distances between symmetry related atoms is larger than it is for symmetry independent atoms. C. Thermal Motion: Uncertainty, and its Effects on Bond Distances The thermal parameters, isotropic or anisotropic, also effect the probability of locating an atom at a given point. Since these parameters adjust the atomic scattering factors for temperature effects, they are generally considered to reflect thermal motion of the atoms. The error associated with these parameters (root—mean- square-error) is calculated from the equations: 103 a) Isotropic thermal parameters: 1/2 B. 150 1 2 SW Cl l b) Anisotropic thermal parameters: 131115.2 + 1322132 + B33C2 + BleBcos y + B13ACcos )3 + B23BCcos a 2 U = - - A 6 W2 Further application of the concept of thermal motion is made to determine the increase in the bond length as a result of a) motion of one atom with reSpect to the other or b) independent motion of both atoms. Relative Thermal Motion: a) Isotropic Md. = 2 401/3 1 Ad 3 Md2 — Md1 = Ad (11,2 (ii-Ea b) Anisotropic _ A. AXa — (dX + dz cos B + dy cos y) d ._ 2 2 2 Md - (AXaBll + AYaBzz + AZaBaa + AXaAYaBlz a 2 + AXaAZaB13 + AYaAZaB23)/27 Ad = AMd a _ Ad (11,2 d+§a. The value d1,2 is the bond distance between two atoms 104 when one atom is in motion. The atom with the smaller Md i (thermal motion) is considered to be the stationary atom. Independent Thermal Motion: When both atoms are considered to be in motion the bond length may be obtained from the equation: +M d - d + Mdl d2 ind _ 2d where Md and Md are obtained from either the iso- 1 2 tropic or anisotropic thermal parameters. D. Angles The "bond" angles, determined when two or more differ- ent atoms are considered to be bound to another atom, may also be determined from the calculated interatomic distances. The problem reduces to the determination of an angle in a Euclidian triangle by application of the Law of Cosines: --1 Cos 6 = (di + d3 - d§)/2d1d2 The standard deviations in the angles are determined by an extension of the standard deviation calculations, described previously, to include three distances and the magnitude of the angle. Similar symmetry considerations are also made for sym- metry related atoms. 105 Least Squares Plane and Line Fitting Program This program fits a least squares plane or line to a selected set of rigid points (atoms) and determines the standard deviation of the plane or line independently of the variations in the lattice parameters or position co— ordinates. The program, outlined here, is an application of the method suggested and described in detail by Schomaker et al.1 Least Squares Plane: The points are considered as vectors of the form 9 r = x151 + x252 + x353 and a general plane is defined by the equation of its normal: I?! = H1161 + [“252 + m353 Vector m can be converted to a unit matrix by matrix multiplication with matrix Gij' A second matrix Aij is set up from the co-ordinates of the atoms. This matrix consists of elements referenced to a new origin which is the centroid determined from the co-ordinates of the atoms. The vector m may be represented by a three element column matrix, for which m. = A g . m. i = 1,2,3 represents the minimum in the standard deviation from the general plane, and A is a Legrange multiplier. The solution to the above equation, which is cubic in A, produces three roots A1 << X2.: X3 corresponding to 106 the best plane, an intermediate.plane, and the worst plane, all at right angles to one another and al1.passing through the centroid. An exact plane corresponds to X1 = 0, and thus the smaller x1 is, the more co-planar the atoms are. The solution to standard eigenvalue problems requires solution of the cubic equation and a set of simultaneous linear equations for the components of the eigenvectors. When x1 is small this solution may be approximated by an iteration technique. This iteration is effected with the equation B.. m. = A.. g.. m. 13 J 13 l] 3 where Aij is the adjoint of Aij' The successive matrix multiplication and the solution of its determinant refines the vector coefficients mj for the equation of the plane. Least Squares Line: The technique used for the generation of a least squares line is similar to that for the plane except that the best line is perpendicular to the worst plane, eigen value x3. Therefore, a good fit to a line requires K3 >> A2. A1. This fit is effected with matrix ng Aij rather than with Bij' ~The equation generated by this technique is of the form: E = E . + tm centrOld 3 where t is a constant. 1) V. Shomaker, G. Wasser, R. E. Marsh and G. Bergman, Acta Cryst., 12/ 600(1959). u. >1 I I ."-.‘.4'“‘.Wn"-il‘l .4. APPENDIX II PARAMETERS FROM THE ANISOTROPIC REFINEMENT OF THE STRUCTURE OF r-C5H5(C5H702)22rC1 v a - Luna-‘WWN...’ . ‘. w-..- 107 Table XVI. Atomic co-ordinates for WvC5H5(C5H702)2ZrCl from the structure refinement with anisotropic thermal factors Atom X Y Z Zr 0.0440 0.1656 0.1414 Cl 0.3359 0.1007 0.1652 C1 -0.0515 0.0030 0.1188 C2 —0.2141 0.0538 0.0764 C3 -0.2213 0.0992 0.1512 C4 -0.0410 0.0836 0.2551 C5 0.0934 0.0306 0.2337 01 -0.1702 0.2662 0.0956 02 -0.0910 0.1620 0.9757 C6 -0.2595 0.1922 0.7917 C7 -0.2110 0.2196 0.9005 C8 —0.2916 0.2882 0.9144 C9 —0.2718 0.3081 0.0074 C10 —0.3671 0.3904 0.0184 03 0.1672 0.2765 0.1191 04 ,0.1884 0.2240 0.2929 C11 0.2547 0.4259 0.1172 C12 0.2239 0.3507 0.1668 C13 0.2689 0.3644 0.2683 C14 0.2490 0.3029 0.3260 C15 0.3072 0.3172 0.4393 .— _-.-..__._...—.__...._I. -i- y '1‘ 4'. 01' mi”. “ 1 108 Table XVII. Anisotropic thermal parameters. Atom Bll B22 B33 312 B13 B23 Zr 4.21 4.97 3.84 0.00 -1.86 —0.05 Cl 4.54 6.54 4.89 -0.15 ~2.06 -0.18 C1 6.01 7.13 7.28 -0.38 —3.06 1.06 C2 7.11 2.19 7.31 0.15 -4.28 0.33 C3 8.13 6.68 7.18 2.07 -5.48 -1.60 C4 7.71 6.77 9.99 0.96 —7.33 1.00 C5 5.94 8.70 4.35 -0.12 —2.96 1.09 01 3.53 4.40 3.49 0.33 -1.04 —1.02 02 4.99 4.72 3.73 0.16 -2.44 0.26 C6 5.98 8.26 3.62 0.51 —3.09 0.05 C7 3.99 3.47 4.55 0.54 -0.91 0.47 C8 5.56 4.67 3.26 -1.59 —2.34 0.58 C9 2.93 9.06 2.50 2.45 0.66 -1.29 C10 6.13 3.14 8.08 -2.35 —2.95 1.65 03 3.67 6.39 4.39 0.36 —2.47 —1.22 04 4.96 4.63 3.92 -0.42 -1.74 -0.32 C11 8.43 5.54 8.69 0.65 -3.94 2.29 C12 3.48 6.99 3.85 —0.26 -1.93 -0.34 C13 2.90 7.39 3.49 —1.01 -0.76 1.09 C14 4.47 4.44 3.85 -0.97 -1.45 —1.26 C15 4.84 6.26 3.37 0.26 -1.74 -1.92 APPENDIX III POWDER X-RAY DIFFRACTION DATA FOR THE Sm(II)-Sm(III) FLUORIDES 109 Table XVIII. Powder X—ray diffraction data for the cubic Sm(II)-Sm(III) fluorides. Sin2 0 h k 3 SmF1.83 SmF2.00 smF2.01 smF2.01 1 1 1 0.05166 0.05170 0.05174 0.05168 2 0 0 0.06892 0.06890 0.06892 0.06888 2 2 0 0.13772 0.13785 0.13789 0.13775 3 1 1 0.18948 0.18946 0.18958 0.18960 2 2 2 0.20659 0.20679 0.20684 0.20678 4 0 0 0.27545 0.27560 0.27595 0.27570 3 3 1 0.32739 0.32760 0.32757 0.32761 4 2 0 0.34478 0.34483 0.34492 0.34485 4 2 2 0.41359 0.41349 0.41346 0.41352 smF2.04 smF2.07 smF2.10 5mF2.14 1 1 1 0.05171 0.05180 0.05190 0.05210 2 0 0 0.06892 0.06914 0.06918 0.06940 2 2 2 0.13802 0.13812 0.13832 0.013867 3 1 1 0.18977 0.19026 0.19046 0.19076 2 2 2 0.20709 0.20745 0.20765 0.20796 4 0 0 0.27612 0.27682 0.27701 0.27757 3 3 1 0.32757 0.32847 0.32927 0.32986 4 2 0 0.34484 0.34539 0.34609 0.34740 4 2 2 0.41360 0.41420 0.41470 0.41560 110 Table LXIX. Powder X-ray diffraction data for the samples in the cubic-tetragonal two—phase region. h k E Sin2 6 Cubic Phase 1 1 1 0.05207(10)* 2 0 0 0.06946(15) 2 2 0 0.13880(20) 3 1 1 0.19125(40) Tetragonal Phase 1 0 1 0.05265(10) 0 0 2 0.06895(12) 1 1 0 0.07055(10) 1 1 2 0.14049(10) 2 0 0 0.14097(5) 1 0 3 0.19377(20) 2 0 0 0.21086(20) 2 1 3 0.33481(30) 3 0 1 0.33523(30) *- Values in parentheses are the average deviations from three different products. 111 Table XX. Powder X—ray diffraction data for the tetragonal SmF2,35 with the superstructure lines also included. h k 2 Sin2 9 0.04510 0.04665 1 0 1 0.05271 0 2 0.06990 1 1 0 0.07058 0.07666 0.07783 1 1 1 0.08783 0.08911 0.09775 1 0 2 0.10316 0.10919 0.12686 0.13089 1 1 2 0.14002 0 0 0.14100 0.15208 0 0 3 0.15587 0.19061 1 0 3 0.19209 2 1 1 0.19367 2 0 2 0.21081 2 2 2 0.28162 0.32874 2 1 3 0.33328 0.35817 112 Table XXI. Powder X-ray diffraction data for the rhombohedral Sm(II)-Sm(III) fluorides. 2 Sin h k B 5mF2.41 5mF2.44 SmF2.46 0 0 6 0.05241 0.05238 0.05243 0 1 2 0.05311 0.05322 0.05327 1 0 4 0.07049 0.07045 0.07078 0 1 8 0.14058 0.14045 0.14071 1 1 0 0.14158 0.14171 0.14241 1 0 10 0119273 0.19317 1 1 6 0.19406 0.19406 0.19471 2 0 2 0.19441 0.19491 0.19659 0 0 2 0.21015 0.2990 0.21004 0 1 14 0.33334 0.33358 0.33499 0 2 10 0.33452 0.33564 0.33795 M‘Cllflillili sllmlml“WWWWIE5 3 1293 03145 9807