A STRUCTURAL AND VAPDRIZATION EXAMINATION 0F YTTERBIUMNI) CHLORIDE AND YTTERBIUM(III) OXIDECI-ILORIDE Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY NORMAN ALLEN FISHEL 1970 LIB RA R Y Michigan Sum ~ University This is to certify that the thesis entitled A STRUCTURAL AND VAPORIZATION EXAMINATION OF YTTERBIUM(II) CHLORIDE AND YTTERBIUM(III) OXIDECHLORIDE presented by Norman Allen Fishel has been accepted towards fulfillment of the requirements for Ph . D . degree in Chemis try o. (/7 Dr. H.A. Eick Major professor Date May 15, 1970 0-169 / BINDING HEY I HOAG & sons 800K mm mc. LIBRAR BINDERS ABSTRACT A STRUCTURAL AND VAPORIZATION EXAMINATION 0F YTTERBIUM(II) CHLORIDE AND YTTERBIUM(III) OXIDECHLORIDE by Norman Allen Fishel The crystal structure of ytterbium(II) chloride has been determined from an eray diffraction study of a single crystal specimen. Eight formula units are contained in an orthorhombic cell (a - 6.693i0.001, b - 13.149i0.003, and c - 6.94310.001 A); space group P 21/b 21/c 21/a. The final R factor is 0.137 for three-dimension counter data collected with CuKa radiation. YbClZ crystallizes in the CeSI-type structure. XrRay powder diffraction data for ytterbium(III) oxidechloride have been indexed on a hexagonal cell (a - 3.726t0.002 and c = 55.61i0.08 A), the dimensions of which were obtained from single crystal diffraction data. TmOCl, LuOCl, and mixed lanthanide oxidechlorides whose average cationic radius is smaller than the Er(III) radius are isostructural with YbOCl. An intermediate chloride, YbClz 26’ has been prepared. The vaporization reaction (1) of YbClZ was characterized by a YbC12(£) - YbClz(g) (l) combination of eray diffraction, weight loss, effusate collection, and high temperature mass spectrometric techniques. Equilibrium vapor pressure measurements (1048 s T 5 1483°K) for reaction (1) have been .made by target collection-Knudsen effusion technique. At the median temperature, 1265 °K, the second law enthalpy and entropy of Norman Allen Fishel vaporization were: AH; 1265 - 55.2il.l kcal mole'"1 and A5; 1265 = 21.310.9 eu. At the extrapolated boiling point (2242 °K), YbC12(2) has a second law enthalpy and entropy of vaporization of: AH; 2242 = 46.8:3.5 kcal mole-1 and As; 2242 - 20.8:1.5 eu. At 298 °K the following values were obtained: Yb012(s)-— AH; 298(2nd Law) - 61.2i2.3 kcal mole’l, A8; 298 - 31.1:2.0 eu, and AH; 298(3rd Law) 8 59.7:0.8 kcal mole-1. The enthalpy and free energy of formation and the standard entropy calculated from second law results are: YbC12(s) - AH; 298 - -181.8i3.6 kcal mole-1, AG; 298 - -175.3:3.6 kcal mole‘l, and SE98 - 30.7i2.5 eu. Reaction (2) is proposed as the decomposition 3YbOCl(s) - Yb203(s) + YbC12(s) + Cl(g) (2) mode for YbOCl and thermodynamic data have been estimated for the reaction. A STRUCTURAL AND VAPORIZATION EXAMINATION 0F YTTERBIUM(II) CHLORIDE AND YTTERBIUM(III) OXIDECHLORIDE Norman Allen Fishel A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1970 / 5'- ! . I i . l G -. luv-I f) ‘5" :r W (’7‘ «I ‘ .0. /P- ell! ”'11.".- ACKNOWLEDGEMENTS The author is especially indebted to Professor Harry A. Eick for his guidance and personal interest throughout the course of this research. This work would not have been possible without the encouragement, support, and patience of my wife Grace. The author is particularly grateful for her’understanding. Particular thanks are due to my colleagues in the High Temperature Group. Their concern and suggestions and the rapport of the laboratory werevery helpful in producing these results. The help extended by the departmental shops was invaluable in establishing some of the experi- mental apparatus. Financial support of this research by the United States Atomic Energy Commission under contract number AT (11-1)-716 has been very welcome. ii II. III. TABLE OF CONTENTS Introduction Previous Investigations of the Ytterbium—Oxygen-Chlorine A. D. System Ytterbium Chlorides l. Preparative and Structural Investigations 2. Thermochemical Investigations Ytterbium Oxidechloride l. Preparative and Structural Investigations 2. Thermochemical Investigations Other Ytterbium Halides and Oxidehalides 1. Fluorides 2. Bromides 3. Iodides 4. Astatides Relevant Non-ytterbium Chlorides and Oxidechlorides Theoretical Considerations Applicable to This Investigation A. Thermodynamic 1. Phase Relationships and Vaporization Behavior 2. Vapor Pressure Measurements 3. Knudsen Effusion a. Requirements and Assumptions b. Target Collection c. Analysis of the Collected Effusate d. Temperature Measurement e. Identification of Vapor Species A. Thermodynamic Calculations a. Second Law Method b. Third Law Method c. Sources of Thermodynamic Data Structural Determination 1. Unit Cell Determination a. Optical Properties b. Symmetry Elements and Systematic Absences c. Unit Cell Axial Lengths and Space Group d. Density Measurements 2. Intensity Data Collection a. Eulerian Geometry Diffractometer b. Eulerian Axes c. Crystal Monochromator d. Intensity Data Collection Techniques iii Page oooooooooo \JNN meow oo 12 12 12 l3 l3 13 15 l6 17 18 18 18 20 21 21 21 22 23 23 24 24 26 27 29 TABLE OF CONTENTS (Cont.) 3. Data Reduction a. Geometrical Factors (1) Polarization Factor (2) Lorentz Factor (3) Monochromator Factor b. Physical Factors (1) Absorption (2) Extinction 4. Solution of the Structure a. Fourier Synthesis b. Patterson Synthesis c. Least Squares Refinement (1) Thermal Parameters (2) Anomalous Dispersion IV. Experimental Materials, Equipment, and Procedures A. B. Materials Sample Preparation 1. Ytterbium Trichloride Hexahydrate 2. Ytterbium Trichloride a. Thionyl Chloride b. Chloroform c. Carbon Tetrachloride d. Chlorine e. Hydrogen Chloride f. Ammonium Chloride 3. Ytterbium Dichloride a. Metallothermic Reduction b. Thermal and Hydrothermic Reduction 4. Ytterbium Oxidechloride 5. Other Oxidechlorides a. Triytterbium Tetraoxidechloride b. Mixed Metal Oxidechlorides Single Crystal Growth Analytical Techniques 1. Chlorine Analysis 2. Ytterbium Analysis 3. Oxygen Analysis Density Measurement XPRay Techniques 1. Powder Methods 2. Single Crystal Methods a. Optical Examination b. Cameras iv Page 31 31 31 31 32 32 32 33 33 34 34 35 35 36 37 37 37 37 37 38 38 38 38 39 39 39 39 4O 4O 40 40 4O 41 41 41 41 42 42 42 42 43 43 44 TABLE OF CONTENTS (cont.) c. Eulerian Cradle d. Menochromator e. Crystal Orientation f. Lattice Parameter Refinement g. Intensity Data Collection 3. Fluorescence Methods a. Spectrometer Operation b. Spectrometer Calibration G. Neutron Activation Analysis H. Vaporization Mode Characterization 1. Weight Loss Measurements 2. Mass Spectrometric Investigation 3. Effusate Collection 4. X-ray Examination I. Target Collection Technique 1. General Procedure 2. Temperature Measurement 3. Orifice Measurement 4. Effusion Cell Design 5. Condensation Coefficient Determination J. Auxilary Equipment Results A. Preparative l. Ytterbium Trichloride Hexahydrate 2. Ytterbium Trichloride 3. Intermediate Ytterbium Chloride (YbC12026) 4. Ytterbium Dichloride 5. Ytterbium Oxidechloride 6. Other Oxidechlorides B. Structural l. Unit-Cell Determination a. Optical Properties b. Systematic Absences and Space Group c. Lattice Parameters d. Density 2. Intensity Data a. Data Collection b. Absorption Correction 3. Computations 4. Patterson Synthesis and Ytterbium Atom Positions 5. Solution of the Chlorine Atom Positions C. Thermodynamic l. XrRay Fluorescence Calibration 2. Neutron Activation Analysis 3. Condensation Coefficient V Page 44 44 44 45 45 46 46 46 47 47 47 47 48 48 48 48 48 48 49 49 51 52 52 52 52 54 54 55 56 57 57 57 S7 58 58 60 6O 61 61 63 66 66 66 66 TABLE OF CONTENTS (cont.) VI. VII. 4. Temperature Measurement 5. Orifice Closure 6. Vaporization Mode a. Weight Loss b. Mass Spectrometer c. Effusate Collection d. XrRay Examination 7. Vapor Pressure Equation 8. Thermodynamic Values Employed in Data Reduction 9. Thermochemical Values Discussion A. E. F. Evaluation of Experimental Conditions 1. Neutron Activation Analysis 2. Fluorescence Analysis 3. Temperature Measurements 4. Orifice Closure 5. Knudsen Conditions 6. Crucible Materials 7. Density Measurement 8. Intensity Data Collection Evaluation of Thermochemical Values Obtained l. Vaporization Mode 2. Thermodynamic Approximations 3. Ytterbium Dichloride Data Structure of Ytterbium Dichloride Structure of Ytterbium Oxidechloride Decomposition of Ytterbium Oxidechloride On Ytterbium(II) as a Group 113 Ion Suggestions for Future Research REFERENCES APPENDICES vi Page 66 67 67 67 67 68 68 68 68 71 73 73 73 74 74 75 75 75 75 76 76 76 77 78 83 85 86 87 89 97 LIST OF APPENDICES APPENDIX I. Properties of Ytterbium Halides II. Orientation and Angle Setting Program III. X-Ray Powder Diffraction Data A. Ytterbium Trichloride Hexahydrate B. Intermediate Ytterbium Chloride (YbC12.26) C. Ytterbium Dichloride D. Ytterbium Oxidechloride E. Triytterbium Tetraoxidechloride Preparation IV. Equilibrium Pressure and Third-Law Enthalpy Data V. Thermodynamic Values for Data Reduction vii .Page 97 98 100 100 101 101 102 102 103 105 TABLE II. III. IV. VI. VII. VIII. LIST OF TABLES Analytical Results Lattice Parameters Properties of Space Group Pbca Positions and Heights of Principal Patterson Peaks Parameters from Least-Squares Refinement A. Atomic Coordinates B. Thermal Parameters Observed and Calculated Structure Factors Experimental Thermochemical Data Compounds with the CeSI-type Structure viii Page 53 53 59 62 64 65 80 80 FIGURE LIST OF FIGURES A Four-circle Normal Beam Eulerian Cradle Eulerian Axes Diffractometer and Monochromator Optics Effusion Cell Enclosed in Graphite Oven Representation of Space Group Pbca Appearance Potential Curves Pressure of YbC12(g) in Equilibrium with YbC12(£) Atomic Packing in Yb612 Chlorine Environment in YbClz ix Page 25 28 30 50 59 69 70 79 81 CHAPTER I INTRODUCTION The pedagogical practice of placing strong emphasis upon various trends and groupings within the periodic table has resulted in neglect of the individuality of the various lanthanides. Although many chemists today are aware that the term "rare earth" is a misnomer, few are aware of the fact that anomalies of chemical behavior are common place among the lanthanides. Industrial interest in the chemistry of the lanthanides has increased greatly with the advent of lanthanide-doped yttrium garnets for lasers, samarium—cobalt alloys for permanent magnets, mixed metal lanthanide petroleum catalysts, and europium phosphors for color tele- vision tubes. Prior uses for the lanthanides were limited to glass decolorization for example and nuclear reactor technology in which the lanthanides are fission by-products. The chemistry of ytterbium has been neglected frequently in general lanthanide studies. While no count has been made, it is the author's opinion that the number of literature citations of ytterbium chemistry exceeds only those of promethium which does not occur naturally, and lutetium, the least abundant of the "rare earths." Inattention to ytterbium chemistry no doubt is in part due to the stability of both di- and trivalent ytterbium. Although trivalent ytterbium chemistry largely parallels the chemistry of the other heavy lanthanides, divalent ytterbium chemistry often contrasts with both the other divalent l 2 lanthanides and with the alkaline earths which have been used as models. The existence of mixed di- and trivalent chemistry introduces yet another complexity to the study of ytterbium compounds. The nature of lanthanide group VIA and VIIA compounds is such that they often lend themselves to high temperature applications. Lack of knowledge about simple binary and ternary compounds in part limits application of the lanthanides to new uses. To make possible design of materials for use at elevated temperatures, it is frequently necessary to understand the nature of the chemical bonding. Two techniques, vapor- ization and crystal structure determination, were used in this investi— gation to aid in the comprehension of the bonding in the ytterbiumr oxygen-chlorine system. The work for the most part was restricted to an examination of ytterbium(II) chloride and ytterbium(III) oxidechloride with ancillary examination of related phases. CHAPTER II PREVIOUS INVESTIGATIONS OF THE YTTERBIUMPOXYGEN-CHLORINE SYSTEM The halides, halo-complexes and oxidehalides of the lanthanide and actinide elements together with those of scandium and yttrium have been reviewed thoroughly in the recent book by Brown.1 The literature through 1967 was examined extensively and the book is recommended as a concise compilation of the then available information on preparation, structure, and thermochemistry. A. Ytterbium Chlorides l. Preparative and Structural Investigations The first significant work on the ytterbium chlorides was carried out by Klemm, Jantsch and their co-workers 2-8. Their work was greatly encumbered by the unavailability of pure lanthanide oxides. The ytter— bium sesquioxide used by Klemm and SchUth3 for preparation of ytterbium dichloride contained almost ten percent of other lanthanides as impurities. However reduction of trivalent ytterbia to divalent YbClz was in effect a purification which removed most of the trivalent impurities which are reduced less readily than is ytterbium(III). The X—ray diffraction pattern for YbC12 was reported by D611 and Klemm7 and was indexed as a pseudo-cubic distorted fluorite structure. Notable work on ytterbium(III) chloride was not undertaken until higher purity ytterbia became readily 3 available around 1955. Various methods for preparation of anhydrous lanthanide halides were reviewed by Taylor9 and more recently by Johnson and Mackenzielo. Novikov and Polyachenokll considered techniques particularly applicable to the preparation of lower valent lanthanide halides. The novel method of preparing in liquid ammonia divalent europium and ytterbium halides free of the corresponding trivalent metal ions was given by Howell and Pytlewskilz, while Mroczkowski” described the preparation of EuCl3 free of divalent contamination. Anhydrous YbC13 crystallizes with the mono- clinic aluminum chloride-type structural“, space group C2/m, which is a distorted sodium chloride structure in which tworthirds of the metal atoms are omitted. Aqueous solutions of YbCl3 are prepared readily by dissolution of szO3 in concentrated hydrochloric acid. The YbCl3 which separates from solution is reported to retain sixls'17 to seven18 waters of crystall- ization. Crystallographic data have been reported for Nd, Sm, and Er19; Gdzo; Eu21; Sm, Eu, Gd, Tb, Dy, Ho, Er, and Tm22 hydrated lanthanide trichlorides and all have been identified as isostructural hexahydrates. The structure20 is monoclinic, space group P2/n, and two molecules are in the unit cell. The structure contains complexes of the type [012Gd(OH2)6]+ which are held together by O-H . - - C1 hydrogen bonds. A third of the chlorine atoms form no bonds with the gadolinium atoms. The shortest bond distance for these atoms is greater than 5 A which is nearly twice the 2.768 A Gd-Cl distance for the other chlorine atoms. Heptahydrated YbCl3 is reported18 to undergo thermal decomposition to tetra- di-, and monohydrates before anhydrous YbCl3 is formed. There are no reports of hydrates of YbClz. Ammoniated YbClz is reported12 to 5 lose ammonia of crystallization upon slight heating or to undergo decomposition3 to an amidechloride according to equation (II-l). YbClz°xNH3(s) - Yb'NHz'Clz(x-1)NH3(S) + l/2H2(g) (II-1) Johnson and Mackenzie10 attempted direct conversion of samarium and ytterbium metals to the dichlorides by an adaptation of Druding and Corbett's23 method for preparation of the trichlorides. The metals were heated at 900° under a HZ—HCI mixture and then cooled under hydrogen alone. The dull green ytterbium product was completely water soluble and elemental analyses were consistent with a composition of 3YbCl3'5YbC12. The samarium product was in the form of lustrous black crystals which exhibited a 0.92 chlorine deficiency (presumed by this author to be with respect to the dichloride composition). The X—ray diffraction data were reported in Mackenzie's Ph.D. Thesis, University of London, 1968, and are not available in the open literature. Efforts by Polyachenok and Novikovzu to obtain SmClz by reduction of SmCl3 with zinc metal always yielded a product containing unreduced SmC13 with a composition of SmC13'4SmC12. 2. Thermochemical Investigations Only limited experimental thermochemical data have been reported for the lanthanide halides. These data are reported in part in Table VII in Chapter VI. The enthalpies of formation of all lanthanide trichlorides other than promethium, ytterbium, and lutetium were determined by Bommer and Hohmanzs. Their values (which are listed in NBS Circular 50026) have been shown27'29 to be up to 10 kcal mole”1 too high. Brewer et al.30931 estimated thermochemical values for both ytterbium trichloride and dichloride. 6 Polyachenok and Novikov32 estimated the enthalpies of formation of all the 1anthanide_dichlorides by using Born-Haber cycles. On the basis of their estimates, they concluded that all lanthanide monochlorides are unstable in the condensed state with respect to disproportionation. By the boiling point method33’3“ the saturated vapor pressures of SmClZ, EuClz, and YbClZ were measured. From these data it was concluded that these dichlorides vaporize without decomposition. Conversely, NdClz was not observed in the sublimate even though its presence in the Nd-NdCl3 system has been confirmed23. The enthalpy of formation of YbClZ has also been determined calorimetrically35"37 by dissolution in 6M_HCl. Recently Johnson38 has recalculated the enthalpies of formation of the lanthanide dichlorides by employing more recent thermodynamic data. Spedding and Flynn”,29 have shown a monotonic relationship between the enthalpies of formation of the lanthanide trichlorides obtained from the enthalpies of solution of the anhydrous chlorides and the atomic number of the metal. Results of the two vaporization studies of YbCl3 are not in agreement. M'oriarity39 using Knudsen effusion found YbC13 to vaporize congruently without decomposition to YbClZ, while Polyachenok and Novikov"o measured the decomposition pressures of SmCl3, EuC13, and YbCl3 according to reaction (II-2). The enthalpies of formation of YbC13 and LnCl3(£) - LnC12(£) + l/ZClz(g) Ln - Sm,aEu, Yb (II—2) TmCl3 were measured by Stuve"1 using solution calorimetry. By considering the reactions of the various lanthanide halides with the respective metals, Novikov and Baev"2 have determined the free energies of dissociation of YbCl and YbClz. 3 Ashcroft and Mortimer18 have reported the thermal decomposition profiles and enthalpies of decomposition of the lanthanide(III) chloride 7 hydrates. 'The DTA curve for YbCl3f7.4H20 shows four maxima in the rate of enthalpy change versus temperature. B. Ytterbium Oxidechloride 1. Preparation and Structural Investigations The oxidechlorides of the type LnOCl have been prepared for all lanthanides except promethium by Templeton and Dauben1+3 by heating sesquioxide in a mixture of hydrogen chloride and water vapor. Several oxidechlorides, including YbOCl, have been prepared“""“5 by thermally decomposing the hydrated perchlorates. Wendlandtls,16 studied the thermal decomposition of YbCl3°6HZO and observed four inflection points in the thermogram. Although the compo- sition at the first point (145°) was not determined, the second point corresponded to a formula of YbOCl'ZYbClB. Further weight loss took place until at 395° the composition was YbOCl. Decomposition to the oxide began at 585°. Haesler and M'atthesl7 have investigated the thermal dehydration of a YbCl3-6H20 sample confined under a mixture of air and hydrogen chloride. They reported as successive dehydration products YbC13°3.5H20, YbCl3-2H20, YbCl3'H20, YbCl3, and YbOCl, but not the temp- eratures at which these changes took place. Templeton and Dauben“3 stated that the oxidechlorides of thulium, ytterbium, and lutetium have an undetermined structure different from the PbFCl-type structureexhibited by the other lanthanide oxidechlorides. They found ErOCl to exist in both structural types. 2. Thermochemical Investigations Mbrozov and Korshunov“5'“7 indicated that both the chlorination of the sesquioxide and the displacement of chlorine by oxygen according to 8 equation (II-3) occurs in one stage without formation of any intermediate 2Ln203(s) + 6C12(g) - 4LnCl3(s) + 302(g) Ln = La, Nd (II-3) oxidechlorides. Baev and Novikov“8 studied the disproporationation reaction (II-4) for lanthanum and neodymium and calculated thermochemical 3LnOC1(s) - LnCl3(s) + Ln203(s) Ln a La, Nd (II-4) values for other lanthanides. C. Other Ytterbium Halides and Oxidehalides l. Fluorides Ytterbium trifluoride is prepared conveniently“9 by reaction of the sesquioxide with ammonium bifluoride. The compound has been well- characterized and a number of the properties of YbF3 along with those of other ytterbium halides are given in Appendix I. The vapor species observed“,51 during the sublimation of YbF3 indicated no decomposition to YbFz. Asprey et a1.52 had difficulty in obtaining stoichiometric YbFZ as evidenced by magnetic susceptibility measurements. Bedford and Catalan053 observed a number of phases between the YbFz and YbF3 stoichiometric compositions. Vorres and Riviellos“ prepared a series of isomorphous rhombohedral stoichiometric LnOF phases for Y, Dy, Er, Tm, Yb, and Lu by hydrolysis of the respective fluorides at 500°. Podberezskaya et al.55 found that hydrolysis of YbF3 at 600° produced only a mixture of YbOF and Yb203, but they were able to prepare the rhombohedral YbOF by heating at 800° an equimolar mixture of Yb203 and YbF3 confined in a platinum crucible which was sealed in quartz. Shinn"9 attempted preparation of YbOF but did not report his results. Roether56 was unable to confirm the findings of Podberezskaya et al.55 but instead found YbOF to crystallize with the 9 monoclinic lattice of the ZrOZ-baddelite type. There are no reports of nonrstoichiometric ytterbium oxidefluorides of the type which have been found for a number of other lanthanides. 2. Bromides Ytterbium tribromide hexahydrate decomposes57 upon heating in air to form a tribromide-oxidebromide mixture which undergoes further oxida— tion to YbOBr and finally to Yb203. Anhydrous YbBr3 decomposes58 to YbBr2 before melting. A more convenient method of preparation of the dibromide is hydrogen reduction of the tribromide. D811 and Klemm7 reported YbBr2 to be isostructural with CaBrZ. A recent single crystal X—ray structure determination of YbBr259 has refined the earlier7 powder diffraction analysis. All of the lanthanides formso’63 LnOBr oxidebromides with a PbFCl-type structure. Neodymium, samarium, europium, and ytterbium form Ln3048r-type oxidebromides which possess orthorhombic symmetrysN’GS. 3. Iodides The compounds Yb1366’67, Yb1258’68, and Yb0169‘7l have been prepared and studied crystallographically. The triiodide is similar to the tri- bromide in that it decomposes before melting to the lower valent YbIz. There are no reports of hydrated iodides or other oxideiodides. 4. Astatides The ytterbium-astatine system has not been examined. D. Relevant Non-ytterbium Chlorides and Oxidechlorides The study conducted by Hastie et al.72 for LaC13, EuCl EuClZ, and 3’ LuCl3 is the only mass spectrometric examination of the lanthanide chlorides. There is evidence of dimerization, perhaps of the A12016 type, 10 for LaCl3 and LuCl3 for which enthalpies of dimerization have been measured. No dimerization or significant disproportionation of EuC12(g) was found. The sublimation pressures for EuCl3 were too low to permit useful ion intensity measurements. At temperatures around the melting point of EuCl3, it decomposed to form EuClZNO. Natansohn73 has described formation of Y3O4Cl analogous to, but not isostructural with, the lanthanide tetraoxidemonobromidessu’65. Attempts to synthesize La3OACl and Gd3O4Cl were unsuccessful. Haschke7” has found recently that Eu3O4Br exhibits at least two polymorphs. Markovskii et al.75 studied the thermal decomposition of YOCl-6H20 and observed compositions of 2YC13°YOCl, YC13°YOC1, and YCl '2YOC1. A 3 compound 2YOC1°Y203 was isolated and X—ray powder diffraction data were listed. A similar profusion of compounds in a divalent oxide-halide system was reported by Frit et al.76 for SrXZ-Sro (X - Cl, Br, I). Haschke77 has pointed out that in the ternary system, MOX, where M is a metal with possible divalent and trivalent character and X is a halogen, the general formulation for all stoichiometric phases can be expressed by (II-5). The coefficients A, m, and n may assume integral M10[(3£-m)/2] - [n/len (”-5) values in accordance with the restrictions that z :_1, O :_m i A, and 0 :_n : (32-m). For the lanthanide-oxygen—chlorine system only three of these potential phases have been reported: LnClz, LnCl3, and LnOCl. There are accounts of lanthanide—oxygen-halogen phases in which the halogen is coordinated to the oxygen rather than the metal but they will not be considered in this work. 11 During recent years there has been much interest in the Ln-LnCl3 systems. Of particular significance are the studies involving dysprosium78 and thulium79. In each system a dichloride isostructural with YbC12 was found. CHAPTER III THEORETICAL CONSIDERATIONS APPLICABLE TO THIS INVESTIGATION A. Thermodynamic 1. Phase Relationships and Vaporization Behavior Gibbs80 in considering the equilibrium of a system stated that it possesses only three independently variable factors - temperature, pressure, and the concentration of the components of the system. From this he deduced what is now generally known as the Phase Rule (III-l) by which the conditions of equilibrium, F, are defined as F - C - P + 2 (III-1) a relationship between the number of phases, P, and the number of components, C, of the system. Generally one works with a univariant system, F = 1, such that fixing the temperature fixes the pressure. In a congruent vaporization the composition of the vapor phase is always the same as that of the condensed phase. For a congruent process, P = 2 (the condensed and ‘vapor phases), and F must equal C. For a binary system C = 2, thus 3F - 2. However, the congruency requirement of constancy of composition Irrovides the additional restriction such that F - 1 and the system is Inmivariant. In other words, the Phase Rule for a congruently vaporizing 8yetem is given by equation (III—2). F 3 C - P + l (III—2) 12 13 2. Vapor Pressure Measurements There are several ways of measuring vapor pressures of substances. The most common ones are the static, boiling point, transpiration, Knudsen effusion, and Langmuir free-evaporation methods. Each of these techniques is considered in reviews by Gilles81 and Caterez. The Knudsen effusion method which is suitable for measuring vapor pressures in the range from 10-9 to 10-3 atmospheres was chosen for this work. From vapor pressure measurements various thermodynamic quantities such as enthalpies, entropies, and free energies of formation may be determined. 3. Knudsen Effusion a. Requirements and Assumptions In the Knudsen effusion method a sample is confined in an inert container (called a Knudsen or effusion cell) which can be heated in vacuum. The rate at which a vapor species effuses through a small orifice is then determined. The method is based upon the kinetic theory of dilute gases which requires that the distribution of molecular veloci- ties in a gas at low pressure obeys the Maxwell-Boltzmann law. The term Inolecule in this usage refers to the gaseous species and does not neces— sarily imply any regular aggregation of atoms. The theoretical treatment of effusion was first considered by Ehuudsen83’8“ and more recently by Catersz. The rate of collision of nualecules on unit area of the container wall, Z, in unit time, is given by (III—3) where N/V is the number of molecules per unit volume and E is z - 0.25NE/V (III-3) the average molecular velocity obtained from the kinetic theory (III-4), E - (8RT/NM)1/2 (III—4) With R.being the ideal gas constant, M the molecular weight of the 14 species, and T the absolute temperature. The rate of effusion of molecules into a perfect vacuum per unit time through a small ideal orifice of area A is ZA. The angular distribution of these effusing molecules is not equally probable in all directions. The randomness of approach leads to the probability (III-5) that a molecule approaches the wall at an angle 6 (N(6)/Z) - (N/V) E cos 6 (dm/4n) (III-5) to the normal within the element of solid angle do where do = 2n sin 9 dB. This result is called the cosine law and it is generally assumed that the effusing molecules obey this law as do those molecules reflected from the wa1182. Non-cosine law reflection of real molecules from the walls and orifice yields effusion rates which differ from theoretical values. Wang and W’ahlbeckes:86 have studied the velocity and angular distributions of the effusate for various orifices. Ward87 has examined the validity of the cosine law distribution for conical orifices and has found devi- ations from ideality to be small for small angles of 6. Effects of sample shape on the vaporization process have also been estimated by Ward88. There are a number of complications inherent in the experimental Knudsen cell and sample. If the orifice is not located in an infinitely thin wall, then some of the molecules which enter the orifice will not escape but rather will be reflected according to the distribution given by the cosine law (III-5). The calculation of the decrease from the ideal effusion rate was first carried out by Clausing for channel orifices and for non-ideal orifices in general by Freeman and Edwardsag. The correction term for this effect is called the Clausing factor. The Knudsen effusion conditions are not truly an equilibrium sit- uation because of continous loss of vapor through the orifice. 15 Displacement from equilibrium may in fact be used to determine if there is a kinetic or thermodynamic barrier to vaporization. Carlson et al.90 have derived an expression (III-6) to correct the observed pressure, P, P - Peq (III—6) [1 + (A/aH to the equilibrium value, P i.e. the value at zero orifice size. In eq’ equation (III-6) A is the ideal orifice area and a is the sample area. Deviations from relationship (III-6) between observed and equilibrium pressures are usually due to a diffusion barrier or a small evaporation coefficient (defined as the ratio of the Langmuir to Knudsen pressures). Balson91 and Carlson et al.90 have considered the consequences of cell geometry on the total rate of effusion and they note that the effects are generally small. Errors in vapor pressure measurements which result from temperature gradients in a Knudsen cell have been described by Stormsgz. The limitations of experimental systems frequently make it very difficult to measure the individual contributions of the various devia- tions from the ideal effusion experiment. System parameters are optimized so as to minimize the magnitudes of the deviations and no corrections are made. The ideal equilibrium vapor pressure, P, in a Knudsen effusion experiment is given by (III-7) where W is the mass of P- w (21rRT/M)1/2 (111-7) At the effusate of molecular weight M passing through an orifice of area A in time t. b. Target Collection The effusion rate can be determined by measuring the momentum of the effusing molecules (torsion effusion) or the number of effusing l6 molecules and their mass (weight-loss experiment). Alternatively, a known fraction of the effusate may be collected and from this, the total rate of effusion and hence the pressure determined. The fraction of molecules striking a circular collector plate of radius r, the center of which is coaxial with the normal to the orifice and at a distance d from it may be calculated from the cosine law (III-5). Equation (III—7) may be restated for target collection (III-8) with P in P - 3.76 x 10‘4 w (T/M)1/2[(d2 + r2)/r2] (III-8) At atm, t in min, A in cm2, and W in g. In this equation it is assumed that all effusing molecules striking the collector plate adhere. An advantage of a target collection exper- iment is that the correction for non-ideality of conical orifices is generally small since only the fraction of the effusate within a small solid angle (dw) from the normal is collected. c. Analysis of the Collected Effusate The fraction of the effusate collected on a target can be analyzed by chemical, electrochemical, X-ray fluorescence, or radiochemical techniques often with a greater sensitivity than is possible by measuring the mass gained by the target. Parrish93 has described the use of secondary or fluorescent X—rays for quantitative analysis. The fluorescent X—ray arises from radiation which is emitted when an inner electron vacancy is filled by an outer electron. The energy of this X-ray is characteristic of the particular transition for that element. Since these transitions are nearly inde— pendent of the chemical environment, the X-ray fluorescence technique can be used conveniently for elemental analyses without the need to know the chemical form of the element. l7 Submicrogram levels of the lanthanides may be analyzed using neutron activation analysis (NAA) since nearly all lanthanide nuclides have high capture cross-sections for thermal neutronsg°. After neutron irradiation of a sample, induced radiation may be counted and used as a quantitative or qualitative measure of the lanthanide present. Again, the chemical environment of the sample is of little consequence since the emitted radiation is predominantly characteristic of the particular nuclides produced by irradiation. d. Temperature Measurement Temperature may be measured with an optical pyrometer by comparing the intensity of light from a standard lamp with the intensity of light radiating from a hot object. The basic principle involved is Planck's quantum relationship of the intensity and wavelength of radiation by a blackbodygs. Corrections must be applied for absorption and reflection of light by the optical elements in the system. The transmissivity, T, of each optical element reduces the apparent temperature according to the relationship96 given by equation (III-9) where Ta is the apparent l - l - Ae(Ta,Tt) lnt E A% (III-9) c2 temperature,.Tt is the.true blackbody temperature, Xe is the effective wavelength of the pyrometer in the interval from T8 to Tt’ and c2 - hc/k - 1.438 cm deg which is the second fundamental radiation constant. Since the pyrometer generally operates over only a small wave- length region through the use of filters, Al is nearly temperature inde- pendent. That the values of A%_for the various optical elements are additive is a consequence of Beer's law which states that equal fractions of the incident radiation are transmitted by equal changes in the path 18 length of the absorbing substance. e. Identification of Vapor Species The nature of the effusing vapor must be determined for character- ization of the reaction and for effusion rate calculations. The mass spectrometer is used extensively for such identifications. Indeed, if the sensitivity of the mass spectrometer can be calibrated in absolute pressure units, it could be used for the total Knudsen effusion experiment. The principle of operation of a time—of-flight mass spectrometer designed for Knudsen studies as described by Pilato97 involves the imparting of equal kinetic energy to all the singly ionized species in the source region of the instrument. These species are then permitted to drift in a field free region to produce velocity discrimination. Since the velocity squared is inversely proportional to the mass of the species, mass separation is effected. 4. Thermodynamic Calculations Under the experimental conditions of a Knudsen vaporization alluded to earlier, the vapor pressure must be much less than one atmosphere so that the vapor may be considered an ideal gas and the activities of the species in the vapor can be taken as their partial pressures. Equili— brium constants of reactions of interest may be obtained from products of activities, and enthalpies and entropies may be obtained from the variation of the equilibrium constants with temperature. a. Second Law Method The standard free energy change, AGE, for a reaction at temperature, T, 19 is given by equation (III-10) where K is the equilibrium constant. do} - -RTan - on} - TAST (III-10) Inherent in the use of partial pressures for equilibrium constant calculations is the assumption that the activity of all condensed phases is unity. This assumption is probably valid in the case of a congruent vaporization but should be examined more critically for an incongruent process. Rearrangement of equation (III-10) to the usual form of an equation of a straight line (III-ll) allows the enthalpy, ART, and la P - 411-} + As} (III-ll) RT R entropy, AS§, of reaction to be obtained from the slope and intercept respectively. Experimental data are usually considered in the form of a log P versus (l/T) plot and the best straight line is fit to the data by a least squares technique. The enthalpy and entropy of reaction are assigned to the median temperature of the experiment. Frequently the plot is linear within experimental uncertainty. This assumption of linearity implies that the change in heat capacity is constant over the measured temperature range. If the heat capacities of the reactants and products are known or can be estimated, the thermochemical values for the experimental median temperature, T m' may be expressed at a reference temperature, Tr, by means of equations (III—12) and (III-13). Tm on}. - AH'I'r + J AdeT (III—12) Tr 20 . T ASEm . AHTr + I m ACE dT (III—l3) T T r The term ACp is the heat capacity difference between the products and reactants. b. Third Law Method The availability of spectroscopic data and determined heat capacities permits computation of free energy data as a function of temperature. These smooth functions, free energy functions (fef), as defined in equation (III-14) for a temperature, T, and a reference temperature, Tr, fefT s (C; - HEr)/T (III-l4) are conveniently extrapolated with a high degree of precision. They provide a check of the second law enthalpy and allow direct comparison of data from different sources. This function can be calculated directly for gases when the spectroscopic energy levels are known98. Equation (III—l4) may be restated as (III-15) by using (III-10). fefT - (HE - H§r)/T - s} - (HT - Hir)/T - (ST - sEr)- s§r (III-15) For a reaction Afef is the difference between the fef of the products and that of the reactants and may also be expressed as (III-l6). The Afef - - ACE + Auir ' (III-l6) T enthalpy of reaction at the reference temperature is then give by (III—17). Auér - -RTln P + TAfef (III—17) Equilibrium data may be treated by the third law method by calculating AH;r or AH; directly from each experimental datum point with tabulated, calculated, or estimated entropies or free energy functions and equations (III-l7) or (III-18). AH; - -RTln P + TAs; (III-18) 21 The third law method is used commonly to test for systematic errors in the measured temperatures or pressures. A temperature dependent trend in the third law enthalpy values is indicative of some systematic error present in the experiment or the free energy function used. On the other hand, disparity between the second and third law enthalpy values may indicate an error in the definition of the vaporization process or a vaporization coefficient (III-A-3—a) that deviates greatly from unity. c. Sources of Thermodynamic Data Compilations of thermodynamic data are available from a number of sourcesgg. However, some of the necessary information frequently is not available and must be estimated. Various techniques for estimating these data have been reviewed by Stull and ProphethO’IOI. B. Structural Determination The solution of a crystal structure by diffraction methods can be separated into two parts. The first is concerned with determination of the size, shape, and symmetry of the crystal lattice from a diffraction pattern. The second is the obtaining of diffracted intensity data which can be related to the distribution of the scattering material (the electrons in the case of eray diffraction) within the lattice. 1. Unit Cell Determination In general many properties of a crystal are not the same in all directions. The variation in properties with direction is a conse- quence of the regular packing of the atoms in the crystal and is of importance in a structural determination. The shape of a crystal is not a fixed characteristic of the substance but is dependent upon the 22 conditions of crystal growth and thus the morphological determination of the unit cell by optical techniques is frequently restricted by practical considerations. a. Optical Properties For monochromatic light cubic crystals are isotropic while all non— cubic crystals divide an entering ray into two polarized rays at least one of which is dependent upon the direction of propagation, that is, birefringence. The certain directions where deviation of the entering ray does not occur are called the optic axesloz. Birefringence may be used to advantage by examining a crystal under crossed polarizing analyzers and determining the optical extinction axes. Tetragonal, I hexagonal, and trigonal crystals are uniaxial, while orthorhombic, monoclinic, and triclinic crystals are biaxial. Thus Optical examination can be used to determine the crystal system of transparent crystals. In general an optical axis is coaxial with a crystallographic axis. b. Symmetry Elements and Systematic Absences The intensity of an eray reflection depends upon the distribution of electrons in the crystal. Absent reflections which are randomly distributed among the possible indices are due to low electron density. Sometimes the absent reflections are systematically distributed and can be related to the presence of symmetry elements in the crystal. If the structure factor expression (III-l9) where fn is the atomic scattering F(hk£) I g fn exp [21ri(hxn + kyn + Ezn)] (III—l9) factor, (xn, yn, 2n) are the coordinates of atom n, and (h, k, 2) the Miller indices, is used to represent the directionalized scattering, the source of systematic absences can be considered. The summation is to be taken over all atoms in the cell. If there are no relations among the 23 various atomic coordinates, the expression cannot be simplified. However, if there is some relationship among the positions, equation (III-l9) may be simplified by collecting into a group those atoms that form a related set. If the relationship arises from a translational symmetry element, the structure factor will be zero for a systematic set of (hki). The conditions for systematic absence of reflections for the various translational symmetry elements are given by Henry and Lonsdale103. c. Unit Cell Axial Leggths and Space Grogp The axial lengths can be deduced from measurements of the diffraction data. The diffraction record is a picture of the reciprocal lattice which describes completely the direct lattice of the crystal. The optical and X-ray diffraction information can be utilized to determine the space group to which the crystal belongslo°. Unfortunately, due to the center of symmetry introduced by the X—ray diffraction phenomenom itself, only translational symmetry elements are detected and these may not uniquely determine the space group. d. Density Measurements Combination of density measurements and dimensions of the unit cell will give a value of the total formula weight of the cell contents. From this weight it is usually possible to deduce the number of asymmetric units in the unit cell. The density, p, of a crystal may be determined from a comparison of the weight of the sample in a fluid of known density, D, with its weight in air according to (III-20). p ' [Nair/(wait ' wfluid)] x Dfluid (III-20) 24 2. Intensity Data Collection a. Eulerian Geometry Diffractometer There are two basic geometrical configurations which have been utilized in the construction of single crystal diffractometers - the equi—inclination and the normal beam setting. In equi-inclination geometry, upper level reflections are measured by tilting the detector while in the normal beam method, the crystal rather than the detector is tilted. Furnas and Harker105 described a normal beam system which permits the detector to rotate only about a vertical axis while the crystal is oriented by rotation about three axes. This crystal support system is called an Eulerian cradle because it permits rotation about each of the Eulerian axes. A diagram of a four-circle Eulerian cradle is given in Figure l. The positive sense of each of the axes as indicated is for a left-handed system. The ¢ - circle is carried on the x - circle which in turn is carried on the m - circle. The entire cradle goniostat is mounted on the 6 — circle of the diffractometer. The 6 - 26 relationship necessary for satisfaction of the Bragg diffraction geometry is maintained by the diffractometer table. To measure the intensity of a reflection, the crystal is adjusted by manipulating the o, x, and m - circles so that the reciprocal lattice point corresponding to the reflection is brought into the zero level with respect to the vertical m - axis. When the cradle is used in the three-circle mode, the to - circle is fixed with respect to the 6 - circle. 25 FIGURE 1. A Four-circle Normal Beam Eulerian Cradle X-Ray Source Crystal Detector 26 b. Eulerian Axes Use of a three— or four-circle X—ray diffractometer requires a knowledge of the size, shape, and orientation of the unit cell. The size and shape of the unit cell are initially most conveniently determined using film techniques although the diffractometer is suited for the precise determination of roughly known lattice constants. The orientation problem is one of fixing the position of the unit cell coordinate system relative to the axes of the diffractometer. The problem is the same as that of describing the rotational motions of a rigid body relative to a set of axes, the orientation of which is fixed in space. A number of systems have been used to describe the transformation between the two coordinate systems; a common one uses the Eulerian angles. The description which follows is based upon one of the coordinate systems being right-handed and the other left-handed. This choice is necessitated by the construction of the Siemens Eulerian cradle used in this investigation and the usual right—handed specification of crystal lattices. The more common situation of a transformation from one right-handed system to another right-handed system is described by Goldsteinlos. If one of the coordinate systems is rigidly attached to the body (the crystal being examined), six parameters are necessary and suff- icient to give the explicit relationship between the coordinate systems. Three of the parameters specify a fixed point in the body, two more are required to define the position of a line fixed in the body and passing through the fixed point and the sixth parameter defines a rotation of the body about this line. If the two coordinate systems are taken to 27 have a common origin, the Eulerian angles as shown in Figure 2 are defined as follows: a is the angle resulting from rotation of the initial set of axes OABC about the z—axis OZ. 8 is the angle obtained by rotating OC about the intermediate axis OK until it is in coincidence with OZ. y is the angle of rotation about OZ which brings 0A to OX and OB to OY. These operations must be performed in the sequence given. The relation- ship between OABC and OXYZ may be obtained by projecting the direction cosines of OX, OY, and 02 and then defining them in relation to the direction cosines of OA, OB, and OC. For example, cos a becomes cos a sin 8 along 02 and cos 8 becomes cos a cos 8 cos 7 along OX. The complete transformation matrix is given below. IOAI I coso cosB cosy sino cosB cosy —sin8 cosyIIOX‘ — sino siny + coso siny OB - -coso cosB siny -sino cosB siny sinB siny OY - sino cosy + coso cosy \OCJ L case sinB sino sinB cosB JKOZ) The determination of the orientation in actual practice is effected with the aid of computer program B—lOl described in Appendix II. c. Crystal Monochromator Limiting factors in the obtaining of an accurate intensity record in a single crystal study are background radiation and the varying resolution of the Kol _ a2 doublet of the filtered incident radiation. The use of a crystal monochromator provides the most satisfactory solution available today for these problems. 28 FIGURE 2. Eulerian Axes. 29 The monochromator used in this work is based on the X-ray optics developed by Johannson107. Figure 3 gives a ray diagram of the diffractometer and monochromator optics. The X—rays are diffracted by a quartz plate which is cut parallel to the plane (lOIl), cylindrically ground to a radius of Zr, and elastically bent to a radius of r. For this geometry the monochromator source (the detector slit of the diffractometer), the surface of the monochromator crystal and the monochromator exit all lie on the focussing circle whose radius is r. d. Intensity Data Collection Techniques For a structural determination the integrated intensity of a reflection, a quantity proportional to the total energy diffracted by the crystal as it passes through the Bragg reflecting position, must be obtained. The observed intensity is related to the integrated intensity by a number of geometrical and physical factors which will be considered in (III-373). There are three measuring procedures which may be used to collect the various reflection intensities with an Eulerian cradle set in normal beam geometry. These are the stationary crystal—stationary detector method, the moving crystal-stationary detector method (m — scan), and the moving crystal-moving detector method (m/26 - scan). Under ideal conditions with strictly monochromatic radiation there is little difference among the accuracies obtained with the three methods. In actual practice the preferred technique108 would be combination of the m - scan and the m/26-scan depending upon the region of reciprocal space being explored. The various systematic errors introduced by each of these methods has been considered by Furnaslog. 30 FIGURE 3. Diffractometer and Monochromator Optics. Specimen crystal Detector position when monochromator is not used / Detector ’ XrRay Source A III \ '1 II ‘ Detector slits Monochromator crystal 3l 3. Data Reduction The ultimate aim in a structural determination is to relate the electron density distribution calculated for the model being used to describe the crystal to the measured intensities. From the observed Iintensities only the absolute amplitudes of the structure factors (III-l9) may be determined. a. Geometrical Factors (l) Polarization Factor The polarization correction arises because the efficiency of reflection of the X-ray beam varies with reflection angle. The incident unpolarized beam may be described in terms of two electric vectors, one parallel to the reflecting plane and the other normal to it. The intensity at any point from an X-ray scattered by an electron is proportional to the angle between the incident radiation and the direction in which the scattering electron is acceleratedllo. Waves having their electric vector parallel to the reflecting plane are reflected to an extent determined by the electron density, while those having their electric vector perpendicular to the plane are scattered to an extent dependent upon both the electron density and scattering angle. The overall polarizing factor, p, is a function of only the reflection angle, 6, and is given by (III-21). p - 1 + c08226 (111-21) 2 (2) Lorentz Factor The intensity of a reflection is proportional to the time during which the corresponding reciprocal lattice point is close to the surface of the reflecting sphere. The Lorentz factor corrects for the different rates at which reciprocal lattice points sweep through 32 the sphere boundry and thus is dependent upon the experimental arrangement. For the normal beam method (reflecting planes parallel to the rotation axis) the angular velocity is dependent only upon the angle between the tangent to the surface of the reflecting sphere and the path of the reciprocal lattice point. This angle, 6, is the Bragg anglelll. The Lorentz factor, L, is given by (III—22). L = l (III-22) sin 26 (3) Monochromator Factor The monochromator correction term is also a polarization correction. However, in this case the incident radiation is partially polarized due to diffraction by the crystal. The form of the correction, m, is given 112 by (III-23) where am is the Bragg angle of the monochromator m = l + c08226m coszze (III—23) l + cosZZGm b. Physical Factors (1) Absorption XrRays are absorbed as well as scattered in their passage through matter. The change in intensity, d1, of the original intensity, I, is given by (III-24) where t is the sample thickness and u is the linear - dl_- udt (III—24) absorption dgefficient. The linear absorption coefficient of a crystal may be computed from a knowledge of its chemical composition, its density, and a table of mass absorption coefficients113 by (III-25) in which n - p Ewnan (III-25) wn is the weight fraction of element n in the compound, an is the mass absorption coefficient of n for the radiation employed, and p is the 33 crystal density. The absorption calculation must be carried out separately for each reflection since it depends upon the paths of the incident and diffracted beams through the crystal. (2) Extinction An ideally perfect crystal is composed entirely of a single sequence of planes in a perfect array. In such a crystal the diffracted beam is at the Bragg angle to be reflected back to the direct beam with resulting destructive interference. This effect, known as primary extinction, appears as enhanced absorption along the direction of Bragg reflection. The net result of these interferences from multiple reflections is to cause the intensity of the diffracted beam to be proportional to IFhkiI and not IFhkzIz' An ideally imperfect crystal is composed of mosaic blocks so small that within each one primary extinction does not occur to an appreciable amount. Secondary extinction results from reduction of the intensity of the incident beam by Bragg reflection. Successive planes in identically aligned mosaic blocks receive an attenuated beam even if there is no primary extinction. Because of the difficulty of describing the "perfectness" of a crystal, the factor upon which extinction is dependent, these corrections are usually effected on an empirical basis. 4. Solution of the Structure The experimentally obtained diffraction intensities contain only part of the information necessary for solution of the structure. The part which cannot be obtained experimentally is the phase of the scattered radiation which is contained in the exponential part of (III-19). The 34 supplying of this missing information for which no general method has been found is the so-called "phase problem" of structural determination. a. Fourier Synthesis A periodic function such as the electron density distribution in a crystal can be represented by a summation of sine and cosine terms called a Fourier series. The structure factor (III-l9) may also be expressed (III-26) as the sum of the wavelets from all the infinitesimal volume hk£ ’ J V elements of electron density, p(x, y, z) dV, where V is the cell volume. F p(x,y,z) exp[2ni(hx + ky + Ez)]dV (III-26) The exponential part of (III-26) may be written in the form of a trigo- nometric function and thus may be stated as a Fourier series (III-27) Fhk2 - JV fi fi E CREE-exp {2ni[(h+h')x + (k+k')y + (2+i')z]}dv (III—27) where the C terms are the coefficients in the series such that after integration over all terms equation (III-28) results. F - C___ dV = VC——— (III-28) th v hkl hkl The relationship between the electron density, p, and the structure factors, F, is that one is the Fourier transform of the other (III-29) =1 — + .. _ p(x,y,z) V'fi i i Fhkl exp[ 2ni(hx + ky £2 ahki)] (III 29) where ahkz is the phase angle ahki - tan"1 2; sin 2n(hx + ky + £2) (III-30) 2; cos 2n(hx + ky + £2) b. Patterson Synthesis The experimentally unobtainable phases prohibit the use of (III—29) for the direct solution of the structure. The Patterson functionll” is a form of Fourier series employing IFhkzlz which does not depend upon 35 phases. If the phases were available, the usual Fourier synthesis would show the distribution of atoms in the cell; the IF]2 Patterson synthesis has peaks corresponding to all the interatomic vectors in the cell. The Patterson function (III-31) has certain propertiesllu which may be used to relate the interatomic vectors to atomic positions. The Patterson - 2 _ A(x,y,z) %§ 12; 923 IFhk£| cos 21t(hx+ky+2.z) (III 31) function is centrosymmetric and as a result all translational symmetry elements in the space group are replaced by their corresponding non— translational elements. Although the translational symmetry elements do not appear, symmetry related atoms produce a concentration of vectors in certain planes called Harker sections. Even though there are ambiguities in their interpre- tation, the Harker sections frequently can be used to determine the heavy atom position in the cell. Once the heavy atom position is known, it is practical to use a synthesis of the type (III—29) or variations of it since the scattering phases are dominated by the heavy atom. Location . of other atoms should proceed rather directly from this pointlls. c. Least-Squares Refinement The least-squares structure refinement consists of systematically varying the atomic parameters to minimize the function R (variously called the reliability or residual factor) as defined in (III-32) where R - zllFeI- [Fell (III-32) XlFoI F0 and Fc are respectively the observed and calculated structure factors. (1) Thermal Parameters A succeeding stage in refinement of a structural model is to introduce a thermal parameter for each atom. The scattering power of 36 a real atom (fn in equation (III-19)) decreases with increasing sin e/A because of the distribution of electrons about the nucleus. Further, such distribution is based upon atoms at rest at their lattice points. The fact that real atoms vibrate has the effect of dispersing the electron cloud over a larger volume of space. As a consequence, the effective scattering power decreases faster than that for a stationary atom. The correction term to the scattering factor for this effect is given by (III-33) where B is the thermal parameter and is related to the mean 2 2 e-B(sin e/A ) 3 ex? I3?<1/dhtl>2I (III-33) square amplitude of the atomic vibration, :7, by relationship (III-34). B . snzfiz (III—34) A further refinement is to allow the model to vibrate anisotropically and for this case (III-33) becomes (III-35). exp [ -(suh2 + Bzzkz + 33322 + 2812hk + 2813h£ + 2823kl)] (III-35) (2) Anomalous Dispersion Although the atomic scattering factor, fn, has heretofore been treated as a real number, the scattering phenomenon in fact introduces a phase change which requires the scattering factor to be represented by a complex expression (III-36) in which (Af' + iAf") are the anomalous £30”: - fn + (Af' + iAf") (III—36) dispersion correction terms. These terms are relatively independent of sin ell. CHAPTER IV EXPERIMENTAL MATERIALS, EQUIPMENT, AND PROCEDURES A. Materials Chemicals and materials used were: (a) chlorine, 99% purity, (b) hydrogen chloride, 96%, (c) argon, 99.8% (d) ultra—pure hydrogen, 99.9+%, Matheson, Joliet, IL (e) helium, 99.9% (f) hydrochloric acid, reagent (g) nitric acid, reagent (h) silver nitrate, reagent (1) thionyl chloride, reagent (j) anhydrous ammonium chloride, reagent (k) carbon tetrachloride, reagent (1) chloroform, reagent (m) 1,2-dibromoethane, reagent (n) zinc metal, 40 mesh, reagent (0) ytterbium metal, distilled ingot, 99.9%, Research Chemicals, Phoenix, AZ (p) Yb203, Tm203, Lu203, H0203 and Dy203, 99.9% lanthanide purity, Michigan Chemical, St. Louis, MI (q) Thoria, 99%, Zirconium Corporation, Solon, OH (r) graphite stock, spectroscopic grade, National Carbon, Bay City, MI (3) quartz, 99.9% (t) molybdenum stock, Kulite Tungsten, Ridgefield, NJ. B. Sample Preparation l. Ytterbium Trichloride Hexahydrate Ytterbium trichloride hexahydrate was prepared by dissolution of Yb203 in concentrated hydrochloric acid. The solution was evaporated to dryness at 80°. 2. Ytterbium Trichloride Six different chlorinating agents were tried in the preparation of anhydrous YbCl3. The starting material for these preparations was either 37 38 the calcined sesquioxide or the hydrated trichloride obtained as in (IV-B-l) above except that the solution was evaporated to dryness at 120°. The crude YbCl3 product obtained by the methods described below was purified by sublimation. The sample contained in a quartz boat was sublimed at 700° under a chlorine atmosphere and collected on the cooler walls of the tube furnace apparatus. a. Thionyl Chloride An argon gas stream was used to sweep $0012 over heated Yb203 in an attempt to repeat the preparation of pure YbCl described by Machlan 3 et a1.35 as taking place according to equation (IV-l). Yb203(s) + 380C12(£) a 2YbCl3(s) + 3802(g) (IV-l) This preparation was attempted at reaction temperatures maintained between 410° and 550°.' The reaction period was approximately four hours at the maximum temperature for the experiment. b. Chloroform A single preparation using CHCl3 swept in an argon stream over the heated hydrated trichloride starting material was effected for two hours at 600°. c. Carbon Tetrachloride The reaction of CCl with lanthanide sesquioxides is reported to occur 4 in accordance with equations (IV-2) and (IV—3)9. These reactions were Ln203(s) + 3CC14(2) - 2LnCl3(s) + 3012(g) + 3CO(g) (IV-2) Ln203(s) + 3CC14(£) - 2LnC13(s) + 3COClz(g) (IV-3) studied by carrying CC14 with an argon flow over Yb203 heated to 550-700° for a period of several hours. d. Chlorine The direct reaction of chlorine gas with the heated hydrated 39 trichloride starting material was conducted at temperatures up to 900° for intervals up to 18 hours. e. Hydrogen Chloride Hydrogen chloride or hydrogen chloride diluted with helium or argon was used as the chlorinating agent in preparations using either of the described starting materials. Preparations were conducted at sample temperatures in the range of 500 to 850°. The reaction period was usually dictated by malfunction of the hydrogen chloride flow regulating equipment. f. Ammonium Chloride A six-fold excess of ammonium chloride was coprecipitated with the hydrated trichloride. The ammonium chloride-ytterbium chloride mixture was air-dried for several days at 120° and then transferred to a quartz tube or graphite crucible. In each case the mixture was heated slowly 12- 33229 to 350°. The heating rate was adjusted to allow removal of water before the excess NHACl was sublimed away at 350°. The overall reaction is described by (IV-4). The product was ultimately heated to at least Yb203(s) + 6NH401 (s) a 2YbCl3(s) + 3H20(g) + 6NH3(g) (IV—4) 500° before terminating the preparative experiment. 3. Ytterbium Dichloride a. Metallothermic Reduction Sublimed YbCl3 was transferred to a quartz tube to which was added either a stoichiometric amount of ytterbium metal or a two-fold excess of zinc metal according to reactions (IV-5) and (IV-6) respectively. The 2YbCl3(s) + Yb(£) - 3YbC12(s) (IV-5) 2YbCl3(s) + Zn(£) I 2YbClz(s) + ZnC12(g) (IV-6) tube was evacuated and the sample region was heated in the flame of an oxygen-gas torch. Heating was continued until the excess zinc distilled 40 from the hot zone and formed a mirror on the cold wall or until the green product distilled from the hot zone. b. Thermal and Hydrothermic Reduction A second technique used for preparation of YbCl2 was to heat YbCl3 prepared in a graphite crucible as in (IV-B-Z-f).ig.§i£g to red heat either in vacuum or under approximately a half atmosphere of hydrogen for an hour. 4. Ytterbium Oxidechloride Thermal decomposition of YbCl '6H20 at 500-600° under an inert 3 atmosphere was used to effect preparation of YbOCl. The decomposition reaction is given in equation (IV-7). Other YbOCl preparative techniques YbCl3-6H20(s) = YbOCl(s) + 5Hé0(g) + 2HCl(g) (IV-7) included the heating of equimolar amounts of Yb203 and YbCl3 at up to 1100° under both chlorine and inert atmospheres and the direct combination of Yb203 and C12 in a manner similar to that described in (IV-B—Z-d). 5. Other Oxidechlorides a. Triytterbium Tetraoxidechloride Two preparations of Yb30401 were attempted. Each involved combination of equimolar amounts of ytterbia and YbOCl according to equation (IV-8); Yb203(s) + YbOC1(s) = Yb30401(s) (IV-8) the first under an inert atmosphere and the second under a chlorine atmosphere. b. Mixed Metal Oxidechlorides The mixed metal oxidechlorides, LnOCl, were prepared by dissolving apprOpriate proportions of the sesquioxides in hydrochloric acid and then thermally decomposing the hydrated chloride as described in (IV—B—4). 41 C. Single ngstal Growth Single crystals of YbCl2 and YbOCl were grown by adaptations of the preparatory conditions. Ytterbium dichloride was transported igflgaggg to the cold lid of the graphite crucible in which YbClszas contained .during a melting experiment. Single crystals were selected from the vapor-transported material. Single crystals of YbOCl were first observed in the downstream end of the quartz boat containing YbOCl powder heated to llOO° under a chlorine gas stream. Additional crystals of YbOCl were prepared by heat— ing to llSO° for periods which varied from a few days to several weeks powdered YbOCl which had been sealed in a quartz ampoule containing one atmosphere of chlorine. D. Analytical Techniques 1. Chlorine Analysis Analysis for chlorine was effected by dissolution of the sample in dilute nitric acid and subsequent determination by a standard silver halide gravimetric technique. 2. Ytterbium Analysis Some ytterbium chloride samples were analyzed for metal content after the gravimetric chloride determination by precipitation of the excess silver with dilute hydrochloric acid, adjustment of the solution pH with sodium hydroxide to the bromcresol green end-point, and precipitation of ytterbium oxalate by addition of saturated oxalic acid solution. The oxalate precipitate was washed, digested, and then carefully ignited with the metal being determined gravimetrically as the sesquioxide. Ytterbium metal content was also determined by direct ignition of other samples to 42 the sesquioxide. 3. Oxygen Analysis Oxygen content was determined by difference. E. Density Measurement The density of YbCl2 was determined by the buoyancy technique. The weight of several crystals contained in a platinum mesh basket which was suspended from the balance pan hanger arm was measured both in the argon atmosphere of the glove box and while the basket and crystals were sub- merged in 1,2-dibromoethane whose temperature had been carefully measured. The density of the dibromoethane immersion medium was extrapolated from published”2 temperature-density data. The density of YbOCl was not determined. F. X—Ray Techniques For various operations a Siemens Kristalloflex IV, Norelco XRG 5000, Norelco,and Picker 809B x-ray generators were used. All work was with copper radiation (ARE - 1.54178A) with the exceptions of the fluorescence analyses which used tungsten radiation and a few Debye-Scherrer photo- graphs taken with iron (AKE - 1.9373A) or chromium (ARE - 2.2909A) radiation. A water-cooled Na(Tl)I scintillation detector was used in conjunction with a Siemens Kompensograph scaling unit for all non-photographic record- ing. Input to the Kompensograph unit could be selected with a pulse height analyzer and a discriminator. 1. Powder Methods Most samples were subjected to X-ray powder diffraction examination for aid in phase identification. Debye-Scherrer and forward focussing 43 Guinier-Hfigg cameras were employed with Cu K5 radiation. Sample prepar— ations and film measurements were essentially identical to those described by Haschke77 and Stezowskilu3. Platinum powder (30 = 3.9238 i 0.0003A)1““ was used as an internal standard. Diffraction data were reduced with the aid of the linear regression program of Lindqvist and Wengeleinlus. Samples of YbOCl were examined through use of a Materials Research Corp. high temperature camera mounted on a Siemens goniostat. The sample was placed on a platinum resistance heater stage, the platinum again serving as an internal standard for calibration of diffraction angle. The atmosphere in the high temperature camera was either helium or a rough vacuum. 2. Single Crystal Methods a. Optical Examination Preliminary examination and selection of crystals was made with the aid of a Bausch and Lomb Dyna-Zoom binocular microscope. The microscope was used with a Donnay optical analyzer for the initial determination of optical properties. Crystals of YbClz were mounted by wedging them into Pyrex capillaries which were subsequently sealed, while YbOCl crystals were mounted to the outside end of the capillaries using Canada Balsam. The optical proper- ties of the mounted crystals were examined with the aid of a Leitz polarizing microscope. The size of a crystal was determined by measuring it with a calibrated graticule in the eyepiece ocular of the Dyna-Zoom microscope or from photographs taken with a Bausch and Lomb metallurgical micro- scope equipped with a Polaroid camera attachment. 44 b. Cameras An equi-inclination Weissenberg camera was used to obtain oscillation, rotation, and Weissenberg photographs. A variable magnification Buerger Precession camera was used to examine those regions of reciprocal space which were not accessible with the Weissenberg camera without remounting the crystal. The photographs were used for space group determination and for selection of crystals for use in intensity data collection. c. Eulerian Cradle A Siemens four-circle Eulerian cradle with motorized w-drive was mounted on a Siemens goniostat. The cradle was aligned using a techn- 1“6 with the aid of a telescope ique described by Samson and Schuelke provided with the cradle and a cathetometer. d. Monochromator The Siemens Johannson-type crystal monochromator was mounted on the detector carriage and was adjusted for strictly Cu Kol (Aol - 1.54051A) radiation by varying the glancing angle and the edge aperture of the crystal. e. Crystal Orientation Mechanical shortcomings of the Siemens goniometer head made it impossible to use the usual method of aligning a crystallographic axis along the o-axis of the cradle. As the crystal was viewed through the detector slits with the cathetometer, it was centered by varying the height and the two translational adjustments. Alignment of the crystal with the eray beam was impractical so further work proceeded with the crystal in a random orientation. 45 The initial set of reflections was detected by setting the 26-circle according to the values obtained from powder work and then scanning the x- and ¢-circles. While the choice of signs of the crystallographic axes is quite arbitrary except in the case of the determination of the absolute configuration of a non-centrosymmetric crystal, the assignment of signs to the various (hki) reflections must be done in a consistent manner. An incorrect set of signs is reflected in the inability of the B—lOl program to compute the projection of the crystallographic axes upon the cradle axes. f. Lattice Parameter Refinement Preliminary lattice parameters were obtained from the linear regression analysis of the powder diffraction data. The refined lattice parameters were determined from diffractometer 26 values measured for pairs of (hkl) and (SKI) reflections. By determining the angle between the pairs of 26 positions without changing the x, ¢. and m settings, errors in the zero position of the diffractometer table as well as errors due to absorption and incorrect crystal centering are eliminated1”7. g. Intensity Data Collection The dead time of the counter and scaling equipment was determined from high count rates obtained from the direct beam with copper foil attenuators. For data collection the stationary crystal-stationary detector method was used. The stability of the experimental setup was determined by periodi- cdfly observing during the course of the data collection several reflections designated as standards. Data for each reflection were collected for 20000 counts or four minutes, whichever came first. 46 3. Fluorescence Methods The fluorescence equipment consisted of a Siemens 4b nonfocussing spectrometer equipped with a LiF analyzing crystal and a 0.15° Soller slit. The tungsten anode X—ray tube was powered with the Siemens Kristalloflex IV generator. a. Spectrometer Operation Optimization procedures described by Neffll’8 were used for maximization of sensitivity. Counting and scanning operations devel- oped by Haschke77 were used without modification. b. Spectrometer Calibration Standard solutions of ytterbium were prepared from Yb203. Calcined ytterbia samples were weighed with a semi-micro balance, dissolved in a minimal quantity of concentrated HCl, and diluted volumetrically to prepare solutions containing from 37 to 104 pg Yb/ ml. Standard targets for the preparation of calibration curves were obtained by placing known amounts of the :solutions onto targets similar in design and material to those used for collection experiments. Volu- metric aliquots were made both by weighing and by use of an ultra precision micro buret (Kontes Glass Co.). The targets were allowed to dry in a desiccator and were then counted using the scanning procedure. A linear calibration curve was obtained from least squares analysis of the number of counts per microgram of Yb. To allow for shifts in the zero setting of the spectrometer table, the scanning range for each day's operation was determined for a bulk sample of ytterbia from a scan of 26 in the vicinity of the Yb Lol (A-l.67l9A) transition. 47 G. Neutron Activation Analysis Samples for neutron activation analysis were prepared in a manner similar to that described for the fluorescence targets (IV-F-3-b) except that the solutions were placed on high purity quartz discs. After drying, the samples were calcined overnight and then individually sealed in polyethylene film. The sample discs along with two blank discs were taken to the University of Michigan's Ford reactor for 24 hours of irradiation at a neutron flux of 8 x 1012 n/cnflsec. The samples were counted for gamma activity on the eighth, tenth, and eleventh days after irradiation. H. Vaporization Mode Characterization 1. Weight Loss Measurements Preliminary vapor pressure measurements were made by measuring weight losses which occurred at fixed temperatures through an orifice of known size. By completely vaporizing a sample and measuring the weight loss, an indication of the interaction of the sample with the crucible was obtained. 2. Mass Spectrometric Investigation A Bendix Time-of-Flight, Model 12, mass spectrometer equipped with a Knudsen source inlet system was employed for determination of the species in the effusate. Crucibles made with channel orifices were heated by radiation and electron bombardment. Electron ionizing beams of up to 75 ev were employed. The appearance potentials of all Yb containing species were obtained by a linear extrapolation technique using mercury and nitrogen as references. 48 3. Effusate Collection A quartz cup was inverted over the orifice of a graphite cell containing YbClz. When the cell was heated inductively in vacuum a condensable effusate collected in the cup. 4. XrRay Examination Solid residues from effusion experiments as well as the condensate collected as described above were examined by X—ray powder diffraction to enable identification of the phases present. 1. Target Collection Technique 1. General Procedure The effusion-target collection apparatus has been described previously by Kent'"9 and Haschke77. After the crucible had been heated to red heat and the target magazine cooled, the crucible to target separation was measured with a cathetometer. The cathetometer was used also to ascertain that the crucible was aligned coaxially with the target magazine. 2. Temperature Measurement Temperature measurements were made with a Leeds and Northrup disappearing filament optical pyrometer. Corrections for prism and window transmissivities were made on the basis of observations of a tungsten strip lamp powered from a constant voltage source. The scale calibration of the pyrometer used for experimental measurements was corrected to the scale calibration of a pyrometer which had been cal— ibrated by the National Bureau of Standards. 3. Orifice Measurement Areas of effusion cell orifices were determined from photographs 49 taken with the metallurgical microscope both before and after vapor- ization experiments. The areas of the photographed orifices were measured with a compensating polar planimeter. Kentl"9 determined that a correction for thermal expansion of the orifice was not necessary. 4. Effusion Cell Desigg Two types of high density graphite effusion cells as described by Haschke77 were used for target collection measurements. In addition, two variations of the symmetrical cell design were used - in one case a tantalum washer was attached to the top surface of the cell and in the other the cell was enclosed in a graphite oven as pictured in Figure 4. 5. Condensation Coefficient Determination To determine if all the effusate striking a target condenses, the target magazine was fitted with two targets in the following manner: a target of 17.10 mm radius, rc, which was nearest the effusion cell had an annular hole of 3.12 mm radius, rb, and was placed 4.85 mm, h, in front of a second target of radius 7.98 mm, r Any effusate after a° passing through the annular hole which does not condense on the second target is re-emitted with a cosine law distribution. Most of the re-emitted effusate passes back through the annular hole of the first target, but some strikes and condenses on its back. The fraction, f, of re-emitted molecules striking the back of the first target is given by equation (IV—9). If both targets are made from the same material f --§%g{r% - rg + [(rg + rfi + hz)2 - 4r§r€]1/2 - [(rg + rg + hz)2 - 4r§r§]1/2} (IV-9) and are at the same temperature, the condensation coefficient should be the same for each. On this basis the condensation coefficient may be 50 FIGURE 4. Effusion Cell Enclosed in Graphite Oven vity Sampl aphite oven Gr // \\\\\\\\\\N\\\\\\\\\\ _C:_ /// .//W/$\ , _ _ w , \\\\\\\.\\\\ . \\\\\\\\ .: _ e # ///./// I .& Optical cavity V/// //// I: — ______ 51 calculated from measurements of the amount of effusate collected on the second target and the back of the annular target. J. Auxiliary Equipment Air sensitive samples were handled in an argon atmosphere glove bOX‘WhiCh was purged of oxygen and water1“3. The vacuum systems employed for preparations and vaporizations were all cryogenically trapped and evacuated with either silicone oil (DC 704) or mercury diffusion pumps backed by mechanical forepumps. Induction heating was accomplished by coupling the 300kHz output of a saturable reactor controlled Thermonic generator either to the work directly or through a water-cooled copper current concentrator. CHAPTER V RESULTS A. Preparative Results of elemental analyses are reported in Table I and lattice parameters are listed in Table II. These results are discussed below. 1. Ytterbium Trichloride Hexahydrate Preparations of YbCl3'6H20 yielded small white needle-like hygro- scopic crystals. These and all other hygroscopic crystals were manipulated in a glove box and protected by a film of paraffin oil during X-ray powder diffraction examination. Observed interplanar d-spacings and intensities together with values calculated on the basis of the atomic positions reported for GdCl3'6H20 are listed in Appendix III-A20. These data indicate that YbCl3'6H20 is isostructural with the other heavy lanthanide trichloride hexahydrates. 2. Ytterbium Trichloride Preparatory procedures which used SOC12, CHC13, or C014 were unsatisfactory due to side reactions which produced sulfur, carbon, or hexachloroethane, respectively. The YbCl3 prepared from ytterbia and chlorine was contaminated with incompletely reacted ytterbia as evidenced by the partial water solubility of the products. Most preparations in which HCl was a reactant were unsatisfactory due to incomplete chlorination which resulted either from equipment 52 53 Table I: Analytical Results Compound wt% Chlorine w Z Ytterbium 1 Observed 2 Calculated % Observed % Calculated YbC12 28.9io.2a 29.0 7l.oro.1a 71.0 me2.26 YbCl2.26:0.05b YbCl2.30:0.05b YbCl2.28:0.05b YbCl3 37.9ro.3c 38.1 62.0ro.2c 61.9 YbOCl 15.6ro.3° 15.8 77.2:o.2c 77.2 a I error is standard deviation b I estimated error for individual determinations of three samples c I estimated error for single determination Table II: Lattice Parameters Phase Symmetry Lattice Constants Structure Space ,(A or deg) Type Group YbCl3°6H20 monoclinic 9.60 10.014 GdCl3'6H20 P2/n 6.524i0.008 7.842:0.007 94.185t0.063 contra: IIII YbCl3 monoclinic 6.741:0.009 A1013 C2/m 11.657i0.017 6.384i0.008 llo.l7io.053 u>n o‘m YbClz orthorhombic I 6.693i0.001 CeSI Pbca I 13.150i0.003 I 6.943i0.001 - 3.726i0.0018 YbOCl 55.605i0.0083 YbOCl hexagonal TmOCl hexagonal I 3.73210.002 YbOCl - 55.78i0.11 LuOCl hexagonal I 3.7l7t0.002 YbOCl I 55.37i0.14 ON 09 O“ OU‘D I 54 malfunction or melting of the YbCl3 initially formed. Melting of YbCl3 caused Yb203 or YbOCl to be occluded and thereby restricted further chlorination. The NH401 method for preparation of YbCl3 proved to be the most satisfactory. The product obtained in this manner was a fine white powder which was rapidly and completely water soluble. The extremely hygroscopic samples were stored over P205 in an evacuated desiccator for periods of less than a week before use. 3. Intermediate Ytterbium Chloride (YbCl9A26) In the course of early attempts to produce YbClz by reduction of YbCl3, an unreported phase was observed by X—ray analysis. Elemental analyses indicated the composition of the phase was intermediate between those of the di- and trichlorides. Analytical results for several pre- parations indicated a Cl/Yb ratio which varied from 2.26 to 2.30. XrRay powder diffraction records are inconclusive as to phase purity because of possible coincidences of diffraction lines with those of YbCl3 and YbClZ. The observed interplanar d-spacings are listed in Appendix III-B. The light green phase disolved in water to yield a similarly colored solution which turned rapidly colorless upon addition of dilute HNO3 - this observation is consistent with the presence of ytterbous ion in solution. Hereafter in this work, the phase will be referred to as YbC12.26 although its exact composition is uncertain. 4. Ytterbium Dichloride All four methods described for the reduction of YbCl3 yielded YbC12. To assure complete reduction to the dichloride, prolonged heating (2 hours) at temperatures above 700° was necessary in the thermal and hydrothermic syntheses. Direct synthesis of Yb612 from the elements was not attempted. 55 The bulk of the YbCl2 used in this investigation was prepared by ‘iq gigu hydrogen reduction of YbC13 as described in (IV-B—3-b). When viewed with reflected daylight, YbClz is colored jade green; samples are light green when viewed with transmitted incadescent light. The interplanar d-spacings for YbClz are listed in Appendix III-C. Ytterbium dichloride is not nearly as hygroscopic as YbCl3 with several days being needed for a sample of YbCl2 a few milimeters thick to hydrolyze completely in air to the hydrous oxide. Powdered samples hydrolyze rapidly. Dissolution of YbCl2 in water also takes place much more slowly than that of YbC13. Dilute aqueous solutions of YbCl2 (=10'%M) remain light green for several hours at room temperature if undisturbed. 5. Ytterbium Oxidechloride Thermal decomposition of YbC13°6H20 yielded a product which on the basis of X-ray powder diffraction analysis contained a major component which gave broad bands on the diffraction photographs and a small amount of Yb203 . The heating of equimolar amounts of YbCl3 and Yb203 under an inert atmosphere produced similar results. At the upper temperature range of preparations only Yb203 was present in the product remaining in the reaction boat since the chloride was swept from the hot zone by the inert gas. All preparations in which a chlorine atmosphere was used yielded YbOCl. The sharpness of powder patterns improved with extended heating at temperatures above 800° under a chlorine atmosphere, with diffraction lines gradually replacing the broad bands observed previously. Annealing times varied from two days at 800° to a few hours at llOO°. Ytterbium oxidechloride is a white, water-insoluble, air-stable solid 56 which is pulverized easily. Interplanar d-spacings of the YbOCl powder pattern and their indexing based upon symmetry and cell parameter information obtained from examination of single crystals of YbOCl are presented in Appendix III-D. 6. Other Oxidechlorides .The attempted preparation of Yb3O4C1 in a chlorine atmosphere produced a new phase of unknown stoichiometry. The diffraction record is reported in Appendix III-E. The oxidechlorides of thulium and lutetium prepared by the thermal decomposition of the respective hydrated trichlorides under a chlorine atmosphere are isostructural with YbOCl. Maxed metal oxidechlorides prepared from mixtures of dysprosia or holmia and ytterbia crystallized in two structures - the PbFCl-type when the effective metal radius, as determined below, was equal to or larger than the so+3 radius, and the YbOCl-type when the effective metal radius was smaller than the Er+3 radius. Those samples with an effective metal radius of Er+3 are dimorphic as is ErOCl. Effective metal radii were determined according to equation (V-l) from Templeton and Dauben's116 set of trivalent lanthanide crystal radii and the mole fractions, x and (l-x), of the sesquioxides used. Exact limits of cationic radius for each structural type were not established. reff ‘ ernl + (1 "' x)an2 (V‘l) 57 B. Structural l. Unit-Cell Determination a. Optical Properties Crystals of YbClz were obtained by fracturing a melt and exhi- bited no regular external morphology. Observation between crossed polarizers indicated YbClz to be biaxial. Crystals of YbOCl were in the form of extremely thin colorless plates with a micaceous cleavage plane coincident with the plane of the plates. Some of the crystals exhibited the morphology of a thin regular hexagonal prism. Internal interfacial angles for a number of crystals were determined to be 120i1°. Observation of YbOCl crystals between crossed polarizers showed either no variation as the crystal was rotated or extinction in only part of the crystal when it was viewed normal to the plane of the plates. The crystals were too thin to be examined along the plane of the plates. b. Systematic Absences and Space Group Preliminary Weissenberg and precession photographs of YbClz established orthorhombic symmetry. Reflections were present for the following conditions: h00, OkO, 00% only when h, k, 2 I 2n, respectively hkO, OkE, hOE only when h, k, E I 2n, respectively hki - no regular extinctions These conditions are uniquely consistent with space group P 21/b 21/c 21/3 (No. 61)95 which will be referred to as Pbca. The conditions governing possible reflections and the coordinates of equivalent positions for the general and special position sets of Pbca are found 58 in Table III. Schematics of the symmetry of the space group are illus- trated in Figure 5. It has not been possible to assign unequivocally a space group for YbOCl. Precession and Weissenberg photographs confirm hexagonal or pseudo-hexagonal symmetry. Systematic absences exist only for 00E I 3n. However, rotation photographs of a second crystal reveal that the translational period of the c*-axis is one-half the period as determined from Weissenberg photographs taken with a* as a rotation axis. Thus the requirement limiting possible reflections is 002 I 6n. This requirement is satisfied for four space groups, P61 and P6122 and the enantimorph of each, P65 and P6522. It appears also that hki reflections for 2 I 2n are much stronger than those for i I 2n + l. c. Lattice Parameters Refined lattice parameters for YbCl2 as listed in Table II were determined from least squares fit diffractometer data for (hki) and (ER?) reflections taken as described previously. No angular dependent weighting or extrapolation function was used for the fit. Refined lattice parameters for YbOCl were obtained from a linear regression fit”5 of powder diffraction data using the symmetry and approximate lattice periods obtained from single crystal photographs. d. Density The density of YbCl2 derived by the buoyancy method is 5.17:0.05 g cm"3 at 23°(the error is estimated). Based upon the observed lattice parameters, this density corresponds to 7.8 molecules per unit cell. The theoretical density for eight molecules per unit cell is 5.34 g cm'3. The density observed by Klemm and Schtith3 at 25° was 5.08 g cm73. The density of YbOCl was not determined. 59 TABLE III: Properties of Space Group Pbca Point Coordinates of Conditions for Positions Symmetry Equivalent Positions Non-extinction 8c 1 i(x,y,z; l/2+x,l/2-y,2; hki: No conditions i,1/2+y,l/2-z; l/2-x,y,l/2+z) Okl k = 2n hOE 2 I 2n hkO h = 2n 4b 1 0,0,l/2;l/2,1/2,l/2;O,l/2,0; l/2,0,0 Special: as above, plus hki: 4a 1 0,0,0;l/2,l/2,0;O,l/2,l/2; h+k, k+£, i+h = 2n 1/2.0.1/2 FIGURE 5. Representation of Space Group Pbca ads: N I I I .....-----..-4---........-.__,. I l I I I” I I I -l -- I I I I «Ir—a j r V .I l | I I I I l I I I I I I I I~ I I I | I l 6 $4 AL.-.-----oo “p ode; 1" s 6O 2. Intensity Data a. Data Collection An approximately right parallelepiped crystal with approximate dimensions of 0.24 x 0.21 x 0.19 mm was mounted and centered on the Eulerian cradle. The o-axis was nearly normal to the (515) plane. Intensities of 495 independent reflections (sin 6/l 5 0.62) were measured at a 5°30' take-off angle. Intensities of 184 reflections which were not absent because of symmetry were recorded as zero. The ratio of intensities observed was 14084:l. No background correction was made since with the monochromator in place and adjusted for strictly Kol radiation no X-ray background was detected. With the monochromator the intensity of the unfiltered beam was decreased by 80 to 85%. Mosaity of the crystal was not checked. More than 40 crystals of YbOCl were examined for suitability for intensity data collection. None was found suitable but all exhibited two properties to a varying degree. The first property was twinning along the c-axis as evidenced by a doubling of spots. The second was that for 2 I 6n the spots were neither sharp nor distinct. In addition for the 2 I 6n case the spots were either badly streaked or on a few occasions absent altogether with only a slight darkening along festoon lines on the Weissenberg photographs. b. Absorption Correction The linear absorption coefficient, u, for YbCl2 is 945 cm'l. Calculated absorption correction factors varied from 32.3 to 1. For these calculations the crystal was described by six faces with a ‘number of less prominent faces not being included. 61 3. Computations Computations were performed on a CDC 3600 or CDC 6500 computer. The programs used for intensity data reduction (INCOR), Fourier functions, and distance and angle calculations (DISTAN) have been described previouslylu3’117. The program used for absorption calc- ulations (ORABSZ) was written by Busing and Levylla. Atomic scattering factors were taken from values compiled by Cromer and Weber119 and corrected for anomalous dispersionlos. 4. Patterson Synthesis and Ytterbium Atom Positions A three dimensional Patterson function was calculated from intensity data which had been corrected for Lorentz, polarization, and monochromator effects, but not absorption. The positions, relative peak heights, and assignments of the larger Patterson peaks are given in Table IV. The assignment of the Patterson vectors for the metals is described below while the other assignments are based on a posteriori observations. According to the notation of Table III, the possible ytterbium atom positions include: 8 Yb in Wycoff set 8c or 4 Yb in set 4b and 4 Yb in set 4a. Use of sets 4a and 4b was incompatible with the Patterson synthesis results. Also, the lack of many strong face- centered reflections ((hkl) all even or all odd) made it unlikely that the metals were in the face-centered positions 43 and 4b. The Yb atoms were located from Harker planes which for Pbca are: i(l/2+2x,1/2,0), i(0,l/2+2y,l/2), and i(l/2,0,l/2+2z). By examining particular sections of the Patterson, namely peaks two, three, and four in Table IV, values for x, y, and 2 can be determined. Peak 1 at the origin contains no information about atomic positions. Initial values for the Yb atom were 62 Positions and Heights of Principal Patterson Peaks TABLE IV: Relative Assignment Height No. (1/2r2x,l/2,0) (l/2,0,l/2i22) (0.1/2i2y.1/2) origin Yb-Yb Yb-Yb Yb-Yb Yb-Yb* Yb-Cl Yb-Cl 9967122288 9718874987 9643211 0020200800 0045415033 0000000000 0007083338 0502522240 0000000000 0000006666 0050550422 0000000000 0 1234567891 50823100885443210077 77665555444444444433 00000000000202088800 52522010550401533352 00000000000000000000 75150010394208174690 01430540401350311315 00000000000000000000 nu,4.U.4,OAUAU.8.U.UAU.QAUAUa4,onU.U.4,o nvozssozozssnv1lnvfisfi.h.9.nvoeqsnvnvozoz nunsnonvnvnvnvnvnunvnvnonvnvnvnunvnunvn. 119.1.4.5.6v7.nva,nu119.1.A.R.Av7.nuo,nv 111.11111.111.11119.9.7.9.7.9.9.7.9.9.Q. * Peak overlap from adjacent octant 63 8c (x, y, z) - (0.25, 0.135, 0.04). 5. Solution of the Chlorine Atom Positions A least-squares refinement which used the phases determined from the Patterson Yb position and the observed structure factor amplitudes refined to an R of 0.36. A difference Fourier synthesis (V-2) calculated from the refined Yb atom position, (0.23, 0.12, 0.04), with an isotropic 1 Z Z 2 (IFOI - IFCI) exp[-2ni(hx+ky+£z)]eh‘ (v-2) V h k l thermal parameter had a peak at (0.01, 0.45, 0.25) which was assigned to a C1 atom in set 8c. Three additional cycles of least-squares refinement for the two atoms with isotropic thermal parameters yielded R - 0.31. The position of the other Cl atom at (0.36, 0.21, 0.40) was located in a second difference synthesis. Additional cycles of least-squares refinement reduced the R factor to 0.28. At this stage during the structural refinement the computations for the absorption effect were completed. With the absorption corrected data and the previously determined positions for the three atoms, three cycles of least-squares refinement with anisotropic thermal parameters yielded R - 0.156. Twelve reflections were deleted from the final calculations because of potential interference from the goniometer head during data collection. The final R value was 0.137. All data were included with unit weighting. Reflections with P0 . 0 were not included in the calculations. Final atomic coordinates and with both isotropic and anisotropic thermal parameters with their standard deviations are found in Table V. The shift in any parameter in the last cycle of refinement was less than 0.12 of its standard deviation. Observed and calculated structure factor amplitudes are given in Table VI. A difference Fourier synthesis indicated \ 64 Table V: Parameters from Least-Squares Refinement. A. Atomic Coordinates Atom x y 2 Yb 0.2293(6)* 0.1121(2) 0.0430(8) Cl(1) 0.355(3) 0.206(2) 0.389(4) Cl(2) 0.503(3) 0.471(1) 0.264(4) B. Thermal Parameters Atom 8 811 822 B33 B12 313 B23 Yb 2.7(1.2) 2.5(0.2) 0.9(0.2) 4.4(O.2) 0.03(0.15) 0.01(0.20) 0.10(0.14) Cl(l) 2.8(2.3) 2.5(0.9) 1.5(0.7) 6.2(1.5) 1.0(0.7) 0.09(0.7) -0.9(0.8) 01(2) 1.6(1.8) 1.5(0.7) 2.0(0.6) 2.4(0.9) 0.2(0.6) 0.7(0.6) 0.5(0.9) *Standard deviations are in parentheses. 65 Observed and Calculated Structure Factors. Table VI 0 tlfl .I.! .COK IA. .u.! 00.! IO- ON.! 091 “.n IO. .Okt ”.0. .0.& ..n. or OCH! I0.! :. com! 01.! .cc! Q.Q! PC! In UJCU f(& C «IN r.. ..k In. IC. rt. Ck. (or «0 cm .P. ¢:g¢LC OC'C‘C‘ C .Ok hrs FO— 0P0 uh. nnn IO. C C.r '9 0‘0 J -a €-I-ncou’- «4c4o-aer o-a.r.o-a.-n.r o1c-Q n-a.o«o-a r —!\r c-n.- I IICCCCOOun—Amuakrrncoo----aaonrrcccoc---a«&- r 0 Fr. I. .I C an. ~N. «~. on. 0.! C I&. ff. 0.! C . c «I! r0 1.! c or! or 0.! ON! C O 0 CK! C C Q C A. (O! .. R CO! It In.! rt. C(_! Ck. .t cc. Ir.! 0 .0. c on o «c. .6. .n c or. no. '1. hr. at. CC. 00‘ C(R (ct C CC.! I.. I.. I.— nle! C (I. ..n (.Q! FCC OC.! .r 00! 0 com! can .NA! CIA o..! 9.. In?! rrh ..! C 0.. «c. Q. C O.r! Fen .tn Con 00! It so. C~I 00! o I. c 6.. I.. I.! C bk. IN. kc. rc. F.! C #0. r. r. C r. .r 0410 vac ~hn0r-aro-o-~pq¢¢-grgmoc.orca—«rcto-aro-«v—anotc—«PCI—RFOO-N' J x ocvvorrccccccccgc------noononrrrnrococclII——-—-onncoorfrrcoqo PP C. Cf! Ob! I.u! 0. 09! If «I! 0.! o. 00! (F! 0.! Or on rm (0. (n.! CI IC.! Q..! «F! «F. I. Org 0c. (n. (I met c¢.! 60. «Ct! QOU OP.! '0‘. C6!l .FQ! c0.! fits! rflu now! can era .0. .CC CF. 0&— (O. C.— UJ‘U C - C C C ac. CC C (c. I.- hr at. .r CCK (K. IO «It be. cm C K.- PC- COR 0C— PF. [CF Ft? 0C. CTR CON PNR OCP ICP CO. (on PC. at. (F. (C. mCO J OC-firc-POIo-wnctoc-Arqco-angco-mrcn-ango-«-nrcICc-mrcCo-0POIc x rererccccccccccoocccccanccccccccccccccccccoooooocoooooocooono x I(one:ccccc—-----naaunaorrrrrrqcovclrcrcc¢——-———n~tkfikfl""" Ce FR CI 0. or! .0 IF.! CC .0A! .0.! .I! (CI (Cl N.! Pk CC! (V. CC- .Cfi .. &. PI PI! P..! .I or. OI (.Q c.! .&n «a! PI. (0.! .t.! «r.! IPA! ra.! 0.0! I(.! CPI IO.! IA. tan! or. 0' ft. U410 If. ‘0“ C.— P!— FCN CC. CC. PO- 9" NC. CO— . 3" $00 .4 r c -u\n700°) YbC12+ and its fragments were observed. c. Effusate Collection The effusate collected from over the YbCl2 vaporization was determined by X-ray powder diffraction analysis to be YbClz. d. XrRay Examination X-Ray examination of residues from YbCl2 vaporizations indicated the presence of only YbClZ. Residues from YbOCl vaporizations contained Yb203 and YbClz, or only Yb203. 7. Vapor Pressure Equation Temperature and corresponding equilibrium vapor pressure values determined for reaction (V-3) are presented in Appendix IV and Figure 7. The pressure equation for 49 independent measurements for gaseous YbCl2 in equilibrium with liquid YbCl together with the standard deviations 2 for the least-squares fit is: - _ 4 - log PYbCl2(atm) (1.127i0.025) x 12 + 4.65:0.20 (V S) for 1048 :_T §_1483°K. 8. Thermodynamic Values Employed in Data Reduction Values for (H; - H298) and (8; - 8393) for YbC12(s) were obtained by graphical interpolation of estimates3°»31. Heat capacity, enthalpy, 1.121 and entropy data are not available for gaseous YbCl Brewer et a 2. reported that available electron diffraction data for the dihalides of 69 FIGURE 6. Appearance Potential Curves. 90r- 60 h 1:012“ 40" Ion Intensity (relative units) or c> l 30" 20- 4 l l 1 l 10 20 30 40 50 60 Electron Energy (ev) 70 FIGURE 7. Pressure of YbC12(g) in Equilibrium with YbC12(2). 1? .— 5500 0 3° N v-i E n. P " c, n. 51 v ~.=° “a 6.0 " at Run 1 ° _. . g a A 4 ° 0 5 I 6 v 7 7.0 - l 1 l 1 I 7.0 8.0 9.0 1/T x 104 (°Kf1) 71 ‘ the alkaline earth and zinc group metals indicate that they possess a linear structure (Dmh). Since the ground and first excited states of the divalent zinc group metals and Yb+2 have the same term symbols and all have a d10 or dlof14 configuration it is reasonable to assume that YbC12(g) is also linear. Therefore the experimental data for gaseous mercuric dichloride122 were selected for YbC12(g) and then corrected for the molecular weight difference by the Sackur relationship123. These data are presented in Appendix V. The absolute entropy of YbC12(s) was determined in two ways. First, Westrum'slz” value for the lattice contribution to entropy for Yb was combined with Latimer's125 value for C1 (3298 YbC12(s) = 30.7 eu). Second, the experimental126 absolute entropy for CaC12(s) was combined with the values for Yb and Ca to obtain another estimate of 3298 YbClz = 31.0 eu. The entropy for YbC12(g) was taken from the -fef298 value for the mass corrected HgC12(g) data and numerically equals 70.3 eu. Free energy functions for both condensed and gaseous YbCl2 were calculated from the estimated and experimental data for HgClZ. Heat capacity data for HgCl2 were also employed. Values for Afef for the vaporization were obtained by graphical interpolation of calculated data. 9. Thermochemical Values Results of the vaporization of YbC12(£) according to equation (V-3) were treated in the following way. From the pressure equation (V-S) (median temperature 1265°K), values of AH1265 - 55.2i1.2 kcal mole’1 and AS1265 - 21.310.94 eu were obtained, and were reduced to 298°K using approximated heat capacity data. For the sublimation of YbC12(s), AH§98 - 61.8i2.3 kcal mole'1 and A8398 = 31.1i2.0 en. The 72 enthalpy and temperature of fusion of YbClz(s) were assumed equal to those for HgClz(s). Combination of the measured pressure data and the extrapolated free energy functions according to equation (III-15) yielded a third law A3598 - 59.7310430 kcal mole-1 with no temperature dependent trend in the values. These independent third law enthalpy data are presented in Appendix IV. The energetics of formation were calculated in the following manner. Combination of the enthalpies of formation of Yb(g)127 and Cl(g)122 and the estimated energy of dissociation of YbC12(g)128 gave an estimated AH? 298YbC12(g) of-119.8i3.6 kcal mole'l. If this value is combined with the second law enthalpy of sublimation, AH? 298YbC12(s) - -181.8i3.6 kcal mole-1. The second law absolute entropy of YbC12(s) (S298 - 31.7 eu) was obtained from the entropy of vaporization and the estimated entropy of YbC12(g). From these values the free energy of formation AGE 298YbC12(s) - -l75.3 kcal mole-1. From the entropy of sublimation and ASE 298YbC12(s) a value of AS? 298YbC12(g) - 36.012.0 eu was obtained. Combination of this value with the estimated enthalpy of formation gives AG; 298YbC12(g) = -109.7 kcal mole-1. The normal boiling point of YbC12(£) was calculated from vapor pressure equation (V-5) to be 2242°K. The enthalpy of vaporization was estimated from the HgC12(£) data to be AH; 2242 YbC12(£) = 48.8 kcal mole’l. Since at the boiling point, As; - AH;/Tb, an entropy of vaporization As; 2242 - 20.8 eu was obtained. CHAPTER VI DISCUSSION A. Evaluation of Experimental Conditions 1. Neutron Activation Analysis Several factors contributed to the lack of success of the NAA experiment. Among these were the unavailability of a multi-channel analyzer which could be used to discriminate the Yb radiation from background and the need to wait more than a week after irradiation before the samples could be transported for counting. Since the integrity of the polyethylene encapsulation was destroyed during irradiation, the possibility that some sample washed off the quartz discs while they were in the water pit of the reactor cannot be discounted. Now that facilities are available at Michigan State for irradiation and counting, NAA experiments should be reconsidered as an external check on the accuracy of the X—ray fluorescence analyses and should verify the gold calibration experiments77. 2. Fluorescence Analysis Fluorescence analysis of the collected effusate proved satis- factory. At the 2 ug level reproducibility is estimated to be i 5%. The major disadvantage was the tedium of the counting procedure. The intercept of the calibration curve deviates from the expected 73 74 0.0 position, even though 0.0 was included as a datum point. This deviation probably results because the Ni K02 transition occurs within 0.1° of the measured Yb transition. Since a 0.5° scan was utilized the Ni transition was always included. Nickel, together with iron and copper, was present as a trace impurity in the aluminum targets. Elimination of the Ni interference by selection of another Yb transition is not practical because of the decreased sensitivity which would result. The recently acquired vacuum spectrometer and associated counting equipment should allow use of a fixed angle rather than a scanning procedure and should result in a reduction of the time necessary for analysis. A second advantage of the vacuum spectrometer is that analysis could have been conducted for chlorine as well as ytterbium. 3. Temperature Measurements The systematic error in temperature measurement due to calibrations of the pyrometers to the 1948 International Temperature Scale is quoted to be 1 4° in the National Bureau of Standards certification. Random errors due to observer error in use of the pyrometer are estimated to be i 3° as determined from a number of successive readings of the standard lamp's temperature taken within a short period. The crucible cavity observed to measure sample temperature had an orifice area to depth ratio of less than 1:9, a value generally aesumed to approach blackbody conditions so that no emissivity correction was made. 4. Orifice Closure A definitive explanation for the closure of the orifice with YbClz during vaporization has not been found. It is possible that 75 some radiative losses immediately adjacent to the orifice area allow condensation of the liquid. Once condensation of a non-conducting sub- stance has occured, rapid orifice plugging would follow. Use of the graphite oven as a susceptor minimized these radiative losses. 5. Knudsen Conditions Attainment of Knudsen conditions is evidenced by consideration of trends in the experimental data. The regularity of the temperature- pressure data with variation of orifice area and with varying temperature suggests that deviations arising from sampling and non- equilibrium problems are less than the experimental uncertainty. 6. Crucible Materials Weight loss data and visual examination indicated that graphite was a suitable material for the vaporization of YbClz. Use of a thoria lined crucible for decomposition of YbOCl prevented the ytterbia formed from reacting with the graphite. 7. Density Measurement For greatest sensitivity in making density measurements by the buoyancy technique, the density of the fluid should be as close to the density of the crystal as is practical. Lack of suitable room- temperature fluids with densities of five to seven 3 cm'3 hampers precise density determination of lanthanide compounds. 8. Intensity Data Collection It was determined after the completion of the collection of the intensity data that alignment of the ¢-axis of the cradle was not rigidly fixed. Since in the stationary crystal-stationary detector method only peak height data are collected, variation in the ¢-axis alignment had the same severe effect as missetting the angles. The 76 ¢—axis spindle and bearing surfaces have been remachined in the hope that future alignment of the Eulerian cradle may be maintained rigidly. A scanning procedure for intensity data collection was not selected because of difficulties encountered in the initial setup of the Eulerian cradle. An w/26-scan was not practical due to low count rates and the inability to mechanically obtain repeated scans. B. Evaluation of Thermochemical Values Obtained l. Vaporization Mode It has been confirmed that YbCl2 vaporizes congruently with molecular YbClz as the only gaseous species. Gilles81 lists the stability of the gaseous phase as being a predominating factor in fixing the vaporization mode. In view of the observation of YbC12 in the residue of YbOCl decompositions which were conducted below 700°, it is concluded that the relative stabilities of YbClz and YbCl3 will be an overriding factor in establishing vaporization modes of phases in the Yb-O-Cl system. The stability of Yb203 is the determining factor for the oxygen-rich portion of the system. 2. Thermodynamic Approximations Other than second-third law enthalpy agreement which serves as a check on the constancy of heat capacity and entropy approximations, little evidence for their accuracy exists. The data do form a consistent set. The error introduced into the data reduction by use of the enthalpy of fusion of HgClz (an; I 4.15 kcal mole-1) is estimated to be i l kcal mole-1. The estimate is based upon a comparison of the enthalpy of fusion of CaC12 (AH; I 6.78 kcal mole'l) with that 77 of HgCl2 on the assumption that YbC12(s) will closely approximate CaC12(s). Justification of this assumption lies in the similarities of ionic sizes and crystal structures. 3. Ytterbium Dichloride Data The value, AH; 298 I -181.8 kcal mole-1, is in agreement with values of -l86 kcal mole"1 obtained by Polyachenok and Novikov31+ and -184.5 kcal mole"l obtained by Machlan et al.35. The entropy of vaporization at the boiling point, 2242°K, of 20.8 eu is in good agreement with Trouton's rule and may be compared with the value of 23.4 eu obtained previously33. The value of the enthalpy of vaporization at the boiling point, 46.8 kcal mole‘l, may be compared with the value of 55.7 kcal mole’1 obtained at Tb I 2105°K reported by Polyachenok and Novikov33. The reason for this apparent discrepancy is difficult to explain since neither the values employed by Polyachenok and Novikov33 for reduction of their pressure-temperature data taken in the range = 1500 to 1700°K nor the details of their experiment were given. The higher enthalpy of vaporization observed for their boiling point experiment may be indicative of a vaporization coefficient (a) for YbClz(g) from the liquid that is much less than unity. Loehman et al.129 have shown that in a Langmuir experiment the vaporization coefficients for SrClz, Can, and BaFZ for the monomeric MX2(g) species are less than unity (0.1 < a < 0.5). However a vaporization coefficient of this magnitude would reduce the discrepancy only by an estimated three to five kcal mole'l. Experimental thermochemical values are listed in Table VII. 78 C. Structure of Ytterbium Dichloride The atomic packing in the YbCl structure is pictured in Figure 8. 2 That it crystallizes in the recently reported130’131 CeSI-type structure is very reasonable when consideration is given to the radius-ratios derived from Pauling's crystal radii132 and the axial ratios which are listed in Table VIII. The two chlorine atoms are chemically as well as crystallographically non-equivalent as can be seen from their environ- ments (Figure 9). The Yb coordination is hard to define. Each Yb atom has chlorine atoms at 2.78, 2.82, 2.85, 3.24, 3.31, 3.39, 3.66, and 4.07 A, Several of the Cl-Cl separations are shorter than the sum of the atomic radii. A situation similar to this is observed in crystals of Pb012133 - the structural type of NdClz, SmClz, and EuClzl. A short Cl-Cl distance is also observed in the PbFCl-type lanthanide oxidechlorides“3. From Pauling's132 crystal radius of 1.81A for C1" the chlorine atoms are computed to occupy 712 of the cell volume as compared with a 76% packing factor in cubic closest packing. Attempts to determine a Madelung constant for YbCl2 to be used in a Born-Haber cycle calcu- lation have not yielded a convergent series. Most MX2 halides may be categorized into two general structural types133. Those halides in which the cation/anion radius-ratio is large (30.7) form predominantly ionic structures which generally belong to the fluorite family of structures. Those halides which are moder- ately ionic crystallize in lattices which are related to the CdIz-type in which the large anions are arranged in sheets or chains which often approximate spherical close packing with the smaller cations residing in the tetrahedral or octahedral voids. For YbClz, the Yb atoms are 79 Figure 8. Atomic Packing in YbClz. 80 Table VII: Experimental Thermochemical Data. Ytterbium(ll)fiChloride Thermodynamic This Polyachenok Machlan Property Work Novikov33’3“ et a1.35 -AH§ 298YbC12(s) 181.6 186 184.5 kcal mole-1 -AG§ 298YbC12(s) 175.3 kcal mole”1 AH; 298Yb012(s) 61.2a kcal mole‘l 59.7b AS; 298YbC12(S) 31.1 an A3; bp YbC12(2) 20.8 23.4 eu 8° 298YbC12(8) 30.7 eu S° 293Yb012(g) 61.8 eu 8Second Law Value; bThird Law Value Table VIII: Compounds with the CeSI-type Structure. Compound Lattice Parameters (A) AxialpRatios Cation/Anion a b c a/c b/c Radius-Ratio CeSI 7.06 14.42 7.35 0.960 1.962 0.51 0.61 LaSI 7.10 14.57 7.38 0.962 1.974 0.62 0.53 LaSBr 7.02 13.99 7.19 0.976 1.946 0.62 0.59 CeSBr 6.94 13.69 7.12 0.975 1.941 0.60 0.57 LaSCl 6.83 13.69 7.04 0.970 1.945 0.62 o. 62 CeSCl 6.76 13.46 7.00 0.966 1.923 0.60 0.61 81 FIGURE 9. Chlorine Environment in YbClz. Yb2.8/ Yb 3.2 Numbers are distances from the central atom in A. 82 arranged between the irregular layers of Cl atoms which are parallel to the (101) plane. The difference in electronegativity between Yb(1.l) and Cl(3.5) leads to an estimated 762 ionic character132 for the Yb-Cl bond which is consistent with the layer-like structure. Reindexing of the powder diffraction data as reported by D611 and Klemm7 for YbCl2 on the basis of the cell determined in this work yields agreement with the powder diffraction records obtained in this work. The DyC1278 and TmC1279 phases should be reexamined to see if the unit cells as reported should be modified to reflect the CeSI-type structure. A combination of bond distance information obtained from the six lanthanide dichlorides may allow a consistent set of Ln+2 radii to be determined. Rations of Ln+2/Ln+3 radii could then be determined to complete the divalent set for all lanthanides since the usual lanthanide contraction would be expected. The division of the lanthanide dichlorides into two structural types is reasonable in view of the fact that the radius-ratios for the PbCl2 structure lie in the range from 0.61 to 0.69 while those of the CeSI-type range from 0.51 to 0.61. The ratios for NdClZ, SmClz, and EuCl2 are 0.66, 0.65, and 0.64 respectively while those of DyClz, TmClZ, and YbClz are 0.61, 0.59, and 0.58. The divalent radii for Nd, Sm, Dy, and Tm were estimated from the Ln+2/Ln‘+3 radius-ratios for Eu and Yb. The size of the crystal used for data collection was ten times the optimum thickness112 of 2/u where u is the linear absorption coefficient. The error in the absorption correction due to imprecise description of the crystal is estimated to be as much as ten percent. No regular variation of (F0 - Fe) was noted, so no extinction correction was applied. Effects of the mechanical shortcomings of the cradle are difficult to 83 assess. In the final least-squares analysis there are a number of reflections with E0 I 0 which on the basis of the large values of FC should have been observed. It may be that the crystal was not in the reflecting position due to variations of the ¢ axis. D. Structure of Ytterbium Oxidechloride Initially YbOCl was indexed using a cell with tetragonal symmetry. Fa The precision of data obtained from Guinier photographs showed a syste- matic error with increasing 6 for the values of (sinzeobs - sinzecalc) ; which led to rejection of the tetragonal cell. The error was so small so as not to have been observable on Debye-Scherrer photographs. The cleavage and single crystal information for YbOCl are consistent with a layer-type structure. Comparisons with CdI2 and SiC-type struc- tures and specifically Cd(OH)Cll3“ and Zn(OH)C1135 show that large values of the c-axis for these hexagonal structures are due to variations in stacking of the layers which are each composed of identical atoms. These stacking variations produce changes in the length of the c-axis without producing corresponding changes in the length of the a-axis or stoichi— ometry. Irregular packing of layers along the c-axis in YbOCl may account for some of the abnormalities observed in the diffraction records. I do not expect that the near extinction of some layers is due to order-disorder of oxygen and chlorine atoms within a layer because of the large difference in their sizes. A strict layer structure is also in agreement with the higher degree of covalency expected for YbOCl when compared with YbCl Total extinction of the (hkz) reflections for 2 odd 2. is not consistent with the observed 001 I 6n extinction. 84 Since the diffraction photographs seem to indicate that the Yb layers are "well-behaved" as evidenced by the sharpness of the diffrac- tion spots for certain layers, it may be that a solution of the Yb atom positions can be obtained in a sub-cell of the 55 A cell. Interatomic distances for all MOCl phases of the PbFCl-type were compared with predicted interatomic distances for PbFCl-type TmOCl, YbOCl, .and LuOCl. Lattice parameters for TmOCl, YbOCl, and LuOCl were extrapolated from r,“ a plot of Ln+3 radii versus lattice parameters for the lighter lantha- nides. No reason for the structural change in LnOCl which takes place 3 at the Er+ radius was deduced from the interatomic distances. If the extrapolated value for the density of PbFCl—type YbOCl is 5; used to calculate the number of molecules in the hexagonal YbOCl unit cell a value near Z I 12 is obtained. If the possibility of partial occupancy is discounted, then 2 I 12 is a reasonable number for the suggested space groups since for these space groups the number of asymmetric units in the cell must be an integral multiple of six. The calculated density for the hexagonal unit cell is 6.7 g cm73, a value some 12% smaller than the extrapolated density of 7.6 g cm."3 for the PbFCl-type. This implies that a rather dramatic volume change takes place for the structural change at the Er+3 radius. It is difficult to reconcile this apparent discontinuity with a possible bonding scheme for the YbOCl-type structure. A sample of YbOF prepared by Shinn“9 was examined in the hope that information which would aid in the solution of the YbOCl structure would be obtained. X-Ray powder diffraction data indicate that YbOF is dimorphic with d-spacings attributable to both the rhombohedralSS and monoclinic56 structures present. It is also possible that the sample contained non-stoichiometric YbOF. The only conclusion is that YbOF is not structurally similar to YbOCl. 85 E. Decomposition of Ytterbium Oxidechloride Baev and Novikov“9 report that the estimated free energy change for reaction (VI-l) is zero at 1390° an indication that YbOCl is stable below 3YbOCl(s) I YbCl3(g) + Yb203(s) (VI—1) 1390° with respect to disproportionation. However, if an alternate disproportionation reaction (VI-2) is considered the observed lower 3Yb0Cl(s) I YbC12(s) + Cl(g) + Yb203(s) (VI—2) temperature of decomposition may be rationalized. Koch and Cunninghaml35’138 studied the vapor phase hydrolysis of the trichlorides of La, Pr, Nd, Sm, and Cd. They found a linear rela- tionship between the enthalpy of hydrolysis at 785°K and the reciprocal radius of the trivalent lanthanide ion. Their data were replotted using Templeton and Dauben's116 radii and the line extrapolated to obtain for reaction (VI-3) AH785 I 11.8 kcal mole—1. This value was reduced to YbC13(s) + H20(g) I YbOCl(s) + 2HC1(g) (VI-3) 298° K using Koch and Cunningham's138 free energy function for the samarium system to obtain AH298 I 12 kcal mole'l. Use of published enthalpy data for HCl(g), H20(g)122 and YbC13(s)3O yielded a value of AH; 298 YbOCl(s) - -299 kcal mole'l. A value of 3298 for YbOCl was estimated by adding the lattice contributions for each of the ions to obtain 24.1 eu. For this estimate, the contribution of oxygen was taken to be 2 eu; reported estimates of entropies attributable to 0"2 range from 0 to 6 eu. Combination of the values of enthalpy and entropy of Yb203(s) from Westrum123, YbC12(s) from this work, and Cl(g)122 yields a free energy 298 the entropy effect which is largely due to the formation of Cl(g) will for reaction (VI-2) of AG I 43 kcal mole-1. At higher temperatures, 86 become increasingly important and at about 600° K the free energy change for reaction (VI-3) should cross zero. The extremum values for the contribution of 0'2 establish a crossover temperature range of 240 §_T §_1l90° K (the enthalpy change for the reaction is assumed independent of temperature). This temperature range is consistent with the observations in this work. The strong dependence of the prOposed decomposition reaction upon chlorine pressure is in agreement with the f5 ability to prepare YbOCl crystals at 1100° in the sealed ampoules containing chlorine. F. 0n Ytterbium(II) as a Group IIB Ion In the course of the YbCl2 study reported herein, I found that references to zinc chemistry were consulted frequently. I propose that consideration needs to be given to classifying Yb with the group IIB elements as well as with the lanthanides. The ground and first two excited states of ytterbium and the zinc group metals are the same. While for Yb+2 the filled 4d orbitals are lower lying than the 4f orbitals, there are many structural similarities between zinc and ytter— bium. In bonding cases where the ionic contribution predominates over the covalent contribution, Yb+2 often is more like the zinc group metals than the alkaline earth metals. The alloys observed in the ytterbium- zinc phase study139 do not support the behavior expected since Hume- Rothery type phases which would be expected for similar metals were not observed. This lack of similarity in the alloy system may result from a size difference. CHAPTER VII SUGGESTIONS FOR FUTURE RESEARCH The number of new questions raised as a result of this investi- gation is larger than the number of questions answered. However, many of these should be examined so as to develop a unified body of information about the Yb-O-Cl system. Completion of the YbOCl structure may allow determination of the reason for the structural transition of LnOCl with cationic radius. A change in the conditions of growth for the YbOCl crystals such as by the addition of a small amount of iodine to alter the vapor transport mechan— ism may produce samples more suitable for a structural study. A definitive vaporization study of YbC13 is necessary to resolve the existing discrepancyuas to the vapor species before explicit vapor- ization studies of Yb-O-Cl phases can be completed. The preparative (possibilities for the Yb-O—Cl system should bear fruition since only YbOCl has been confirmed and minimal evidence exists for a second ternary phase. An examination of the Yb-Cl phase diagram in the YbClz-YbCl3 region would be an important step in the testing of Corbett'sll+o hypothesis that the sublimation energies of the metals determines the observed stability trend. As has been noted77 a system of this type may be amenable to an equilibrium study using spectroscopic determination of equilibrium chlorine pressures. 87 88 The structure of stoichiometric YbOF needs to be established as a starting point for a study of the Yb-O-F system of the type in progressl“1 for Sm-O-F and Euro-F. Experience gained from work with the halides should be used as a basis from which to begin examination of the potentially interesting lanthanide mixed-halide and pseudo-halide systems. ‘1'... ...,. REFERENCES REFERENCES l) D. Brown, "Halides of the Lanthanides and Actinides," John Wiley and Sons Ltd., London 1968. 2) W. Klemm and J. Rockstroh, Z. AnorgpiAllg. Chem., 116, 181 (1928). u. 3) W. Klemm and W. Schfith, ibid., 184, 352 (1929). 4) G. Jantsch, H. Grubitsch, and H. Alber, ibid., 185, 49 (1929). 5) G. Jantsch, N. Skalla, and H. Jawurek, ibid., 201, 207 (1931). 6) W. Klemm and W. D611, ibid., 241, 233 (1939). 7) W. D611 and W. Klemm, ibid., 241, 239 (1939). 8) G. Jantsch, H. Alber, and H. Grubitsch, Monatsh. Chem., 53-54, 305 (1929). ”““”“ 9) M. Taylor, Chem. Rev., 6%, 503 (1962). 10) K. E. Johnson and J. R. Mackenzie, J. Inorg: Nucl. Chem., 32, 43 (1970). 11) G. I. Novikov and 0. G. Polyachenok, Usp. Khim. , 33, 732 (1964); Chem. Rev. USSR, m3, 342 (1964). 12) J. K. Howell and L. L. Pytlewski, J. Less—Common Metals, 18, 437 (1969). 13) S. Mroczkowski, J. Crystal Growth, 6, 147 (1970). 14) D. H. Templeton and G. F. Carter, J. Phys. Chem., 58, 940 (1954). 15) W. W. Wendlandt and J. L. Bear, Anal. Chim. Acta, 21, 439 (1959). 16) W. W. Wendlandt, J. Inorg. Nucl. Chem., 2, 136 (1959). 17) G. Haeseler and F. Matthes, J. Less-Common Metals, 2, 133 (1965). 18) S. J. Ashcroft and C. T. Mortimer, ibid., 14, 403 (1968). 19) A. Pabst, Amer. J. Sci., 22, 426 (1931). 89 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 90 M. Marezio, H. A. Plettinger, and W. H. Zachariasen, Acta Crystallogr., 14, 234 (1961). N. K. Bel'skii and Yu. T. Struchkov, Soviet. Fiz. ngst., 19, 15 (1965). E. J. Graeber, G. H. Conrad, and S. F. Duliere, Acta Crystallogr., 21, 1012 (1966). L. F. Druding and J. D. Corbett, J. Amer. Chem. Soc., 8%, 2462 (1961). O. G. Polyachenok and G. I. Novikov, Zh. Obsch. Khim., 33, 2797 (1963); J. Gen. Chem. USSR, 3%, 2900 (1963). H. Bommer and E. Hohmann, Z. Anorg. Allg. Chem., 248, 373 (1941). "Selected Values of Chemical Thermodynamic Properties," National Bureau of Standards Circular 500, U. 8. Government Printing Office, washington, D. C., 1950. F. H. Spedding and C. F. Miller, J. Amer. Chem. Soc., 74, 4195 (1952). F. H. Spedding and J. P. Flynn, ibid., 76, 1474 (1954). F. H. Spedding and J. P. Flynn, ibid., 16, 1477 (1954). L. Brewer, L. A. Bromley, P. W. Gilles, and N. L. Lofgren, "Chemistry and Metallurgy of Miscellaneous Materials: Thermo- dynamics," L. L. Quill, Ed., McGraw—Hill Book Co., Inc., New York, NY, 1950, paper 6. L. Brewer, ibid., paper 7. O. G. Polyachenok and G. I. Novikov, Zh. Neopg. Khim. , 8,1567 (1963); J. Inorg. Chem. USSR, 8, 816 (1963). O. G. Polyachenok and G. I. Novikov, ibid., 8, 2631 (1963); ibid., g, 1378 (1963). 0. G. Polyachenok and G. I. Novikov, Vestn. Leningr. Univ., Ser. Fiz. Khim., l8, 133 (1963); Chem. Abstr., 69, 4875b (1964). G. R. Machlan, C. T. Stubblefield, and L. Eyring, J. Amer. Chem. Soc., 77, 2975 (1955). -—-—- mm C. T. Stubblefield and L. Eyring, ibid., 71, 3004 (1955). C. T. Stubblefield, Ph. D. Thesis, State University of Iowa, Iowa City, IA, 1954; 0188. Abstr., lg, 1180 (1955). 91 38) D. A. Johnson, J. Chem. Soc., A, W, 2578 (1969). 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) 51) 52) 53) 54) 55) 56) J. L. Moriarty, J. Chem. Eng, Data, 8, 422 (1963). 0. G. Polyachenok and G. I. Novikov, Zh. Neorg. Khim. , 9, 773 (1964); J. Inorg. Chem. USSR, 9, 429 (1964). J. M. Stuve,'U. S. Bur. Mines, Rep. Invest., No. 6902 (1967). G. I. Novikov and A. K. Baev, Izv. Vysshikh. Uchebn. Zavedenii, Khim. Khim. Tekhnol., 2, 180 (1966); Chem. Abstr., 65, 9824g (1966). D. H. Templeton and C. H. Dauben, J. Amer. Chem. Soc., 75, 1. 6069 (1953). ”m I!) R. I. Slavkina, G. E. Sorokina, and V. V. Serebrennikov, Tr. Tomsk. Gos. Univ. , Ser. Khim. , 157,135 (1960); Chem. ; Abstr. “, 61, 7927h (1964). g M. M. Bel' kova and L. A. Alekseenko, Zh. Neorg. Khim. , 10, E-” 1374 (1965); J. Inorg. Chem. USSR, 10, 747 (1965). C! I. S. Morozov and B. G. Korshunov, Zh. Neorg3 Khim., l, 2606 (1956). I. S. Morozov and B. G. Korshunov, Dokl. Akad. Nauk SSSR, 119 525 (1958). A. K. Baev and Q I. Novikov, Zh. Neorg. Khim. , 10, 2457 (1965); J. Inorg. Chem. USSR, 10, 1337 (1965). D. B. Shinn, Ph. D. Thesis, Michigan State University, East Lansing, M1,1968. K. F. Zmbov and J. L. Margrave, J. Less-Common Metals, 12, 494 (1967). K. F. Zmbov and J. L. Margrave, "Mass Spectrometry in Inorganic Chemistry," Advances in Chemistry Series, No. 72, American Chemical Society, washington, D. C., 1968, pp 267-290. L. B. Asprey, F. H. Ellinger, and E. Staritzky in "Rare Earth Research," Vol. II, K. S. Vorres, Ed., Gorden and Breach, New York, NY, 1964, p 11. R. G. Bedford and E. Catalano in "8th Rare Earth Research Conference," T. A. Henrie and R. E. Lindstrom, Eds., Reno, NV, Apr. 1970, pp 388—399. K. S. Vorres and R. Riviello in "Rare Earth Research IV," Gorden and Breach, New York, NY, 1964, p 521. 1N. V. Podberezskaya, L. R. Batsanova, and L. S. Egorova, Zh. Strukt. Khim., 2, 850 (1965); J. Struct. Chem. USSR, ’6’, 815 (1965). lJ..Roether, Ph. D. Thesis, Albert Ludwigs University, Freiburg, Breisgau, 1967. 57) 58) 59) 60) 61) 62) 63) 64) 65) 66) 67) 68) 69) 70) 71) 72) 73) 74) 75) 76) 77) 92 I; Mayer and S. Zolotov, J. Inopg3 Nucl. Chem., 27, 1905 (1965). F.1L Spedding and A. H. Daane, Metallurgical Rev., 2, 297 (1960). H. Czeskleba, Michigan State University, personal communication, 1970. W. H. ZaChariasen, Acta Crystallogr., 2, 388 (1949). S. Fried, F. Hagemann, and W. H. Zachariasen, J. Amer. Chem. Soc., 72, 771 (1950). I. Mayer, S. Zolotov, and F. Kassierer, Inorg. Chem. , 4,1637 (1965). F. Weiger and V. Scherrer, Radiochim. Acta, 1, 40 (1967). N. Schultz and G. Reiter, Naturwissenschaften, 24, 469 (1967). H. Barnighausen, G. Brauer, and N. Schultz, Z. Anorgg Allg. Chem., 222, 250 (1965). L. B. Asprey, T. K. Keenan, and F. H. Kruse, Inogg. Chem., 3, 1137 (1964). "’ A. A. Men' kov and L. N. Kommissarova, Zh. Neorg. Khim. , 9, 766, (1964); J. Inorg;_Chem. USSR, 9, 425 (1964). L. B. Asprey and F. H. Kruse, J. Inopg. Nucl. Chem., 12, 32 (1960). F. H. Kruse, L. B. Asprey, and B. Morosin, Acta Crystallogp., 14, 541 (1961). H. Barnighausen, Agnew. Chem., 12, 1109 (1963). H. Barnighausen, J. Prakt. Chem., 14, 313 (1961). J. W. Hastie, P. Ficalora, and J. L. Margrave, J. Less—Common Metals, 14, 83 (1968). -—-‘—— mm S. Natansohn, J. Inorg; Nucl. Chem., 32, 3123 (1968). J. M. Haschke, Arizona State University, personal communication, 1970. L. Ya. Markovskii, E. Ya. Pesina, Yu. A. Omel' chenko, and Yu. D. Kondrashev, Zh. NeorgLthim. , 14,14 (1969); L Inorg; Chem. USSR, 14, 7 (1969) B. Frit, M. Moakil Chbany, B. Tanguy, and P. Hagenmuller, Bull. Soc. Chim. Fr., 1228», 127 (1968). J. M. Haschke, Ph. D. Thesis, Michigan State University, East Lansing, MI, 1969. 78) 79) 80) 81) 82) 83) 84) 85) 86) 87) 88) 89) 90) 91) 92) 93) 94) 95) 96) 93 J. D. Corbett and B. C. McCollum, Inorg. Chem., 5, 938 (1969). P. E. Caro and J. D. Corbett, J. Less-Common Metals, 18, 1 (1969). J. Wk Gibbs, "The Scientific Papers of J. Willard Gibbs," Vol. 1, Dover Publishing Ltd., New York, NY, 1961. P. W. Gilles, "Vaporization Processes" in "The Characterization of High-Temperature Vapors," J. L. Margrave, Ed., John Wiley and Sons, Inc., New York, NY, 1967, Chapter 2. E. D. Cater in "Techniques in Metals Research,” Vol. IV, R. A. Rapp, Ed., Wiley-Interscience, Inc., New York, NY, in press. fi‘i M. Knudsen, Ann. Phys., 28, 75 (1909); English Translation by i L. Venters, Argonne National Laboratory, Lemont, IL (1958). I M. Knudsen, ibid., 28, 999 (1909); English Translation by K. D. Carlson and E. D. Cater, Argonne National Laboratory, Lemont, IL j, (1958). K. C. Wang and P. G. Wahlbeck, J. Chem. Phys., 47, 4799 (1967). K. C. Wang and P. G. wahlbeck, ibid., 42, 1617 (1968). J. W. Ward, AEC Report LA-3509, Los Alamos, NM, Jan. 1966. J. W. Ward, J. Chem. Phys., 47, 4030 (1967). R. D. Freeman and J. G. Edwards, "Transmission Probabilities and Recoil Force Correction Factors for Conical Orifices" in "The Characterization of High-Temperature Vapors," J. L. Margrave, Ed., John. Wiley and Sons, Inc., New York, NY, 1967, Appendix C. K. D. Carlson, P. W. Gilles, and R. J. Thorn, J. Chem. Phys., 38, 2064 (1963). U! E. W. Balson, J. Phys. Chem., 6 , 115 (1961). S E. Storms, J. Hi. Temp. Sci., , 456 (1969). 8H W. Parrish, "Advances in X-ray Diffraction," Centurex Publishing Co., Eindhoven, 1962. C. M. Lederer, J. M. Hollander, and I. Perlman, "Table of Isotopes," 6th Ed., John Wiley and Sons, Inc., New York, NY, 1967. H. J. Kostkowski and R. D. Lee, "Theory and Methods of Optical Pyrometry," National Bureau of Standards Monograph 41, U. 8. Government Printing Office, Washington, DC, 1962. J. L. Margrave, "Physiochemical Measurements at High Temperature," J. Bockris, J. White, and J. Mackenzie, Eds., Academic Press, Inc., New York, NY, 1959, Chapter 2. 97) 98) 99) 100) 101) 102) 103) 104) 105) 106) 107) 108) 109) 110) 111) 112) 113) 94 P. A. Pilato, Ph. D. Thesis, Michigan State University, East Lansing, MI, 1968. G. N. Lewis and M. Randall, "Thermodynamics," Revised by K. S. Pitzer and L. Brewer, McCraw Hill Book Co., Inc., New York, NY, 1961, Chapter 27. G. N. Lewis and M. Randall, ibid., Chapter 15 and Appendix 7. D. R. Stull and H. Prophet, "The Calculation of Thermodynamic Properties of Materials over Wide Temperature Ranges," in "The Characterization of High-Temperature Vapors," J. L. Margrave, Ed., John Wiley and Sons, Inc., New York, NY, 1967, Chapter 13. D. R. Stull and H. Prophet in "JANAF Interim Thermochemical Tables," D. R. Stull, Project Director, Dow Chemical Co., Midland, MI, 1960, pp 3-16. E. A. Wood, "Crystal Orientation Manual," Columbia Univ. Press, New York, NY, 1963, p 60. N. F. M. Henry and K. Lonsdale, Eds., "International Tables for X-Ray Crystallography," Vol. I, International Union of Crystallography, Kynoch Press, Birmingham, 1952. N. F. M. Henry, H. Lipson, and W. A. Wooster, "Interpretation of X-Ray Diffraction Photographs," Macmillan Co., London, 1951. T. C. Furnas and D. Harker, Rev. Sci. Instrum., 2Q, 449 (1955). H. Goldstein, "Classical Mechanics," Addison-Wesley Press, Cambridge, MA, 1950, p 107. T. Johannson, Naturwissenschaften, 20, 758 (1932). U. W. Arndt and B. T. M. Willis, "Single Crystal Diffractometry," Cambridge Univ. Press, Cambridge, 1966, pp 265-267. T. C. Furnas, Trans. Am. Cryst. Assoc., l, 67 (1965). M. J. Buerger, "Crystal Structure Analysis," John Wiley and Sons, Inc., New York, NY, 1960, Chapter 3. M. J. Buerger, ibid., Chapter 7. U. W. Arndt and B. T. M. Willis, "Single Crystal Diffractometry," Cambridge Univ. Press, Cambridge, 1966, pp 286-288. C. H. MacGillavry, G. D. Reick, and K. Lonsdale, Eds., "International Tables for XrRay Crystallography," Vol. 111, International Union of Crystallography, Kynoch Press, Birmingham, 1962. 95 114) M. J. Buerger, "Vector Space," John Wiley and Sons, Inc., New York, NY, 1959. 115) H. Lipson and W. Cochran, "The Determination of Crystal Structures," G. Bell and Sons, Ltd., London, 1966. 116) D. H. Templeton and C. H. Dauben, J. Amer. Chem. Soc., 76, 5237 (1954). 117) W. R. Busing and H. A. Levy, 0RNL—3832, Oak Ridge, TN, Sep. 1965, p 110-150. 118) W. R. Busing and H. A. Levy, 0RNL-TM-229-4059, Oak Ridge, TN, 1964. 119) D. T. Cromer and J. T. Waber, Acta Crystallogr., 18, 104 (1965). 120) A. C. Parr and F. A. Elder, J. Chem. Phys., 42, 2665 (1968). 121) L. Brewer, G. R. Somayajulu, and E. Brackett, Chem. Rev., 63, 111 (1963). m“ 122) "JANAF Interim Thermbchemical Tables," D. R. Stull, Project Director, Dow Chemical Co., Midland, MI, 1960 and Supplements. 123) G. N. Lewis and M. Randall, "Thermodynamics," Revised by K. S. Pitzer and L. Brewer, McGraw Hill Book Co., Inc., New York, NY, 1961, p 420. 124) E. F. Westrum, Jr., "Advances in Chemistry Series, No. 71, Lanthanide/Actinide Chemistry," R. F. Gould, Ed., American Chemical Society, Washington, D. C., 1967, pp 25-50. 125) W. M. Latimer, "Oxidation Potentials," 2nd Edition, Prentice Hall, Englewood Cliffs, NJ, 1952, Appendix III. 126) C. E. Wicks and F. E. Block, "Thermodynamic Properties of 65 Elements - Their Oxides, Halides, Carbides and Nitrides," U. S. Department of the Interior, Bureau of Mines Bulletin 605, U. S. Government Printing Office, Washington, D. C., 1963. 127) R. Hultgren, R. L. Orr, P. D. Anderson, and K. K. Kelley, "Selected Values of Thermodynamic Properties of Metals and Alloys," John Wiley and Sons, Inc., New York, NY, 1963. 128) R. C. Feber, ABC Report LA23164, Los Alamos, NM, 1965. 129) R. E. Loehman, R. A. Kent, and J. L. Margrave, J. Chem. Eng; Data, 12, 296 (1965). 130) J. Etienne, Bull. Soc. Fr. Mineral. Cristallogr., 22, 134 (1969). 131) C. Dagron, J. Etienne, J. Flahaut, M. Julien-Pouzol, P. Laruelle, N. Rysanek, N. Savigny, G. Sfez, and F. Thevet in "8th Rare Earth Research Conference," T. A. Henrie and R. E. Lindstrom, Eds., Reno, NV, Apr. 1970, pp 127-139. 96 132) L. Pauling, "The Nature of the Chemical Bond," 3rd Edition, Cornell Univ. Press, Ithaca, NY, 1960. 133) A. F. Wells, "Structural Inorganic Chemistry," 3rd Edition, Oxford Univ. Press, Oxford, 1962. 134) J. L. Haord and J. D. Grenko, Z. Kristallogr., 87, 110 (1934). 135) W. Feitknecht, Fortschr. Chem. Forsch., 2, 670 (1953). 136) C. W. Koch, A. Broido, and B. B. Cunningham, J. Amer. Chem. Soc., 74, 2349 (1952). 137) C. W. Koch and B. B. Cunningham, ibid., 72, 796 (1953). 138) C. W. Koch and B. B. Cunningham, ibid., 76, 1471 (1954). 139) J. T. Mason and P. Chiotti, Trans. Met. Soc. AIME, 24%, 1176 (1968). 140) J. D. Corbett, D. L. Pollard, and J. E. Mee, Inong. Chem., 5, 761 (1966). 141) R. G. Bedford and E. Catalano in "8th Rare Earth Research Conference," T. A. Henrie and R. E. Lindstrom, Eds., Reno, NV, Apr. 1970, pp 213-223. 142) B. Prager and P. Jacobsen, Eds., "Beilstein Handbuch der Organischen Chemie," Vol. I, Springer Verlag, Berlin, 1918, p 90. 143) J. J. Stezowski, Ph. D. Thesis, Michigan State University, East Lansing, MI, 1968. 144) J. D. H. Donnay, Ed., "Crystal Data Determinative Tables," 2nd Edition, American Crystallographic Assn., Washington, D. C., 1963, p 841. 145) O. Lindqvist and F. wengelein, Ark. Kemi, 28, 179 (1967). 146) S. Samson and W. W. Schuelke, Rev. Sci. Instrum., 38, 1273 (1967). 147) W. L. Bond, Acta Crystallo r., 1%, 814 (1960). 148) H. J. Neff, Arch. Eisenhuettenw., 34, 903 (1963); Siemens Pamphlet Eg 4/10e, Siemens and Halgke Aktiengesellschaft, Karlsruhe, 1964. 149) R. A. Kent, Ph. D. Thesis, Michigan State University, East Lansing, MI, 1963. 97 .voumawumm mum ammonuamumm a“ womoaoam wonam> Aces Aamv Ammav No.0uu mom.sum Namovco Hmaowmxms Aoooflv «an xumfln Npr 1548 .. Amado -.o~uu um¢.aum MHHm Hmaowmxmn momoaaooov moans «Hp» Acme Aqu Asmav mm.eno “mo.aua “no.8um ~umao .auonuuo AooHNV mac coup» Nuns» Aces .. Amado HH.aHuu “ma.oum magma .noaeogu mumoaaoowu «saga mama» Hm ~.Ho m.HmH «a.ouo "mH.MHun “ao.ouu Hmoo .suonuuo a~e-v Nos sauna «Hon» q.oaaum “mm.ouo Ammo -- a.a- ”no.HHup “ma.eum ma0a< .aaHuoaoa Agave new manna. macaw Acme Ammo AomNV an.nua Name conga Acneuv heed .. Nap» «n.4uo "a“.o-n "-.ena mac; n Acme Acme thmV \Nm.wuu mam.sum \mm» nuuo\an Aconwv “mad manna any so HImHoa Amos .m ”man “man Amy Momma muoumamuom woauuoa unha muuoaahm Acovnn Acovna uoaou vquogaoo .mmvaamz Emanuouuw may mo mwuuummoum ”H NH92mmm< APPENDICES APPENDIX II: Orientation and Angle Setting Program This program was written under the title B-lOl by J. Gvildys of the Applied Mathematics Division of Argonne National Laboratory. The program is intended for use with goniostats for obtaining accurate three dimensional diffraction data without the necessity of precise alignment of the crystal. The input consists of a limited number of fa} indexed reflections, their measured cradle settings of 26, x, and ¢, and the wavelength of the radiation employed. Crystal lattice and goniostat constants are computed by the method of least squares from Egg the input data. From the determined constants of the experiment, the I program generates for each (hkz) reflection the instrument angles 28, x, and o. First, least squares constants,’(A,B,C,D,E,F), are determined by minimization of the function: 2 2W1{(h1A + kiB + 21c + ZhikiD + 2h121E + 2kiniF) - 3—§%fl—91}2 1 where W1 is the weight assigned to the i-th reflection. Using the constants determined above, the cell volume is computed by: v - l/(ABC - AFZ - BE2 - CD2 + 2FED)1/2 and the unit cell constants calculated from: a a V(BC - F2)1/2 b - V(AC - E2)1/2 C = V(AB _ D2)1/2 a - cos‘1{(ED - AF)/[(AC - E2)(AB - D2)]1/2} s - cos‘l{(DF - BE)/[(AB - D2)(BC - F2)]1/2} y = cos‘1{(FE — CD)/[(BC - F2)(AC - E2)]1/2}. 98 99 Second, the components of a unit vector A(uvw) which lies along the ctr-axis of the goniostat when x - O are determined by minimization of the function: 2 sin X E C08 xi(hiu + kiV + 11W " Tl) then: xicalc 8 sin"1 [d1(hiu + kiv + Biw)]. Third, the components of a unit vector §(xyz) which is perpendicular to A and lies in the x-plane of the instrument when 4: = O are determined by minimization of the function: E {cos xicalc di[(h1A + k1” + 21E)x + (hiD + kin + 21F)y + (hiE + kiF + 21C)z] - cos xicalc cos ¢}2 then: ¢1ca1c a tan"1 [whip + Riv + £1W] hix + kiY + £12 , where u - y[u(DF - BE) + v(ED - AF) + w(AB - D2)] - z[u(FE - CD) + v(AC - E2) + w(ED - AF)] v - z[u(BC - F2) + v(FE - CD) + w(DF - 33)] - x[u(DF - BE) + v(ED - AF) + w(AB - D2)] w . x[u(FE - CD) + v(AC - E2) + w(ED - AF)] - y[u(BC - F2) + v(FE - CD) + w(DF - BE)] X - xA‘+ yD + zE Y - xD + yB + 2F 2 - xE + yF + 2C. The angles (26, x, ¢) are then calculated for each (hki) reflection permitted under the various extinction, octant, and angle options selected by the user. 100 APPENDIX III: X-Ray Powder Diffraction Data. APPENDIX IIIA: Ytterbium Trichloride Hexahydrate Observed Calculated hkl Relative d-value Relative d—value Intensity (A) Intensity (A) 010 30* 6.484 20 6.524 101 80 6.252 51 6.288 101 90 5.871 59 5.854 110 20 5.369 24 5.393 011 20 4.988 26 5.010 200 60 4.776 46 4.792 111 20 4.494 23 4.527 111 20 4.342 28 4.357 002 100 3.904 100 3.910 210 10 3.846 7 3.862 211 10 3.521 7 3.546 211 10 3.376 7 3.384 012 20 3.353 14 3.354 202 20 3.128 16 3.144 021 10 3.014 1 3.011 202 20 2.932 20 2.927 310 30 2.859 27 2.869 212 10 2.832 3 2.832 311 20 2.644 14 2.638 103 30 2.564 15 2.563 221. 50 2.509 39 2.517 *Visually estimated. 1!; , 101 APPENDIX IIIB: Intermediate Ytterbium Chloride (Yb012.26) Relative d-value Relative d-value Intensity (A) Intensity (A) 7 9.24 4 4.24 1 6.46 1 3.96 4 5.97 10 3.88 3 5.76 1 3.48 l 5.32 2 3.41 3 4.77 4 3.38 2 4.39 2 3.36 APPENDIX IIIC: Ytterbium Dichloride hkl Relative d-value hkl Relative d-value Intensity (A) Intensity (A) 020 2 6.575 122 2 2.786 021 4 4.768 221 3 2.739 111 2 4.520 141 1 2.715 121 10 3.884 230 2 2.660 002 5 3.462 202 7 2.406 200 4 3.347 042 8 2.384 040 4 3.288 240 8 2.345 210/131 1 3.243 142 6 2.246 102 1 3.075 023 4 2.178 022 1 3.064 311 2 2.096 112 2 2.995 123 5 2.071 041 1 2.970 321 7 2.021 102 APPENDIX IIID: Ytterbium Oxidechloride hk2* Relative d—value hk£* Relative d-value Intensity (A) Intensity (A) 003 9 9.438 110 10 1.863 006 5 4.668 114 7 1.827 101 7 3.215 116 5 1.729 102 8 3.153 201 5 1.611 009 6 3.100 202 4 1.604 104 7 2.939 119 6 1.596 105 7 2.798 204 5 1.571 107 4 2.510 205 4 1.550 108 3 2.369 207 3 1.495 00°12 4 2.321 208 2 1.467 10°10 2 2.105 11°12 6 1.453 10‘11 2 1.990 20°10 2 1.392 *Indexing based on a-3.726, c-27.80 A APPENDIX IIIE: Triytterbium Tetraoxidechloride Preparation Relative d-value Relative d-value Intensity (A) Intensity (A) 10 9.339* 6 2.996 3 4.804 7 2.594 2 4.244 1 2.031 3 3.660 8 1.850 4 3.186* 5 1.883* 5 3.086* 5 1.814 *Possible coincidence with YbOCl 103 APPENDIX IV: Equilibrium Pressure and Third-Law Enthalpy Data 4 _ . “lg- (OK-1) (25m; (kcggvmg 2‘1) 7.49 4.38 ' 58.25 8.53 5.70 60.74 7.96 4.97 58.47 7.73 4.66 59.84 7.36 4.21 60.06 7.76 4.73 59.20 7.98 4.94 58.35 8.18 5.20 60.74 8.18 5.26 59.06 8.26 5.32 59.40 8.33 5.38 60.72 8.77 5.54 59.83 8.57 5.72 60.61 9.55 7.00 59.69 9.41 6.78 60.38 9.18 6.50 60.47 9.18 6.50 60.42 8.98 6.24 61.19 8.52 5.64 60.12 8.32 5.38 58.70 8.76 5.93 60.60 9.02 6.35 60.95 9.10 6.36 60.95 wk:- APPENDIX IV: 8.58 8.28 8.26 8.02 8.64 7.87 7.80 7.70 7.60 7.47 7.91 6.74 7.12 7.22 7.28 7.32 7.56 7.84 7.83 7.33 7.60 7.65 8.06 8.40 8.60 8.47 (cont.) 104 5.76 5.37 5.31 5.01 5.82 4.72 4.72 4.60 4.54 4.37 4.88 3.70 3.97 3.99 4.09 4.14 4.36 4.70 4.61 4.20 4.46 4.58 5.02 5.51 5.79 5.63 60.64 58.63 60.63 61.02 59.77 59.60 59.60 59.79 60.36 60.14 59.11 60.89 59.23 59.96 60.31 58.88 59.56 60.04 60.16 59.52 59.87 59.52 59.15 59.83 58.95 59.74 105 APPENDIX V: Thermodynamic Values for Data Reduction. Phase ’532’298 S298 -(Gi-H§98)/T (6“) (kcal mole'l) (eu) 500 1000 1500 2000 (°K) Yb203(s) 433.68121° 31.812“ Yb(s) 0.0 13.112“ 17.8 21.3 r11 Yb(g) -36.35127 47.4127 YbC12(s) . 3030 40 48 57 YbClz(g) 72 78 82 86 1? 112(3) 0.0 35 I; 820(3) 60 41 47 51 53 Cl(g) 29 40 42 44 45