ABSTRACT A PHASE STUDY AND THERMODYNAMIC INVESTIGATION OF THE EUROPIUM-OXYGEN-BROMINE SYSTEM BY John Maurice Haschke Eight binary and ternary europium phases have been ob- served in the europium-oxygen-bromine system. The phases: trieuropium tetraoxide (Eu304), europium monoxide (EuO), europium dibromide (EuBrz), europium tribromide (EuBra), trieuropium tetraoxide monobromide (Eu3O4Br), europium mon— oxide monobromide (EuOBr), and trieuropium monoxide tetra- bromide (Eu30Br4), have been prepared from the sesquioxide and were analyzed by chemical and X-ray crystallographic procedures. Guinier X—ray powder diffraction data, which were collected for all phases, have been indexed. Single crystal diffraction data were collected for the dibromide and tetraoxide monobromide. Lattice parameters were also determined for europium dibromide monohydrate (EuBrz'HZO) and europium tribromide hexahydrate (EuBr3-6H20). The following vaporization reactions were characterized by a combination of X-ray diffraction, weight loss, effusate collection, and high temperature mass spectrometric tech- niques: John Maurice Haschke 3 Eu304(s) -—> 4Eu203(s, monoclinic) + Eu(g). (1) 4Eu0(s) > Eu304(s) + Eu(g). (2) 3Eu3O4Br(s) > 4Eu203(s, monoclinic) + EuBr2(g) + Br(g). (3) EuBr2(£) > EuBr2(g). (4) 4EuOBr(s) > Eu3O4Br(s) + EuBr2(g) + Br(g). (5) Equilibrium vapor pressure measurements for reactions (1—4) have been made by target collection Knudsen effusion tech- niques. .Microgram quantities of the condensed effusates were analyzed by an X-ray fluorescence procedure, which involved the establishment of linear external calibration curves. The following second law enthalpies and entropies of vaporization were obtained for the median measurement tem- peratures: Eu304(s), AHgslo = 86.2 i 1.4 kcal/gfw, Asgslo = 28.20 i 0.82 eu; Eu0(s), A32546 = 75.91 i 0.94 kcal/gfw, A32546 = 28.66 i 0.61 eu; Eu3O4Br(s), A3239. = 129.0 i 1°1 kcal/gfw, Asgsgg = 50.81 i 0.81 eu; and EuBr2(£). AH2377 = 58.27 i 0.76 kcal/gfw, A5237, = 23.03 i 0.56 eu. At its boiling point (2530 i 350K), EuBr2(£) has a second law enthalpy and entropy of AH: = 52.0 i 3.0 kcal/gfw and A5: = 20.6 i 1.9 eu. A general scheme for approximation of heat capacities of the solid phases has been derived, and the ensuing estimated values have been combined with approxi— mated entropies in the calculation of free energy functions. 2 John Maurice Haschke At 2980K, the following second and third law enthalpies and second law entropies of vaporization were obtained: Eu304(s), AH398 (2nd) = 93.5 i 2.5 kcal/gfw, Anggs (3rd) - 92.28 i 0.56 kcal/gfw, A3398 = 39.4 i 1.7 eu; EuO(s), A3398 (2nd) = 80.3 i 2.0 kcal/gfw, AH398 (3rd) = 80.00 i 0.42 kcal/gfw, A3398 = 33.9 i 1.3 eu; EuBr2(s ), AH298 (2nd) = 71.4 i 2.7 kcal/gfw, Anggs (3rd) = 69.54 i 0.40 kcal/gfw, A5398 = 36.8 i 2.8 eu; and Eu304Br(s), AHggs (2nd) = 137.6 i 2.0 kcal/gfw, AHggs (3rd) = 139.47 i 0.92 kcal/gfw, A5398 = 64.7 i 2.9 en. The enthalpies and free energies of formation and the standard entropies calculated from second law results are: Eu304(s), AH; 293 = -542.4 i 3.6 kcal/gfw, AGf 298 = -510.4 i 3.6 kcal/gfw, 5298 = 48.6 i 2.6 eu; EuO(s), AH; 293 = 4145.2 i 4.1 kcal/gfw, AGf 293 = -136.6 i 4.1 kcal/gfw, 5393 = 15.0 i 3.0 eu; EuBr2(s), AHO f 293 - -178.o i 3.0 kcal/gfw, AGO = f 298 -173.2 i 3.0 kcal/gfw, 3398 = 39.5 i 3.0 eu; and Eu3O4Br(s), AH° = -597.7 i 5.1 kcal/gfw, AGO f 298 f 298 = ’565'0 i 5'1 kcal/gfw, 8398 = 64.5 i 3.1 eu. Thermodynamic data have been estimated for the vaporization of EuOBr(s) according to reaction (5) and the following thermochemical values ob- tained for the phase: AH; 298 = -203.3 i 6.5 kcal/gfw, AG; 298 = —193.4 i 6.5 kcal/gfw. The thermochemical data obtained for europium oxides and oxide bromides have been employed in calculations which indicate that the lower ox- ides of ytterbium and of other lanthanides (LnO and Ln304) are unstable at temperatures greater than 2980K. 3 A PHASE STUDY AND THERMODYNAMIC INVESTIGATION OF THE EUROPIUM-OXYGEN-BROMINE SYSTEM BY John Maurice Haschke A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1969 7. ./'/- (‘3’ ACKNOWLEDGMENTS The author wishes to express his sincere appreciation to Dr. Harry A. Eick for the encouragement, the suggestions, and the assistance which he has generously given during this investigation. A deep expression of gratitude is also extended to the author's wife, Bernadette, and to his parents for their assistance and encouragement in the attainment of this edu- cational goal. The aid of past and present members of the High Tempera- ture Group is appreciated, and the assistance of Dr. Philip Pilato and Mr. Donald Werner in mass spectrometric analysis is gratefully acknowledged. A special expression of appreciation is extended to Dr. W. W. Wendlandt for the insight and guidance which he has offered. The financial support of the Atomic Energy Commission under Contract AT (11-1)-716 and the National Science Founda- tion is gratefully acknowledged. ii TABLE OF CONTENTS I. INTRODUCTION . . . . . . . . . . . . . . . . . . 1 II. PREVIOUS INVESTIGATIONS OF THE EUROPIUM- OXYGEN-BROMINE SYSTEM . . . . . . . . . . . . . 4 .A. The Oxides of Europium . . . . . . . . . . . . 4 1. Preparative and Structural Investigations 4 2. Thermodynamic Investigations . . . . . . 5 B. The Bromide and Hydrated Bromides of Europium. 6 1. Preparative and Structural Investigations 6 a. vEuropium Bromides . . . . . . . . . . 6 b. Hydrated Europium Bromides . . . . . . 7 2. Thermodynamic Investigations of Europium Bromides . . . . . . . . . . . . . . . . 7 C. The Oxides of Bromine . . . . . . . . . . . . 8 D. The Oxide Bromides of Europium . . . . . . . . 8 1. Preparative and Structural Investigations 8 2. ~Thermodynamic Investigations . . . . . . 9 III. THEORETICAL CONSIDERATIONS PERTINENT TO THIS INVESTIGATION . . . . . . . . . . . . . . . . . 10 A. Phase Relationships . . . . . . . . . . . . . 10 1. Possible Phases in the Europium-Oxygen Bromine System . . . . . . . . . . . . 10 2. Vaporization and the Phase Rule . . . . . 11 a. Vaporization Modes . . . . . . . . . . 11 b. The Phase Rule . . . . . . . . . . . . 11 c. The Pressure-Composition Diagram . . . 12 B. Vapor Pressure Measurement by the Knudsen Effusion Technique . . . . . . . . . . . . . . 12 1. General Introduction . . . . . . . . . . 12 2. Theoretical Considerations of the Target Collection Method . . . . . . . . . . . . 13 3. Limitations of the Knudsen Method . . . . 15 iii TABLE OF CONTENTS (Cont.) C. D. E. a. Non-Ideal Cell . . . . . . . . . . . 1 Non-Ideal Orifice . . . . . . . 2 Non-Ideal Collection Geometry . 3 Thermal Expansion of the Orifice b. The Non—Ideal Gas . . . . . . . . . c. Non-Equilibrium Conditions . . . g1 Sampling and the "Orifice Effect“ 2 The Vaporization Coefficient . . 3 Diffusion . . . . . . . . . . . d. Additional Limitations to Target Collection Effusion Measurements . . X-Ray Fluorescence . . . . . . . . . . . . . 1. The Basic Phenomenon . . . . . . . . . 2. The Bragg Equation . . . . . . . . . . Temperature Correction . . . . . . . . . . . Thermodynamic Calculations . . . . . . . . . Second Law Calculations . . . . . . . . 1. a. b. C. d. Derivation of Relationships . . . . Assumptions of the Second Law Treatment . . . . . . . . . . . . . Data Reduction to the Reference Temperature . . . . . . . . . . . . Calculation of the Second Law Entropy Third Law Calculations . . . . . . . . a. b. Derivation of Relationships . . . . The Value of Third Law Calculations. Energetics of Formation . . . . . . . . Approximation of Thermodynamic Functions a. b. c. E Approximation of High Temperature Heat Capacities . . . . . . . . . . . . . 1; Solids . . . . . . . . . . . . . 2 Simple Polyatomic Gases . . . . rApproximation of Standard Entropies Estimation of Enthalpy and Entropy Functions . . . . . . . . . . . . . Statistical Methods . . . . . . . . . . a. b. Least Squares and Standard Error . . Combination of Errors . . . . . . . iv Page 15 15 16 17 17 17 18 18 19 20 20 21 21 23 23 23 24 25 26 27 27 28 29 30 3O 3O 31 32 34 34 34 TABLE OF CONTENTS (Cont.) IV. A. B. D. E. F. G. H. J. K. L. EXPERIMENTAL EQUIPMENT AND MATERIALS Target Collection Apparatus . . . X-Ray Fluorescence Equipment . . . 1. Spectrometer . . . . . . . . 2. Specimen Mount . . . . . . . 3. Effusate Geometry . . . . . . X-Ray Diffraction Equipment . . . 1. Powder Diffraction Equipment 2. Single Crystal Diffraction Equipment Temperature Measuring Equipment . High Temperature Mass Spectrometer Micrograph . . . . . . . . . . . . Miscellaneous Measuring Equipment Heating Equipment . . . . . . . . Vacuum Systems . . . . . . . . . . Inert Atmosphere Glove Box . . . . Effusion Cell Design . . . . . . . 1. Target Collection Cells . . . 2. Mass Spectrometer Cells . . . Chemicals and Materials . . . . . V. TEXPERIMENTAL PROCEDURES . . . . . . A. Preparative Techniques . . . . . . 1. Trieuropium Tetraoxide . . . 2. Europium Monoxide . . . . . . 3. Europium Dibromide . . . . . 4. Europium Monoxide Monobromide 5. Trieuropium Tetraoxide Monobromide. 6. Europium Tribromide . . . . . 7. Hydrated Bromide Phases . . . a. Europium Tribromide Hexahydrate b. Europium Dibromide Monohydrate V 0 O O Page 36 36 36 36 37 37 37 37 38 38 38 38' 39 39 4O 4O 4O 40 41 41 43 43 43 44 44 45 46 46 47 47 47 TABLE OF CONTENTS (Cont.) B. Additional Preparative and Phase Studies . . 1. Attempts to Prepare Europium Tribromide 2. Attempts to Prepare Additional Oxide Bromide Phases . . . . . . . . . . . . a. Direct Combination of Europium Tri- bromide and Sesquioxide . . . . . . b. Oxidation of Europium Dibromide . . c. Direct Combination of Europium Mon- oxide and Dibromide . . . . . . . . C. Analytical Techniques . . . . . . . . . . . 1. Europium Analysis . . . . . . . . . . . 2. Bromine Analysis . . . . . . . . . . . 3. Oxygen Analysis . . . . . . . . . . . . D. Density Measurement . . . . . . . . . . . . E. X-Ray Diffraction Procedures . . . . . . . . 1. Powder Diffraction Techniques . . . . . 2. Single Crystal Techniques . . . . . . . F. Characterization of Vaporization Reactions . 1. Weight Loss Measurements . . . . . . . . .Mass Spectrometric Investigations . . . . Effusate Collection Experiments . . . . . X—Ray Investigations . . . . . . . . . AUDIO G. X-Ray Fluorescence Procedures . . . . . . . 1° Optimization of Spectrometer Parameters 2. .Counting Procedures . . . . . . . . . . 3. Preparation of Standard Solutions . . . 4. Preparation of Calibration Curves . . . H. Target Collection Technique . . . . . . . . 1. General Collection Procedures . . . . . 2. .Measurement of Orifice Areas . . . . . 3. .Specific Experimental Procedures and Conditions . . . . . . . . . . . . . . I. Sticking Coefficient Experiments . . . . . . vi Page 48 48 49 49 49 49 50 5O 50 5O 5O 51 51 51 52 52 53 54 54 54 55 56 56 57 57 59 59 6O TABLE OF CONTENTS (Cont.) VI. A. B. C. D. E. F. G. Page RESULTS . . . . . . . . . . . . . . . . . . . 62 .Results of Preparative Techniques . , , , 62 1. The Europium-Oxygen-Bromine System . . 62 2. Results of Additional Preparative and Phase Investigations. . . . . . . . . . 62 3. The Hydrated Bromide Phases . . . . . 65 4. Observed Physical and Chemical Properties of the Binary and Ternary Phases . . . 65 Analytical Results . . .'. . . . . . . . . 66 1. Results of Chemical Analysis . . . . . 66 2. X-Ray Powder Diffraction Results . . . 66 3. Single Crystal and Density Results . . 69 Results of X-Ray Fluorescence Calibration . 70 Vaporization Results . . . . . . . . . . . . 71 1. The Vaporization Mode of Trieuropium Tetraoxide . . . . . . . . . . . . . . 71 2. The Vaporization Mode of Europium Monoxide 71 3. The Vaporization Mode of Europium Dibromide . . . . . . . . . . . . . . . 72 4. The Vaporization Mode of Trieuropium Tetraoxide Monobromide . . . . . . . . 72 5. The Vaporization Mode of Europium Monoxide Monobromide . . . . . . . . . 76 6. Pressure-Composition Diagrams . . . . . 76 The Results of Sticking Coefficient Measurements79 Vapor Pressure Equations . . . . . . . . . . 80 Thermodynamic Values Employed in Data Reduction . . . . . . . . . . . . . . . . . 85 1. Heat Capacity, Enthalpy and Entropy Functions . . . . . . . . . . . . . . . 85 a. Literature Values . . . . . . . . . 85 b. Approximated Values for Solid Phases 85 c. Approximated Values for Gaseous Phases . . . . . . . . . . . . . . . 86 2. Absolute Entropies . . . . . . . . . 87 a. Approximated Values for Solids . . . 87 b. Entropy Values for Gaseous Species . 87 3. Free Energy Functions . . . . . . . . . 88 4. vAdditional Thermochemical Values . . . 89 vii TABLE OF CONTENTS (Cont.) VII. H. A. C. Thermodynamic Results . . . . . . . . . . . 1. Treatment of Trieuropium Tetraoxide Data 2. Treatment of Europium Monoxide Data . . 3. Treatment of Europium Dibromide Data . 4. Treatment of Trieuropium Tetraoxide .Monobromide Data . . . . . . . . . . . 5. .Estimation of Thermodynamic Data for Europium Monoxide Monobromide . . . . . 6. Oaxfilation of Thermodynamic Results . . DISCUSSION . . . . . . . . . . . . . . . . . The Phase Diagram . . . . . . . . . . . . . 1. Phases in the Europium-Oxygen-Bromine System . . . . . . . . . . . . . . . . 2. Discrepancies Between the Present Results and the Literature . . . . . . . . . . a. On the Crystal Structure of Europium Dibromide . . . . . . . . . . . . . b. On the Preparation of Europium Tri— bromide and Triiodide . . . . . . . c. On the Composition of the Hexagonal Oxide Bromide . . . . . . . . . . . 3. The Stabilities of Phases . . . . . . . a° Elucidation of the Vaporization Process . . . . . . . . . . . . . . b. Disproportionation of the Oxide Bromides . . . . . . . . . . . . . . :The X-Ray Fluorescence Technique . . . . . . The Target Collection Knudsen Effusion Technique . . . . . . . . . . . . . . . . . 1. The Attainment of Knudsen Conditions. . 2. Temperature Gradients . . . . . . . . . 3. Crucible Materials . . . . . . . . . . Evaluation of Thermodynamic Approximations . 1. Heat Capacity Approximations . . . . . 2. Entropy Approximations . . . . . . . . Evaluation of Vaporization and Thermo- dynamic Results . . . . . . . . . . . . . . 1. Trieuropium Tetraoxide Data . . . . . . 2. Europium Monoxide Data . . . . . . . . 3. -Europium Dibromide Data . . . . . . . 4. Trieuropium Tetraoxide Monobromide and Europium Monoxide Monobromide Data . . viii Page 89 89 90 91 93 95 97 100 100 100 101 101 102 104 105 105 107 109 112 112 113 114 115 115 117 118 118 120 123 123 TABLE OF CONTENTS (Cont.) Page F. On the Existence of Lower Oxides of Ytterbium 124 VIII. SUGGESTIONS FOR FUTURE INVESTIGATIONS . . . . 131 REFERENCES . . . . . . . . . . . . . . . . . . . 132 APPENDICES . . . . . . . . . . . . . . . . . . . 139 ix LIST OF APPENDICES APPENDIX Page I. Observed Sin29(l = 1.54051 8) and Inter- planar d-Values . . . . . . . . . . . . . . . 139 A. Tetragonal Europium Dibromide . . . . . . . 139 B. Orthorhombic Europium Dibromide Monohydrate. 139 C. Orthorhombic Europium Tribromide . . . . . . 140 D. Monoclinic Europium Tribromide Hexahydrate . 140 II. .X-Ray Fluorescence . . . . . . . . . . . . . . 141 A. Linear Calibration Curves for X-Ray Fluorescence . . . . . . . . . . . . . . . 141 B. The Vapor Pressure of Gold . . . . . . . . . 141 C. Equilibrium Pressures and Third Law Enthal- pies for Gold . . . . . . . . . . . . . . . 143 III. Equilbrium Pressures and Third Law Enthalpies. 144 A. Trieuropium Tetraoxide Vaporization . . . . 144 B. Europium Monoxide Vaporization . . . . . . . 144 C. Europium Dibromide Vaporization .. . . . . . 145 D. Trieuropium Tetraoxide Monobromide Vaporization145 IV. Thermodynamic Values for Data Reduction . . . 146 A. Approximated Heat Capacity, Enthalpy, and Entropy Values . . . . . . . . . . . . . . . 146 B. Enthalpy, Entropy, and Free Energy Functions 146 C. Free Energy Function Changes for the 'Vaporization Reactions . . . . . . . . . . . 148 D. Thermodynamic Functions from the Literature 148 V. Data for Thermodynamic Calculations . . . . . 149 TABLE II. III. IV. V. VI. VII. VIII. Ix. LIST OF TABLES Page .Analytical results . . . . . . . . . . . . . . 67 Powder diffraction results . . . . . . . . . . 68 Second law results at median measurement temperature . . . . . . . . . . . . . . . . . 98 Thermodynamic results at 2980K . . . . . . . . 99 Thermodynamic results for liquid europium dibromide at the boiling point . . . . . . . . 99 Comparison of estimated and experimental 3298 118 Correlation of the divalent radii and enthalpies Of formation of metal monoxides . . . . . . . 122 Free energy changes calculated for the reduc- tion of europium and ytterbium oxide bromides with lithium hydride . . . . . . . . . . . . 129 Free energy changes for the reaction of europium and ytterbium with their sesquioxides at various temperatures . . . . . . . . . . . . 129 xi FIGURE 1. 10. LIST OF FIGURES Page A schematic of the X-ray fluorescence spectrometer . . . . . . . . . . . . . . . . . 22 Asymmetric Knudsen cell design . . . . . . . . 42 Symmetric Knudsen cell design . . . . . . . . 42 The europium—oxygen-bromine phase diagram . . 63‘ The europium-oxygen pressure-composition phase diagram . . . . . . . . . . . . . . . . 77 The europium-bromine pressure-composition phase diagram . . . . . . . . . . . . . . . . 78 The europium sesquioxide-europium tribromide pseudobinary pressure-composition phase diagram 78 The pressure Of Eufgg in equilibrium with EU3O4(S) and 31.1203 5 o . . . . . o o . . . . 81 The pressure of Eu(g) in equilibrium with EuO(s) and Eu3O4(s) . . . . . . . . . . . . . 82 The pressure of EuBr2(g) in equilibrium with EuBr2(£) . . . . . . . . . . . . . . . . . . . 83 The pressure of EuBr2(g) in equilibrium with Eu3O4Br(s), Eu203(s), and Br(g) . . . . . . . 84 xii CHAPTER I INTRODUCTION In a day when the inorganic chemist is concerned with a variety of complex molecular species, it is often sur~ prising to discover that the present knowledge of the simple binary compounds of the alkaline earths and lanthanides with the nonmetal elements of groups IVA - VIIA is incomplete and often inaccurate. Many of the investigations of these binary systems were conducted prior to 1940, and as a re- sult of either impure materials or less accurate methods of data collection and treatment than are presently avail— able, the results are often in error. Therefore, the present investigation was initiated to characterize the phase diagrams, the crystal structures, and the thermodynamic properties of some binary and ternary phases. Since metal carbides, pnictides, chalcogenides, and halides tend to be refractory, high temperature techniques are generally employed in preparative procedures and may be used to provide information about the vaporization reactions. vapor pressures, and, hence, the thermodynamic data of the phases. In high temperature studies, additional knowledge may be obtained about the stabilities of gaseous species, 1 2 the properties of high temperature container materials in the presence of reactive compound, and the phase diagrams of the investigated systems. Because of the magnetic nature of europium phases, many more physical than chemical properties of its compounds have been measured. Chemically, europium is probably the most unusual of the lanthanides because it appears to ex- hibit not only the true divalent character Of alkaline earths, but also the trivalent character of other lanthan- ides. The former behavior allows for comparison of chemical properties with those of the alkaline earths, ytterbium, samarium, and possibly thulium, while the latter often en— ables prediction of properties for analogous materials of neighboring lanthanides and permits establishment of trends within the lanthanide series. The potential for variation of both the ratio of di— and trivalent europium and the ratio of the two anions makes the europium—oxygen-bromine system particularly intriguing. The general plan for this investigation was to charac- terize as fully as possible the europium-oxygen-bromine phase diagram and the properties of its phases by X-ray diffraction and high temperature Knudsen effusion techniques. If possible, the ensuing thermodynamic results were to be employed in an attempt to resolve certain problems in lanth- anide chemistry. A secondary goal was the development of X-ray fluorescence spectroscopy for quantitative analyses in 3 target collection effusion measurements and the evaluation of this technique by collection of vapor pressure data for a previously measured system. CHAPTER II PREVIOUS INVESTIGATIONS OF THE EUROPIUM-OXYGEN-BROMINE SYSTEM A. The Oxides of Europium 1. Preparative and Structural Investigations The phase diagram of the europium-oxygen system is probably the most studied and best characterized portion of the entire europium-oxygen—bromine ternary. The sesqui- oxide, Eu203, exists in both the monoclinic B- and cubic C-forms. 1H0wever, the lattice constants reported by Gschneidner1 in his review of the structural chemistry of these phases differ from those more recently reported 2:1 The first reported lower oxide of europium, the monoxide. described by Eick et al.4, was prepared by reduction of the sesquioxide with elemental lanthanum and reported to possess a NaCl-type structure. The monoxide subsequently has been prepared by reduction of the sesquioxide with either graphite5 or europium metal,6:7 and by reduction of europium monoxide 'monochloride, EuOCl, with lithium hydride 3. A second lower oxide, trieuropium tetraoxide, was first prepared by reduc- tion of the sesquioxide with graphite8 and subsequently by reduction Of Eu203 with EuO 9. An orthorhombic calcium 4 5 ferrite-type structure was first reported for this phase9 and this assignment has since been Confirmed by both powder2 and single-crystal10 measurements. More recently, Baernighausen has reported the preparation of the tetra— oxide by reduction of a mixture of either EuOCl and Eu203,3 or of trieuropium tetraoxide monobromide, Eu304Br, with lithium hydride 1% 2. Thermodynamic Investigations Only fragmentary thermodynamic data have been determined on the otherwise well-characterized europium-oxygen binary phases. The enthalpies of formation of both B- and C-forms of the sesquioxide have been measured by bomb calorimetry,12 while that of the C-form has also been determined by solu- tion calorimetry 1% The high temperature heat capacities of both its B— and C-forms, and the enthalpy and temperature of transition have been reported 14. Only one vaporization study has been performed——that by Panish15 who measured mass-spectrometrically the pressures of the species in equi- librium with the congruently vaporizing sesquioxide at 2000°K. Less is known about europium monoxide. Its enthalpy of formation has been measured by solution calorimetry,7 and its low temperature heat capacity investigated over a limited temperature range 16. NO thermochemical measurements of trieuropium tetraoxide are available. However, Westrum17 has estimated some of the thermodynamic values for the monoxide and sesquioxide phases. 6 B. The Bromides and Hydrated Bromides of Europium 1. Preparative and Structural Investigations a. Europium Bromides The preparative procedures for and the properties of anhydrous lanthanide bromides are given in several reports. Taylor and Carter18 have described a preparative procedure for europium tribromide--the careful heating of a‘hydrated tribromide-ammonium bromide matrix in vacuum. They report the results of chemical analysis, the color of the phase, and the color of its aqueous solution. Europium tribromide has also been reported as an intermediate product in the thermogravimetric studies of the hydrated tribromide 19. Controlled vacuum dehydration of the hexahydrates has yielded impure tribromides of the heavy lanthanides (Gd-Lu),20 but no corresponding data are reported for the europium phase. However, application of radius ratio rules to the ions indicates that EuBr3 should crystallize in the ortho- rhombic PuBr3-type structure,20 while GdBr3 should form the Observed hexagonal FeCla-type structure. Europium dibromide is also poorly characterized. In 1939, Klemm andDoell21 reported preparation of a chocolate-colored phase by heating the hydrated tribromide under a stream of hydrogen bromide. When this phase was subsequently reduced under hydrogen, a colorless phase resulted. Magnetic measurements on the chocolate-colored phase indicated 90% divalent europium. In 7 additional investigations of the dibromides, Doell and Klemm22 obtained an X-ray powder diffraction pattern which was similar to that obtained for strontium and samarium dibromides and indicated that the three phases were isostructural, but they were unable to index it. In the same year, the single-crystal data of Kammermans23 indicated an ortho- rhombic structure for SrBrz. These two results have been interpreted to mean24 that the europium phase has the struc— ture described by Kammermans. However, SrBr2 recently has been shown to possess tetragonal symmetry25; Kammermans determined the structure of SrBr2°H20. In addition to the preparative procedures reviewed by Taylor,26 Cotton and Wilkinson24 report that europium dibromide may also be pre— pared by thermal decomposition of the tribromide. b. Hydrated Eurgpium Bromides Although europium tribromide hexahydrate is occasionally mentioned as a starting material for other investigations,18.21 conformation of the hexahydrate composition19 is the only information reported for hydrated europium bromide phases. 2. Thermodynamic Investigations of Europium Bromides As Nikova and Polyachenok27 noted in their recent re- view, no experimental thermodynamic data have been reported for either lanthanide dibromides or tribromides. However, estimated values for heat capacities and thermodynamics of fusion, vaporization, formation, and dissociation have been 8 compiled by Brewer,28 Brewer et al.,29 Feber,30 and Wicks and Block 31. C. The Oxides Of Bromine The following oxides have been reported for bromine: Brzo, BrO, Broz- Br02.5, Br02.57, and Br0332'35, but none ap- pears to be stable at room temperature unless under an atmos— phere of ozone. Since the presence of binary bromine—oxygen compounds is not expected at high temperatures, these phases will not be considered further in this investigation. D. The Oxide Bromides of Europium 1. Preparative and Structural Investigations Of the limited work expended on lanthanide oxide bromide phases, investigations of the europium system have been most numerous. Baernighausen et al.36 have prepared the monoxide monobromide, EuOBr, both by bromination of the sesquioxide at 7000 under a bromine-laden inert gas stream, and by heating the tribromide hexahydrate at 3500 for 1-2 d in air. For this phase, their X-ray powder diffraction data indicated the tetragonal PbFCl—type structure charac— teristic Of other lanthanide oxide bromides 3K. The second preparative technique is consistent with the thermogravi- metric study of Mayer and Zoltov19 who found EuOBr to be the only oxide bromide of europium. However, this result disagrees with additional experiments of Baernighausen36 who 9 obtained previously unreported trieuropium tetraoxide mono- bromide, Eu304Br, by heating an equimolar mixture of EuOBr and Eu203 in a nitrogen atmosphere at 950°. Analogous samarium and ytterbium phases were prepared by heating the monoxide monobromides in air at 680° and 440°, respectively. rMore recently, the preparation of Nd304Br has been reported33. The X-ray powder diffraction data for these phases have been indexed on orthorhombic symmetry, but neither the space group nor the structure type has been reported. 2. Thermodynamic Investigations Although thermodynamic measurements have been made on selected monoxide monochlorides by two different static equilibrium techniques,39"‘=3 no measurement has been_made on any lanthanide oxide bromide phase. CHAPTER III THEORETICAL CONSIDERATIONS PERTINENT TO THIS INVESTIGATION A. Phase Relationships 1. Possible Phases in the Europium-Oxygen-Bromine System A general formulation for all stoichiometric phases in the europium-oxygen-bromine ternary system where all pos— sible Eu(II)-Eu(III) and all possible oxygen-bromine ratios may occur istu£O[(3£_m)/2]_[n/2]Brn. The coefficients z, m, and n may assume integral values in accordance with the restriction that 2 3,1, 0 j_m j,£, and 0 j n.: (3z-m). The metal oxygen and metal-halide binary systems are defined by n = 0 and n = (3Z-m), respectively. -Numerous values are degenerate as a result of successive multiplication of their simplest formulas; however, no possible stoichiometric phase is excluded. Although one would not anticipate the existence of an exceedingly large number of phases, the ternary system does possess potential for preparative inves— tigations. 10 11 2. Vaporization and the Phase Rule a. Vgporization Modes The vaporization behavior of a single phase may be either congruent or incongruent. Congruent vaporization occurs when the composition of the vapor is always the same as that of the condensed phase. The vaporization of a condensed phase to give a second condensed phase and a vapor of different composition is an incongruent process. b. The Phase Rule One of the most useful relationships in vaporization studies is Gibb's phase rule: F = C - P + 2. (III-1) The number of degrees of freedom, F, is expressed in terms of the number of components, C, and the number of phases, P. When a vaporizing system is fixed at its equilibrium pressure, the system is invarient, igg; F = 0. Application of the phase rule to vaporization processes falls into two classes according to the congruency or in— congruency of the behavior. For congruent processes, P = 2 (condensed phase and vapor), and F = C. Even though C = 2 in a binary system, only the temperature need be fixed since the one necessary additional restriction-—that the composition of the vapor and condensed/phase be the same (i;34_fixed)—-is implied in the congruency definition. For incongruent processes, P = 3 (2 condensed phases and vapor), 12 and F = C-1. In a binary system (C = 2), a definition of temperature fixes the pressure, but in a ternary system (C = 3), the temperature plus the composition of either the second condensed phase or of the vapor phase (one fixes the other) must be defined. One point which must be mentioned is that the phase rule only fixes the composition of the vapor phase, and in no way defines the vapor species. c. The Pressure—Composition Diagram The qualitative results of vaporization studies for two-component systems may be presented easily by a pressure— composition diagram drawn for a constant temperature. Such a diagram conveniently defines all stoichiometric and non- stoichiometric phases, whether incongruently or congruently vaporizing, and the compositions of their vapors. Examples of pressure—composition diagrams are given by Gilles 44. B. Vapor Pressure Measurement by the Knudsen Effusion Technigge 1. General Introduction Vapor pressures in the range 10—9 to 10-3 atm may be measured by either Langmuir (free) vaporization or Knudsen effusion techniques 4A The latter method, which is based on the rate of effusion of the vapor through an orifice, may assume one of several forms: vacuum microbalance, torsion effusion, target collection, mass spectrometric measurement, or various combinations of these. 13 2. Theoretical Considerations of the Targgt Collection Method If an isotropic vapor in thermal, chemical, and mechan- ical equilibrium with a condensed phase is confined in a volume, its motion may be described by the kinetic theory of gases. In the theoretical treatment first described by Knudsen46:47 and more recently by Ackermann48 and Ward49, the number of molecules striking the container per unit time, Z, is related to the number of molecules per unit volume, n, and the average molecular velocity, 5, by equation (III-2). Z = nV/4 molecules cm-zsec-l. (III-2) If a small, circular, ideal (infinitesmally thin) orifice is placed in the container wall, such that vapor is allowed to effuse into a perfect void in such small quantities that equilibrium in the container is not destroyed, the number Of molecules passing through an orifice of area So is simply S0(n5/4). The fraction of the effusing molecules striking a cir- cular collector plate of radius r, the center of which is located at a perpendicular distance d from the orifice, may be calculated from the cosine distribution law. The flux of molecules leaving the orifice and arriving at an area increment dN on the collection plate is given by: dN = W 1 N0 Cos 9 dw, (III-3) 14 where No is the total molecular flux at the orifice and 9 is the angle between the perpendicular and the axis of dw, the solid angle increment of the effusate intersected by area dN. Qualitatively, 7-1 cos 6 dw is the fraction of the total flux moving in a specific direction. Substi- tution in terms of the variables r, d, So, and Z into the cosine function and integration over the hemisphere of space above the orifice gives relationship (III-4). N = Z So(r2/d2 + r2) molecules sec—1. (III—4) If the pressure in the container is :10"3 atm, the gas may be assumed ideal, and n = p/kT. Multiplication of equation (III-4) by a time interval, t, combination with relationship . . - 1 . . (III—2), substitution of v = (8RT/v) /2 from k1net1c theory, and inclusion of the ideal gas assumption gives equation (III-5) for the equilibrium vapor pressure. 1 P = [w/Sot][2vRT/M] /2[(d2 + r2)/r2]. (III-5) If W grams of effusate of molecular weight M is collected in t minutes by a circular collector of radius r cm located at a perpendicular distance d cm above an orifice of area So cm2, and if R is defined in ergs deg—lmole—l, P is obtained in units of dynes cm—2 and may be converted easily to atmospheres. The terms in equation (III-5) may be combined to give the following: 4 P = [3.760 x 10- W/Sot][T/M]1/2[(d2 + r2)/r2] atm.(III-6) 15 Measurement of the parameters in equation (III-6) constitute vapor pressure determination by the target collection Knudsen effusion technique. 3. Limitations of the Knudsen Method a. Non-Ideal Cells (1) The Non-Ideal Orifice One basic assumption in the derivation of the Knudsen equation is that the orifice is ideal (infitesmally thin). However, since attainment of such orifices is impossible, the channeling effect (resistance of a tube to a passing vapor) of an orifice as a function of its geometry must be considered. As Clausing first demonstrated5°, the effusion probability (so—called Clausing factor), W0, can be cal« culated as a function of the length L and the radius R of the orifice channel by W0 = 8R/3L51. Clausing correc- tions are often only applicable to total effusion (weight loss) measurements, in which W0 appears in the right-hand denominator of equation (III—5) and the term for the frac- tion of effusate collected (a function of r and d) is unity. Correction factors for channel orifices as a func- tion of both L/R and 9, the angle defining the fraction of effusate collected, have recently been tabulated5zc53, so that corrections may also be made for target collection experiments in which cylindrical orifices are employed. The effusion probabilities of conical orifice geometries have also been treated by Iczkowski et al.54. 16 (2) Non-Ideal Collection Geometry Ward49 has recently examined the validity and limits of the cosine distribution law for real "knife-edged" (conical) orifices by both collection experiments and Monte Carlo calculations. Both sets of results confirm that the orifice and Knudsen cell geometries have little effect on the cosine distribution for small angles of 9, 'i;g; in the forward direction, while severe deviations may be observed for large angles of 9. Irregularities in the cell walls or the sample surface may give rise to corre- sponding deviations in the cosine distribution by a "pinhole camera effect". Ward concludes that total effusion meas- urements (weight loss) will probably be in error, but, if the collection geometry is chosen properly, target col- lection results will be less ambiguous than those of weight loss experiments. (3) Thermal Expansion of the Orifice The change in orifice area as a function of the linear expansion coefficient of the crucible material, a function of temperature, must be considered. However, the results of Kent55 indicate that Changes in orifice diameters between room temperature (measurement temperature) and 2500° is of the order of 0.1% for most materials. -Such corrections are negligible and are not considered further in this investi- gation. 17 b. Non—Ideal Gas In the derivation of the Knudsen equation, the ideal gas assumption is invoked. So—called "viscous flow% and not the "free molecular flow" prescribed by Knudsen condi— tions, results if the vapor is too concentrated. Dushman56 states that the ratio of mean free path of the vapor to the radius of the orifice should be equal to or greater than unity. The experiments of Mayer57 indicate that the cosine law is obeyed at pressures up to 5 x 10—3 atm with 4 orifices of 10’ —1o"5 cmz. c. Non-Equilibrium Conditions (1) Sampling and the "Orifice Effect" The derivation of the Knudsen equation assumes that the vapor is in physical equilibrium in the cell, but the presence of even the smallest orifice upsets this condition. An expression derived by Carlson et al.58 may be employed to correct the observed pressure to the equilibrium value, a function of the observed pressure, the orifice area, and the sample area. -Experimentally, large deviations from vapor saturation result in the so-called "orifice effect". If equilibrium is severely displaced by the presence of an orifice, a large change in orifice area will be accompanied by an inverse change in the measured pressure for any given set of conditions. 18 (2) The Vaporization Coefficient The vaporization coefficient, av, is defined as the ratio of the rate of evaporation into a void to the rate at which a saturated (equilibriqu vapor impinges on the sample, or simply the ratio of the Langmuir pressure to the Knudsen pressure. Values of av may vary from .O to 1. The condensation coefficient, ac' may also be defined, but ambiguity often arises. 'As Margrave has noted45, av and do are generally assumed equal. Regardless of the defini- tion, the net effect is the same; namely, a system with a non-unity vaporization coefficient is only able to attain a steady state and not a true equilibrium pressure. Ackermann et al.59 have analyzed the problem of a non- unity vaporization coefficient by a nonequilibrium thermo- dynamic treatment and indicate that difficulties may arise from a temperature gradient at the surface, or from surface contamination or strain. Experimental results°° agree with these postulates in that av for the formation of tetrameric arsenic gas from the solid is 4.6 x 10-4. The difficulty apparently lies in the energetics or strain of the mechanism by which the tetramer forms on the surface. 'Rosenblatt61 notes that av is usually unity if the sample is finely divided so that the effective vaporization area is large. (3) Diffusion Additional difficulties arise in incongruently vaporizing systems where a solid product tends to grow on the surface of 19 the reactant such that contact of the vapor phase with the reactant is hindered. The calculation of Ackermann et al.59 indicates that most vapor species escape from the outermost atomic layer. Diffusion of species through the solid Coat— ing would appear to be the only mechanism for their reach- ing the surface. Several experimental procedures which may be employed to detect the effects of diffusion in Knudsen experiments are: (a) comparison of the measured pressures at a given temperature as a function of time, (b) comparison of data collected for samples of different particle size (different surface area), and (c) comparison of pressures measured at successively increasing and decreasing tempera- tures. If no systematic trends are observed in these com- parisons, diffusion effects are probably negligible. d. Additional Limitations to Target Collection Effusion Measurements Many of the problems often encountered in collection experiments are obvious, but should be mentioned. (1) All effusate impinging on the collection plate must adhere. Experiments may be designed to measure the sticking coefficient, which may vary with target temperature. (2) Evaporation of effusate from the walls of the vacuum system must not occur. This problem could be very significant for conducting effusates when induction heating is employed. 20 (3) Residual pressures must be low enough to preclude scattering of the effusate between orifice and collector, or appreciable effusion of residual gas into the Knudsen cell. (4) Temperature gradients within the effusion cell must be avoided. (5) Changes in the thermodynamic acitivity of a sample by contamination from reaction with either the atmosphere or the crucible material must be avoided. C. X-Ray Fluorescence 1. The Basic Phenomenon When an atom has sufficient energy as a result of radioactive decay or excitation by an electron beam, gamma ray, or X-ray, the atom may de-excite by ejection of an electron from an inner atomic shell. If atomic structure is treated by the Bohr,model, the filling of an electron vacancy by decay of a second electron from a higher level results in emission of a photon of fixed energy. Since the inner atomic structure is only slightly affected by Chemical bonding, quantitative and qualitative analysis may be ac- complished without concern for the chemical environment of the sample. Thorough treatments of the origin of primary and secondary (fluorescent) X-rays are available°2I°3. 21 2. The Bragg Equation Analysis of the energies of fluorescent X-rays may be accomplished by the principle of X-ray diffraction given by the Bragg equation: nA = 2d sin e. In the normal diffrac— tion experiment, a fixed X-ray energy, A, is diffracted at different angles, 9, by various crystallographic planes of separation d. Analysis of photon energies may be accom- plished by fixing d with a given analyzing crystal so that the various energies are diffracted at different 9 values. A schematic representation of the spectrometer is given in Figure 1. D. Temperature Correction Measurement of temperature by optical pyrometry pre- sents difficulties in that the transmission loss from optical windows and prisms results in a low observed temperature. As Margrave has indicated64, consideration of Wein's radia- tion law leads to a relationship between the reciprocal of the true temperature, T, and that of the observed tempera— ture, To, as follows: (l/T — 1/T.) = F. (III-7) where F is a constant. Values of F for a given optical path may be obtained by measuring the temperature of a refer- ence source directly and via the optical path. 22 .12 omEQ W 23.5 autumn»: \ 335.1118 mm oqu 3 M! I m _ \. 33.56 3.1365. Em Em I ll... Em @8225 use. .85.». i .Hmumfionpommm mochmmuosam MMHIX Tau mo Odumfimflom G .H onsmflm 23 E. Thermodynamic Calculations 1. Second Law Calculations a. Derivation of Relationships The free energy change in a reaction at a given tempera— ture T is related to the changes in enthalpy and entropy of reaction and to the equilibrium constant by equations (III—8) and (111-9), respectively. 0 0 0 AGT _ AHT TAST . (III 8) 0 _ I _ AGT _.R T log KT. (III 9) The product of 2.3026 and the gas constant, R, is designated by R'. Combination of these equations gives the following linear relationship: log KT = -(AHg/R'T) + Asg/R'. (III-10) Treatment of experimental log K versus l/T data by a linear least squares regression (9:. III, 5, 1) gives an equation of the form log KT = (m/T) + b. By equating coefficients, values for the enthalpy and entropy of reaction are obtained as follows: AH; = - R'm. (III-11) AS° = R'b. (III-12) 24 b. Assumptions of the Second Law Treatment Several assumptions are made in the second law treatment of equilibrium vapor pressure data. First, the equilibrium constant for a general reaction, in which Vi and Vj are the stoichiometric coefficients and ai and aj are the thermodynamic activities of the products and reactants, re- spectively, is given by equation (III—13). v. v. 1 K =‘U(ai) [3179].) 3 . (III—13) The activities of all solid phases are assumed to be unity, while those of all gaseous species are replaced by their fugacities. For an ideal gas, the fugacity is equated with its partial pressure. .For high temperature effusion measure- ments, the vapor is sufficiently dilute so that it may be assumed ideal (pf, III, B, 3, b). However, the assumption that the activities of the solid phases are unity rests on more tenuous ground, and is most difficult to validate experi— mentally. .Even if the mutual solubilities of condensed phases, the solubility of contaminant or container materials in the equilibrium phases, or slight variations from stoi- chiometry could be accurately determined at the reaction temperature, their effect on the various activities is yet another problem. Though very unrepresentative, examination of the equilibrium phases at room temperature by X-ray dif- fraction can give indications of contamination or stoichio— metric changes by variation in lattice parameter. A second 25 assumption is that the log K versus 1/T equation is linear. Because ACp for the reaction over the temperature range of the measurements is generally non—zero, the data should exhibit slight curvature. The Z—plot treatment, which em— ploys heat capacity equations65 or tabulated thermochemical data56, allows correction of this difficulty. c. Data Reduction to the Reference Temperature If the enthalpy change for a reaction is measured at some median temperature, T, it may be expressed in terms of the enthalpy change at a reference temperature (298°K is selected here) and the Change in heat capacity for the re— action as follows: T AHO = AH398 + f ACp dT. (III—14) T 298 Similarly for the entropy change of the reaction, it fol- lows that: T 0 0 AS = AS + AC T dT. III-15 T 293 f298 P/ ( ) For a general reaction where Vi and Vj are coefficients of the products and reactants, respectively, ACp is given by equation (III-16). ACp - i Vi Cpi - i Vj ij. (III-16) However, since enthalpy and entropy functions are most often 26 tabulated, equations (III-14) and (III—15) are generally more useful in their following integrated and rearranged forms. Ange. = AH° - I; v 0 0 T l '(HT-H298)i_;v'(H 0 1. J T - H298)j] '(III-17) .3 _ _ o _ o _ o _ o _ AS [; Vi(ST S298)i ; Vj(ST 5298)j]-(III 13) o T l 3 If heat capacity data are not available, they may often be approximated as described in a following section (3:. III. E, 4). d. Calculation of the Second Law Entrppy The standard entropy at the reference temperature of any one of the reactants or products may be obtained from the measured entropy change for the reaction, provided the standard entropies of all other reactants and products are known. The entropy Change may again be expressed in terms of the general coefficients, V1 for products and Vj for reactants, as follows: 0 _ o o AS298 ‘ 2 Vi $2981 ‘ ; Vj S298j ° (111‘19) 1 3 Since vaporization reactions are a special case in that there is only one reactant, the summation on j may be dropped, and the standard entropy of a vaporizing phase j is obtained as follows: 0 _ o o S298j ‘ (1/Vj)(; Vi 32981 ’ AS298)- (III—20) l 27 2. Thirdeaw Calculations a. Derivation of Relationships In addition to its usefulness as a quantity which may be interpolated easily, the free energy function may be employed to reduce thermodynamic data to the reference tem- perature65. The free energy function, hereafter abbreviated as fef, is defined as follows: fef s (G; -'H398)/T. (III-21) Substitution of basic thermodynamic relationships leads to another expression. fef = (H; - H298)/T ‘ S; = (H; ‘ H398)/T - (S; ‘ 8398)‘Sg98' ' (III-22) When free energy functions are not tabulated they may be readily calculated from tabulated data and equation (III-22). The necessary enthalpy and entropy functions and standard entropy may also be approximated (pf, III, E, 4). If fef values for the products and reactants with coefficients Vi and Vj' respectively, are known, Afef for the reaction may be calculated as follows: ’ Afef - 2 v. fef. - 2 v. fef. . (III—23) i l 1 j J 3 Like fef, values of Afef may be accurately interpolated by graphing Afef versus T. From equation (III-21), Afef may also be expressed by the following relationship: 28 Afef = (AG; — AHg98)/T. (III-24) Substitution from equation (III-9) for the free energy change and rearrangement of the relationship leads to an equation for the enthalpy change at the reference temperature. AH398 =-(Afef + R' log KT)T. (III-25) Since a value for log K is obtained at each measurement temperature, the Afef value for that temperature may be employed to calculate a AHggs for each data point. b. The Value of Third Law Calculations Because each experimental point yields an enthalpy value at the reference temperature, the individual values may be examined for consistency and trend, either with tem- perature or chronological sequence. A temperature trend may arise from a systematic error in pressure or temperature measurement or in the free energy function change for the reaction. Large discrepancies between second and third law results may be interpreted as a gross error in measurement, or an incorrect definition of the vaporization process. Large deviations of the vaporization coefficient from unity also result in second-third law disagreement. .A second utility of the comparison lies in the evaluation of approxi- mated thermodynamic values such as high temperature heat capacities and absolute entropies of solids. .Since second and third law methods employ the same approximated Cp data 29 through different paths, agreement of the results is at least indicative of internal consistency in the estimated values, if not of the accuracy. 3. Energetics of Formation The results of a vaporization reaction may be employed to Obtain entalpies, entropies, and free energies of forma- tion of one reactant or product if the values are known for all other reactants and products. For a general reaction, an equation in terms of a general variable Q° (Q° = GO, Ho, S0) may be written for any temperature (usually 298°K) as follows: 0 o A0398 ' (2 Vi Aszgsi ‘ g V' AQf298j)- (111‘25) 3 1 3 Since AQggs is obtained experimentally for the vaporization reaction, any of the other quantities may be calculated. For a vaporization reaction, the summation on j may again be dropped and the value of AQ%298 for a vaporizing phase j becomes: 0 o AQf298 = (1/Vj)(; ViAszgsi ‘ A0398)- (III-27) 1 Since the entropies of the elements in their standard states are generally available at the reference temperature, and since 5298 for a given compound may also be evaluated from second law results (pf. III, E, 1, d) or estimated (3:, III, E, 4, b), Asgzgs for that compound may be evalu— ated from relationship (III-28). 30 o _ o o ASf29si ‘ 8298i ‘ 2 Vj Szgsj . (III—28) J In this case, Vj designates the coefficients of the reacting elements j in the formation reaction for compound i. 4. Approximation of Thermodynamic Functions a. The Approximation of High Temperature Heat Capacities (1) Solids The lack of heat capacity data for many of the com- pounds studied in this investigation has necessitated ap- proximation of the values. .Attempts to employ measured enthalpy functions (H; - H398) of stoichiometrically identi- cal phases by exchanging the (H; - H398) value of one element with that of the desired element has proven unsatisfactory, even though the approach has been used successfully for some systems°7:°8. However, if high temperature heat capacity data as a function of temperature are available for any phase, Aqu’ in a binary system, a heat capacity equation may be obtained for any other binary phase AXBy by use of the following formula: CprBy : [x/u][CpAuBV] + [(uy - vx)/2][3R] . (III-29) The second term arises through application of Kopp's rule65 which states that at high temperatures, the contribution to the heat capacity by each atom in a solid is 3R. .The same type of equation is also applicable to ternary systems of 31 one metal and two cations. For a compound AxByCz’ the heat capacity of any binary phase Aqu may be employed as follows: CprBYCz = [x/u][CpAuBV] + [(uy - vx)/2 + (2)][3R]. (III-30) Experimental data may come from either the A-B or the A-C binary system. Care should be taken in use of equations (III-29) and(III—30) to the extent that; (a) element A represents the component with highest molecular weight, £;§. the largest contributor to the heat capacity, (b) the phases considered have comparable degrees of ionic character, and (c) the approximations not be extended below 298°K where anomolous heat capacity functions are common. 2. Simple Polyatomic Gases In the absence of spectroscopic and structural data for a gaseous molecule, a normal statistical thermodynamic treatment is impossible, and other approximations must be made. Vibrational frequencies or force constants and ground state electronic levels might be estimated, but the like— lihood of success is small. Data for gaseous metal di- bromides, the only polyatomic species encountered in this investigation, are scant, but values are available69 for linear (pooh) TiBrz and HgBrz, and bent (sz) PbBr2 (Br—Pb-Br angle = 95°) and ZrBr2 (Br-Zr-Br angle = 120°). The heat capacities of the linear molecules differ by only 0.06 an (0.025%) at 298°K and converge at higher temperatures, 32 even though a large mass difference exists between Ti and Hg. A similar deviation is observed for the bent case (0.875%), while the two sets of values (linear versus bent) differ by 1.5 eu (> 10%). Based on theSe data, the high temperature heat capacity of a gaseous dihalide seems to be most dependent upon molecular symmetry, with negligible effects from molecular weight, or even the magnitude of molecular bend. -Therefore, satisfactory approximations of heat capacities and (H; - H298) or (s; - $393) functions may be made by identification of the molecular geometry. From the preceding discussion, mass effects appear to be unimportant in approximations. However, if the free energy functions of the previously mentioned gases°9, or those estimated for a large number of metal dibromides7o are examined according to molecular weight, a definite trend with mass is observed. Why is there an apparent discrepancy? The answer lies in the low temperature heat capacities of I the gases. ,Marked differences occur below 2000K, and these effects appear in two thermodynamic functions--the standard entropy and, hence, the free energy function. Though high Itemperature heat capacity functions and second law calcula- tions are essentially unaffected by mass differences of gaseous molecules, free energy functions and third law calculation are dependent on mass effects. b. Approximation of Standard Entropies of Solids From the measured entropies of numerous solids, Latimer71 33 has tabulated the average lattice contribution per atom to the total entropy at 298°K. Single values are listed for cations, while those given for anions take cognizance of the ionic charge normally assigned both to the cation and its anion. From equation (III-31), the entropy of a solid of n components, (Ai)xi (where 1 j_i :.n), is calculated from the sum of the lattice contributions, SE, for each component multiplied by its coefficient, xi, in the molecu- lar formula. 0 _ - 0 5298(Ai)xi - E x1 si . (III-31) Gr¢nvold and Westrum72 have reevaluated Latimer's scheme, and Westrum17 has made specific application to the lanthanide oxides. These more recent contribution values are recom- mended when approximations are necessary for binary oxide phases. In addition to the entropy obtained by equation (III-31), the total entropy may also include magnetic contributions. Westrum17 gives the estimated magnetic contribution per atom for various lanthanide ions. When the magnetic properties must be considered, equation (III-31) is modified to include an additional set of terms based on the magnetic contribu- tion, .Mi, such that: o = . o . _ 8298(A. . 2 x1 Si + T Xi Mi' (III 32) 1 x1 1 1 These estimated values should be comparable with the second law entropy (3;. III, E, 1, d). 34 c. .The Estimation of Enthalpy and Entropy Functions If heat capacity functions are available or have been approximated as described in parts a and b of this sec- tion, the functions (H; - H398) and (s; - 5398) are obtained by integration of the following equations. 0 o T H - H = C dT. III-33 ( T 298) f298 P ( ) o o T (sT - 5298) = f Cp/T dT. (III—34) 298 5. Statistical Methods a. Least Squares and Standard Error A least squares regression with associated standard error analysis has been employed for evaluation of all linear data, while a least squares method has been employed for tabular values73. All deviations are reported as i O. b. Combination of Errors In thermochemical cycles, the summation of values, each having an associated error, becomes necessary. A common solution to this problem of error estimation appears to be: (a) ignore the problem, (b) give the error of only the present measurement, or (c) average the errors. -None of these is a representative estimator. However, this problem has been treated by Feller74 as follows. If xi (1.: i.i n) is a set of variables with standard deviations Oi, the 35 deviation in their sum, Y, is 0y, where, O?)1/2. 1 (III—35) 0-( “MD 1 1 If X1 is not an internally independent set, a second term must be included to describe the covariance. -However, the data encountered in thermochemical cycles are generally independent. CHAPTER IV EXPERIMENTAL EQUIPMENT AND MATERIALS A. Target Collection Apparatus The target collection apparatus used in these measure- ments has been described previously by Kent55. .However, the quartz effusate shutter was replaced by one of 0.16 cm copper sheet, and the collimator was not employed for the definition of 9 , the subtended effusate collection angle (pf, IV, B, 3). Residual pressures were maintained at _ -6 . . 10 5-10 torr dur1ng data collect1on. B. X—Ray Fluorescence Equipment 1. Spectrometer The instrumentation employed in analysis of the col- lected effusate was the Siemens Model 4b nonfocussing spectrometer equipped with a LiF analyzing crystal, tungsten tube, water-cooled scintillation detector (0.1 mm beryllium window) and Siemens Kompensograph scaling unit. At various times, three different generators (Siemens Kristalloflex IV. Norelco, and Norelco XRG-5000), two different analysing crystals (normal and high intensity) and two different X-ray tubes (AGOW and AGW60) were used. 36 37 2. ~Specimen Mount The sample mount in the spectrometer was modified to accommodate the 2.6 cm diameter copper targets, which were machined with a 0.19 cm high rim and an internal diameter of 2.0 cm. The original spectrometer geometry was maintained in the modified mount and in a second holder equipped with an eight rpm electric motor for continuous specimen rotation. 3. ~Effusate Geometry The fraction of effusate sampled was defined by control- ling the amount of target surface exposed to the primary X-ray beam, not by the usual method of limiting the amount of target surface exposed to the effusate. A 45° beveled aluminum insert placed inside the rim of the targets re— producibily defined the area (2.00 cmz) exposed to the primary X-rays. C. rX-Ray Diffraction Equipment 1. Powder Diffractionygquipment An 80 mm radius Haegg-type focussing x-ray diffraction camera75 was utilized for crystallographic analyses of powdered samples. -Diffraction data were occasionally ob- tained with 114.7 mm Debye-Scherrer cameras. 38 2. Single Crystal Diffraction Equipment An equi-inclination Weissenberg camera (Charles Supper Co., Watertown, Mass.) was used in the investigation of Single crystals. D. Temperature Measuring Equipment Temperature measurements in vaporization experiments were made with a National Bureau Of Standards-calibrated Leeds and Northrup disappearing filament pyrometer (serial number 1572579). The NBS calibration data allowed for cor— rection of the measured temperature55. Additional tempera- ture measurements during preparative reactions were made either with a platinum-platinum-10% rhodium thermocouple and a Honeywen.potentiometer, or with a chromel-alumel thermocouple and a Sym—Ply-Trol meter. -E. High Temperature Mass Spectrometer Mass spectrometric investigation of effusate species was effected with the Model 12, Bendix Time of Flight instru- ment described previously°7. F. ~Micrograph A Bausch and Lomb Dynazoom micrograph,equipped with a Polaroid 4 X 5 Land camera attachment,was used to obtain photographs of orifices for orifice area determination. 39 G. .Miscellaneous Measuring Equipment The measurement of various distance, area, volume, and time parameters critical to the vaporization experiments were made with the following equipment. .A cathetometer (Gaertner Scientific Co.) was employed in the measurement Of orifice-target rim distances. The diameter of the insert defining the collection geometry and the distances from tar- get rim to target face were measured with precision calipers or micrometers. -A compensating polar planimeter (Keuffel and Esser Co.) and a micrometer slide with 0.01 mm divisions (American Optical CO.) were used for the measurement of ori- fice areas. Time intervals of vaporization were measured with a Lab—Chron (Labhxma Inc.) 60 cycle timer. -An ultra precision micrometer buret (Kontes Glass Co.) with a 0.25 ml capacity, 0.00001 ml division, and 0.04% accuracy was employed for volumetric measurements in X—ray fluorescence standardization. H. -Heating Equipment A 20—kva Thermonic high—frequency induction generator was employed for heating effusion cells and selected prepara- tive reactants. Additional heating equipment used in preparative experiments were a Marshall Products Co. platinum- 40% rhodium wound tube furnace and ordinary laboratory tube furnaces. 40 I. Vacuum Systems In addition to the previously mentioned target col- lection apparatus, the following three vacuum systems were used in this investigation: (a) the water-cooled Pyrex and Vycor system described by Kent55, (b) the fast pumping system equipped with a current concentrator67, and (c) a second glass system constructed of Pyrex for lower tempera- ture reactions. This latter system consisted of a 2 cm o.d. reaction tube which was mounted vertically into the Marshall furnace. The reaction tube was connected yia_ground glass joints to a manifold with outlets to a cryogenic trap for condensation of volatile reaction products and to a tube which led to a larger cryogenic trap, a mercury diffusion pump, and a forepump. J. Inert Atmosphere Glove Box The glove box with a recirculated, argon atmosphere and with oxygen (BASAF catalyst) and water (alumina and phosphorus pentoxide) removal systems described by StezowSki75 was employed during manipulation of air sensitive samples. .K. -§ffusion Cell Design 1. Target Collection Cells Two types of effusion cells were used in the target collection measurements: one asymmetric with a black body hole drilled in its bottom, and the other symmetric with an 41 optical cavity identical to the sample cavity. Cells of the asymmetric design, which were machined from molybdenum, are sketched in Figure 2a, while those of symmetric design, which were of both molybdenum and graphite, are illustrated in Figure 2b. 2. vMass Spectrometer Cells The effusion crucibles employed in mass spectrometric measurements were of the design described by Pilat067. L. Chemicals and Materials Chemicals and materials used were: (a) europium ses- quioxide, (99.9% lanthanide content) spectrographic analysis; 0.05% La203, 0.01% Nd203, other lanthanides below detectable limits, 0.02% Zn; American Potash and Chemical Corp., West Chicago, 111., (b) europium metal; 99.9%, Michigan Chemical Corp., St. Louis, Mi., (c) bromine, technical grade; Dow Chemical Co., Midland, Mi., (d) hydrobromic acid; 48%, re- agent grade; Matheson Coleman and Bell, East RutherfOrd, N.J., (e) ammonium bromide; 99.8%, reagent grade; Matheson Coleman and Bell, East Rutherford, N.J., (f) lithium hydride; unspecified purity; Metal Hydrides Inc., Beverley,.Mass., (g) bromoform; purified; Allied Chemical Corp., Morristown, N.J., (h) potassium bromide; spectrographic grade; Matheson Coleman and Bell, East Rutherford, N.J., (i) molybdenum stock; Kulite Tungsten Corp., Ridgefield, N.J., (j) graphite stock; spectrographic grade; Becker Brothers Carbon Co., Cicero, Ill., and (k) quartz; Englehardt Industries Inc., Hillside, N.J. I . 'I) II.) 'I III 42 aa-—--.9x -——-4> “i|i|i! g'-—a>:: ‘\!IEIEI! T.‘ 0.0625 in = 900 1.21“ 0.64: -> ‘- Figure 2a. Asymmetric Knudsen cell design. Figure 2b. Symmetric Knudsen cell design. ‘F---l()x ---—4> ' 1 6x 9! x=0.159 cm = 0.0625 in a = 90° ' /// _. r’ 2 A (1 3/69 CHAPTER V EXPERIMENTAL PROCEDURES A. Preparative Techniques 1. Trieuropium Tetraoxide Trieuropium tetraoxide was prepared by an adaptation of the method reported by Baernighausen3. Europium monoxide monochloride was prepared by dissolving the sesquioxide in 6 M HCl, evaporating the solution to Obtain the hydrated trichloride, and igniting in air at 500° for several hours3. This EuOCl, which was identified by its X-ray diffraction pattern, was combined in'a 1:1:2 stoichiometric ratio with Eu203 and LiH. The blended reactants were placed in an outgassed tungsten crucible in the glove box and were sub- sequently heated by induction in the water-cooled vycor vacuum system in which the residual pressure was 10.6-10-7 torr. The temperature was increased slowly to 900° so that the pressure never exceeded 10.3 torr. Heating was continued for approXimately 5 hr, by which time the pressure had de- creased tO 10-3 torr, an indication that the loss of H2. LiC1,and excess LiH, and consequently the reaction, was com- plete. The product often contained a few small particles of a white phase which could be separated physically from the 43 44 reddish black-Eu304. The powder x-ray diffraction pat— tern of this white phase did not correspond to that of any known lithium—europium-oxygen, or lithiumpor europium-oxygen phase. These white particles were combined with additional EuOCl and LiH on the assumption that their molecular weight corresponded to that of Eu203, and were mixed with the Eu304 phase before the entire sample was reheated to a maxi- mum of about 1200°. 2. Europium Monoxide Like the tetraoxide, europium monoxide was prepared by lithium hydride reduction of the monoxide monochloride. The EuOCl and L1H were combined in a 1:2 stoichiometric ratio, placed in a nickel crucible,and heated in vacuum by induction. The temperature was increased slowly to 900° as described previously for Eu304. After the reaction was complete, the sample was removed, crushed, and reheated at 1000° for 2 hr to remove occluded LiCl. 3. Europium Dibromide Europium dibromide was prepared by dehydration of a tribromide hexahydrate—ammonium bromide matrix as described by Taylor and Carter18 for the preparation of the tribromide. >Each gram of europium sesquioxide was combined with 15 ml of 48% HBr and 3.5 g of NngBr, dissolved with heating and stirring, and finally concentrated at 100° with aeration. The resultant, solid product was placed in the reaction tube 45 of the Pyrex vacuum system and heated with the Marshall furnace to 200° for 12—15 hr. The final product was ob— tained by increasing the temperature slowly over an 8 hr period to a maximum of 350° and then decreasing it slowly (3—4 hr) to room temperature. The vacuum system, which contained two liquid nitrogen traps and a mercury diffusion -5 torr when no pump, attained residual pressures of 10-4-10 sample was present; however, pressure measurements were not made during the heating cycle because of the corrosive nature of the ammonia and bromine vapors. -Single crystal samples of the dibromide were prepared by a vapor transport technique. A sample of the product obtained by the matrix dehydration procedure described above was placed in a 1 cm o.d. quartz tube which had been sealed on one end and connected to the fast pumping vacuum system. This tube was inclined at a 45° angle, and the closed end containing the dibromide was heated at approximately 1000° with a Meeker burner for 36-48 hr. 4. Europium Monoxide Monobromide Since attempts to prepare europium monoxide monobromide by extended heating of the hydrated tribromide in air at 400° produced impure, amorphous products, samples were prepared by direct bromination of the sesquioxide. A continuous helium flow, which was swept through a reservoir containing liquid bromine, carried the halogen vapor through a tube furnace system constructed of quartz and over a sample of 46 ’Eu203 confined in a quartz boat. After the oxide had been heated at 400° under a purge of helium, the bromine reser- voir was switched into the system. The sample was then heated at 750-800° for 8 hr under the helium-bromine vapor, cooled to room temperature, and subsequently removed to the glove box. 5. Trieuropium Tetraoxide Monobromide Samples of trieuropium tetraoxide monobromide were prepared by two techniques-—combination of EuOBr and Eu203 and bromination of the sesquioxide. .Mixtures of EuOBr prepared by direct bromination of Eu203 were blended with the sesquioxide in a 1:1 stoichiometric ratio and placed in 7-10 mm o.d. quartz ampoules which previously had been outgassed in air at 1000°. ~After the ampoules had been prepared, they were removed from the glove box, evacuated, sealed, and heated in a tube furnace at 900-1050° for 12 hr. Samples of Eu3O4Br were also prepared by use of the bromina— tion procedure described for the preparation of EuOBr, with the following exceptions: (a) the system was not initially purged with helium; (b) a very low flow rate of the carrier gas was used to maintain a relatively high partial pressure of oxygen in the vapor. 6. Europium Tribromide Europium tribromide was prepared by direct reaction of europium dibromide and bromine. Heavy-walled quartz ampoules 47 (7 cm o.d., 3 cm i.dJ were outgassed as described previously and charged with 0.3-0.7 g samples of EuBrz. The ampoules were stoppered and removed from the glove box before an ex- cess (1-2 ml) of liquid bromine was added. .After the bromine had been frozen in the closed end of the ampoule by immer- sion in liquid nitrogen, the ampoule was evacuated and sealed. Various ampoules were heated at 60°, 110°, 225°, and 275° (1, 12, 53, and 69 atm of bromine pressure,respec- tively) in a tube furnace for 12-18 hr. After reaction, the solid products were separated from the excess bromine by cryogenically trapping the halogen vapor. 7. Hydrated Bromide Phases a. Europium Tribromide Hexahydrate Europium tribromide hexahydrate was prepared by de- hydration of a tribromide solution which was formed by dis— solving europium sesquioxide in 48% HBr. The solid, which resulted from evaporation of this solution, was subsequently contained in a porcelain crucible and heated at 125° in a muffle furnace for 30 hr. b. Europium Dibromide Monohydrate Although europium dibromide monohydrate was not pre— pared in pure form, it was observed as an intermediate phase when europium dibromide hydrolyzed in situ in the Guinier camera. Successive X-ray diffraction patterns were obtained to indicate its formation and disappearance. 48 B. Additional Preparative Reactions and Phase Studies / 1. Attempts to Prepare Europium Tribromide Several attempts were made to prepare the tribromide. In addition to numerous trials to dehydrate a tribromide hexahydrate-ammonium bromide matrix in a manner similar to that described previously, bromination with bromoform and direct combination of the elements were attempted. A sample of europium oxide bromide of unknown oxygen or bromine com- position was placed in a quartz boat in a flow system similar to that used for direct bromination procedures. For 4 hr, bromoform vapor was swept by a helium flow from a reservoir containing the liquid at its boiling point into the tube furnace containing the sample at 625°. In the direct com- bination experiment, a sample of europium metal was placed in an outgassed quartz ampoule. The sample was removed from the glove box, and excess bromine was added and frozen in the closed end of the ampoule, which was then evacuated and sealed. The ampoule (30 cm in length) was placed in a tube furnace so that the end containing the metal sample was in the heat zone, while the other end extended outside the furnace and served as a pressure control. The temperature of the metal was slowly increased to BOO—900° and maintained at that value for 12 hr. . 49 2. Attempts to Prepare Additional Oxide Bromide Phases a. Direct Combination of Eurppium Tribromide and Sesquioxide In an attempt to prepare europium(III)-oxide—bromide phases which are more bromine rich than EuOBr, a 4:1 molar ratio of EuBra and Eu203 was sealed in an evacuated quartz ampoule (pf, IV, A, 5), heated at 425° for 12 hr, and cooled slowly. b. The Oxidation of Eurppium Dibromide Another attempt to prepare bromide rich ternary phases involved oxidation of europium dibromide. A sample of EuBr2 was placed in a quartz boat in a tube furnace while oxygen was passed through the system. The oxygen was dried with a dry ice—ethylene glycol trap and a magnesium per- chlorate drying tower. Back—flow of air was prevented by a paraffin oil bubbler and a second magnesium perchlorate drying tube. The sample was heated successively for 12 hr at 200°, 250°, and 300°, and heating was discontinued after a change was observed in the sample. c. Direct Combination of Europium Monoxide and Dibromide Attempts to prepare divalent oxide bromides were ef— fected as follows. Mixtures of EuO and EuBrz in the stoichio- metric ratios 1:3, 1:2, 2:3, and 1:1 were prepared and heated in evacuated quartz ampoules at 650-700° for 5 hours. 50 Several of the stoichiometries were annealed for 2-5 d at 400°. C. Analytical Techniques 1. Europium Analysis Metal analysis was effected by conversion of samples to the sesquioxide. Samples were weighed directly into constant-weight crucibles and ignited to the sesquioxide at 1000° in a muffle furnace. Air sensitive samples were weighed in the glove box. 2. Bromide Analysis Analysis of bromine was accomplished by a gravimetric silver bromide technique. Weighed samples were dissolved in HNO3 or water as necessary and a standard gravimetric silver halide analysis effected76. However, the bromine percentage of monoxide monobromide samples was obtained from the weight gain observed in bromination reactions of the sesquioxide. 3. Oxygen Analysis Direct analysis for oxygen was not attempted. D. Density Measurement The density of europium dibromide was determined by the buoyancy technique. The mass of a crystalline fragment 51 (approximately 0.1 g), which was hung by a fine nylon fiber, was measured both while the crystal was suspended in the argon atmosphere of the glove box and while it was submerged in dibromomethane at a carefully measured temperature. E. X—Ray_Qiffraction Procedures 1. Powder Diffractionygechniques The techniques of sample preparation and film measure- ment were essentially identical to those described previously for the Guinier camera by Stezowski75. All bromide and oxide bromide samples, except those in which hydrolysis was being investigated, were prepared in the glove box and coated with paraffin Oil to prevent decomposition. Both annealed potassium chloride (a0 = 6.29300 i 0.00009 R)77 and platinum (a0 = 3.9237 i 0.0003 R)78 were employed as internal standards. The diffraction data were reduced with the least squares regression program of Lindqvist and Wengelin79. 2. Single Crystal Techniques Oscillation and equi—inclination Weissenberg photo— graphs were obtained by the usual procedures32,3°. However, because of their hydroscopic nature, crystals were pre- served under paraffin oil during both selection and manipula— tion. Since coatings of Canada balsam and Duco cement were found unsatisfactory for protection of the dibromide, crys- tals were wedged tightly in 0.2 mm Pyrex Debye—Scherrer 52 capillaries which were then sealed with a microburner to form capsules (5-6 mm in length). The encapsuled crystals were mounted and examined optically. ‘The air stable tri- europium tetraoxide monobromide crystals were mounted with Canada balsam. F. Characterization of Vaporization Reactions 1. Weight Loss Measurements Weight loss data were collected to help characterize the vaporization process and to indicate interaction between sample and crucible. The general procedure involved out- gassing a crucible to constant weight, charging it with a known weight of pure sample, and measuring the weight loss which occurred upon complete vaporization, i;34.0n disap- pearance of the initial sample. By measuring the rate of vaporization of a sample (weight loss through an orifice in a given time) at different temperatures, data were simultane- ously collected for preliminary vapor pressure estimates needed for the initial target collection experiments. A sample of Eu304 was heated by inductiOn to constant weight at 1400-1500° in a molybdenum cell. Similarly a sample of EuO was vaporized in one-hour increments until .X-ray diffraction patterns indicated only the presence of Eu304. Several attempts were made to find a suitable con- tainer for vaporization of Eu3O4Br. Molybdenum and tungsten cells, both with and without quartz liners, and thoria lined graphite cells were employed. However, the final weight 53 loss measurements were made with a quartz lined graphite effusion cell in which a sample of Eu304Br was heated to constant weight at 1000-1200°. 2. Mass Spectrometric Ipvestigations The quilibrium vapors were also analyzed mass spectro- metrically employing effusion cells of the materials de- scribed in the weight loss experiments. The crucibles were heated by electron bombardment and electron ionizing beams of 10-70 eV were employed. The following temperature ranges were examined for the various compounds: Eu3O4, 1400-1700°; EuO, 1100-1450°; and-Eu304Br, 900-1350°; and the relative intensities of all effusate species were measured. The ap- pearance potentials of europium (Eu+) and europium bromide (EuBr+) were obtained by the linear extrapolation technique using mercury as a reference. 3. Effusate Collection Experiments Large quantities of the condensable effusates from tri— europium tetraoxide monobromide and europium monoxide mono- bromide were collected in a quartz cup (1.5 cm o.d., 2 cm high), which was inverted over the orifice of a large quartz-lined crucible (internal diameter = internal height = 2.5 cm). The condensates from Eu3O4Br and EuOBr samples, which were heated by induction in the Vycor vacuum system at 950—11500 and 950-10500, respectively, and the solid residues were transferred to a vacuum desiccator and removed to the glove box, where eray diffraction samples were prepared. 54 4. x—Ray Investigations The solid residues from the various target collection experiments were examined crystallographically by powder .X—ray diffraction techniques. The diffraction data were examined not only for the presence of the equilibrium phases, but also for changes in spacing or relative intensity and for the presence of any additional phases. Samples were obtained from both the bulk residues and the residue-cruc cible interfaces. G. .X—Ray Fluorescence Procedures 1. Optimization of_§pectrometer Parameters The operating parameters of the spectrometer were ad- justed to Obtain maximum sensitivity with pulse height discrimination. The spectra of the analyzed elements81 were recorded and compared with those of the selected target material to check for possible background interferences, £42, spectra of target material, of contaminents in the target, or of scattered tungsten radiation. The operating maxima for the most interference-free emission were selected by one of two procedures. The first method employed a large sample of the element of interest. The various parameters affecting sensitivity (kilovoltage and milliamperage of the tube, and attenuation, pulse height, and channel width of the discriminator) were adjusted for greatest recorded intensity at the spectral maximum. The second technique 55 was the procedure for maximization of sensitivity in micro— analysis described by Neffsz. In this technique, 5-10 ug samples of the elements were employed, and both background and standard counting rates,(rb and rs) were measured as a function of the previously mentioned parameters. Conditions for maximum detectability were selected by minimization of the function (rb)1/2/(rs-r for each parameter. b) 2. Counting Procedures Because a given diffraction angle could not be repro- duced accurately with the available instrumentation, a scanning procedure was selected. The 29 region of i 0.25° bracketing the spectral maximum was scanned at a rate of 0.125°/min (equivalent to a 4 min preset time) for both background and sample counting. In an identical way, a control target was counted either before or after each ordinary target, such that variations in conditions or sensi- tivity which occurred between initial and final counting could be determined. The observed counts/4 min was taken as the average of four successive measurements. When the static sample holder was employed, these counting rates were obtained at four orthogonal target positions. Prior to each Set of measurements, the angular position of the spectral maximum was determined such that scanning always covered a reproducible 0.50° region. This counting procedure was employed for both the preparation Of calibration curves and for the analysis of condensed effusates. 56 3. Preparation of Standard Solutions Standard solutions of europium and bromine were pre- pared from europium sesquioxide and Spectroscopic grade potassium bromide. For europium analysis, samples of calcined Euzoa (0.02-0.09 g) were weighed with a semi-micro balance, dissolved in a minimal quantity of 6 M HCl, and diluted volumetrically to prepare solutions of 40-100 ug Eu/ml. For simultaneous europium and bromine analyses, weighed samples of calcined Eu203 and dried (110°) KBr were combined to prepare standard solutions of 40-100 ug Eu/ml and 75-200 ug Br/ml. 4. Preparation of Calibration Curves Data for linear external calibration curves were ob- tained by measuring the counting rate from characteristic radiation of standard targets. These standards were prepared by adding known volumes of standard solution to the copper targets which had previously been subjected to background counting. The targets employed were identical in material and design to those used in the collection experiments. Volumetric additions were made both by weighing and by use of the ultra precision microburet. ~In the first procedure, the mass of added solution at a measured temperature was determined with a semi-micro balance. Between the initial and final weighings, approximate quantities Of solution (0.025-0.150 ml) were added with a 10 ml buret. During 57 the weighing procedure, the targets were enclosed in weigh— ing bottles for the minimization of evaporation effects. In the second method, precise volumes of standard were added directly to the targets with the microburet. The standards were then dried over phosphorus pentoxide and subjected to the final counting procedure. The corrected observed count- ing rate for a given quantity of an element was obtained by subtracting the initial background rate from the corrected final rate, which was the product of the observed final counts and the ratio of initial to final counts of the con- trol target. The linear calibration data (counts/4 min versus ug of element) were treated by a least squares re- gression, and the slope was employed as the sensitivity factor for analysis. H. Target Collection Technique 1. General Collection Procedures The following procedures were common to all vaporiza— tion experiments. The glass portions of the collection ap— paratus were washed with dilute hydrochloric acid to remove deposits from previous vaporization studies, scrubbed thoroughly with detergent solution, rinsed with distilled water, and allowed to dry in air. The metal target magazine, the copper shutter, and the copper targets were washed with dilute hydrochloric acid, burnished with steel wool, rinsed, and dried with Kimwipes. After their background counts had 58 been determined, the targets were placed in the magazine, the effusion cell was positioned, and the apparatus assembled and evacuated. After the collection apparatus had attained a 10.5 torr residual pressure, liquid nitrogen was added to the magazine dewar, and the orifice to target rim separation was measured with the cathetometer. The effective orifice— target distance was obtained by adding the orifice-rim dis- tance to that from target rim to target face (determined with a micrometer). The effusion cell was heated by induc- tion to the desired temperature and the attainment of thermal equilibrium was determined by repeated temperature measure- ment with an optical pyrometer. At the beginning of an ex- periment, temperature measurements also were made through the wall of the vacuum system, and the induction coil ad- justed such that both halves of the cell were at the same temperature. .After a constant temperature had been attained in the black body cavity;the shutter was opened for the de- sired time interval (measured with a laboratory timer). Temperature measurements were made repeatedly during the ex- posure period. After exposure, the target was ejected, and the procedure repeated at a different temperature. rExposure times varied from 2 min to 2 hr per target. Data points were collected at both successively increasing and decreas— ing temperatures. At the conclusion of some experiments, the target magazine was replaced by an optical window, and the temperatures of the sample and black body cavities were measured over the temperature range. The transmission cor- rection of the optical windows was determined as outlined previously (pf, III. D). 59 2. .Measurement of Orifice Areas The areas of effusion cell orifices were measured both before and after vaporization experiments. Sharp photographs of the orifices were obtained with the bench micrograph by placing the inverted cell lid on the sample stage and employ- ing an external light source above the lid. The areas of the photographed orifices were measured with the compensat- ing polar planimeter. Since a 100x magnification was em— ployed, the true orifice area was 10—4 times the measured value. To verify the accuracy of this procedure, the areas of several circular orifices were also determined by photo- graphing the orifice over the 0.01 mm division micrometer slide, and thereby measuring the orifice diameters directly. The two procedures yielded identical results within the pre- cision of the measurements. 3. -§pecific Experimental Procedures and Conditions In addition to the general procedures described in a pre- vious section (pf. V, H, 1), specific techniques and condi- tions were employed for each system investigated. All measurements involving trieuropium tetraoxide were made with asymmetric molybdenum cells which were charged with 0.4-0.5 g of Eu304 and 0.05—0.10 g Eu203. *Measurements were made in the temperature range 1330-1745° with orifices of 4 4 2 areas 6.7 x 10— . 21.1 X 10-4, and 59.9 x 10- cm . For europium monoxide, both symmetric and asymmetric molybdenum 60 cells (orifice areas 8.0 x 10", 42.5 x 10", and 60.5 x 10.4 cm”) were charged with 0.3-0.4 g EuO and 0.05—0.10 g of Eu304. Collection measurements were made from 1060— 1489°. For europium dibromide, symmetric graphite cells (orifice areas 8.6 x 10-4 and 59.0 x 10-4 cm2) were employed over the temperature range 912-1295°. A crucible was charged with a 0.1-0.2 9 single crystal sample of the di- bromide in the glove box, and the orifice was closed with a drop of paraffin oil before the cell was removed to the collection apparatus, where the oil was pumped off under vacuum. These same graphite cells, when fitted with quartz liners, were employed in the vaporization of trieuropium tetraoxide monobromide. Initial samples of 0.25-0.35 g of Eu304Br and 0.05-0.10 g Eu203 were employed,and measurements were made over the temperature range 925-1327°. On the basis of the initial and final sample weight, vaporization measurements were conducted to approximately 50% of sample depletion for Eu3O4, EuO, and EuBrz, and up to 95% for Eu3O4Br. >I. StiCking Coefficient Experiments Although the sticking behavior of a gaseous lanthanide metal on a cold metal surface had been examined previouslyss, no such experiments have been reported for gaseous halides. To determine the sticking coefficient “rehability) of the dibromide on copper targets, the following apparatus was constructed. A disk (2.38 cm diameter) of 0.2 mm copper 61 sheet in which a centered 6.4 mm diameter hole had been blanked was fitted into a target and its X-ray fluorescence background determined. The disk was then placed in the tar- get magazine in front of a copper target so that the disk rested 2 mm from the target face with its counted side facing the target. If a significant quantity of effusate struck the target, but did not stick, it would presumably be scat- tered and would adhere in measureable quantities on the back of the disk. This experimental design was employed for collection of effusate from Eu304Br at a temperature (1193°) well above the median value of the measurements. The exposure time was adjusted so that the quantity of ef- fusate collected on the target was approximately equal to that normally obtained in the collection measurements. Both the target face and the back side of the disk were analyzed for europium. CHAPTER VI RESULTS A. Results of Preparative Techniques 1. Thefiguropium-Oxygen:§romine System The eight binary and ternary phases observed in the course of this investigation: europium sesquioxide, tri- europium tetraoxide, europium monoxide, europium tribromide, europium dibromide, trieuropium tetraoxide monobromide, europium monoxide monobromide, and trieuropium monoxide tetrabromide, are indicated in the ternary phase diagram of the system (2:. Figure 3). Seven of the phases were ob— tained from the sesquioxide yi§_the preparative procedures described previously. The tie lines indicated in the diagram are related to the vaporization behavior of the phases and will be considered in a later section (pf, VI. D, 6). 2. Results of Additional Preparative and Phase Investi- gations The attempts to prepare europium tribromide by tech— niques other than bromination of the dibromide were unsuc- cessful. The direct combination of europium and bromine 62 Figure 3. Eu 63 The eurOpium-oxygen—bromine phase diagram. 64 yielded pure dibromide, while the reaction of bromoform with the oxide halide produced a mixture of the monoxide mono— bromide and the dibromide. NO evidence for the tribromide was found in either product. Although attempted preparations of additional trivalent europium phases were unsuccessful, a previously unreported europium(II) oxide bromide phase was obtained. Combination of the tribromide and sesquioxide in a EuZOBr4 stoichiometry (marked by a cross in Figure 3) produced a mixture of EuBra and EuOBr. At the maximum temperature of this reaction, the concentration of free bromine vapor in the ampoule was very high, but as the vessel cooled, the bromine reacted completely with the solid phase. The direct oxidation of EuBrz failed to produce any new di- or mixed-valent oxide bromides; only EuOBr was observed. The reaction of the various stoichiometric ratios of EuO and EuBrz (all of which necessarily fall along the dashed line in Figure 3) produced a hexagonal phase. However, powder x-ray diffraction data indicated that EuBrz was present in the products from EuO:EuBrz ratios < 1:2, while a third phase of unknown sym— metry, x, was observed for ratios > 1:2. After the latter ratios were annealed, two distinct portions (dark green and light brown) were observed. The dark green color was char- acteristic of the 1:2 composition, which exhibited only X-ray diffraction lines assignable to the hexagonal phase. a ‘Europium.analysis of the green—colored portion from the 2:3 composition was consistent with the stoichiometry Eu30Br4 (EuO:EuBr2 = 1:2). The identity of phase X was not determined. 65 3. The Hydrated Bromine Phases Europium tribromide hexahydrate and europium dibromide monohydrate were also characterized. The tribromide hexa- hydrate forms white, deliquescent crystals and exhibits the monoclinic symmetry characteristic of other lanthanide tri- halide hexahydratesz°'33. Two successive phases were ob- served upon slow hydrolysis of the dibromide. The first of these exhibited the orthorhombic symmetry (2:. VI, B, 2) incorrectly reported for strontium dibromide. By analogy to the x-ray diffraction data reported for BaBr2°H2084, this phase was identified as europium dibromide monohydrate. The second phase, which resulted from continued hydrolysis of the monohydrate, was the tribromide hexahydrate, which probably formed together with amorphous hydrous oxide and hydrogen. 4. Observed Physical and Chemical Properties of the Binapy and Ternarnyhases Various physical and chemical properties were exhibited by the oxide, bromide, and oxide bromide phases. Trieuropium tetraoxide, a reddish black phase, was stable in air, water, and dilute acetic acid, but reacted at a moderate rate with dilute hydrochloric or nitric acid. Europium monoxide, a brownish-black phase, was stable in air, but reacted rapidly with water to produce hydrous oxide and hydrogen. Europium dibromide formed in clear or white crystals while the tri- bromide formed as a rust-red phase. Both bromides were 66 extremely hydroscopic and reacted violently with water. Trieuropium tetraoxide monobromide, europium monoxide mono- bromide, and trieuropium monoxide tetrabromide exhibited ivory, white, and greenish-black colors, respectively. .While Eu304Br was stable in air, EuOBr reacted slowly and Eu30Br4 reacted rapidly with moisture. The behavior of europium monoxide in the presence of a magnetic field in— dicated that the phase is ferromagnetic. B. ‘Analytical Results 1. Results of Chemical Analysis The results of chemical analyses presented in Table I confirm the existence of the previously mentioned stoichio- metric phases. ‘Except for the values of europium dibromide and tribromide, the data presented were from analyses of the phases employed in the vaporization experiments. For EuBrz, products of ammonium bromide matrix dehydration were analyzed. The error represents the standard deviation of the analyses. 2. -X-Ray Powder Diffraction Results The X-ray powder diffraction data are tabulated in Table II. Except fOr EuBrz, which was also studied by single crystal tehcniques, the structure types and space groups were obtained by consideration of crystal symmetry, lattice con- stants, Molecular formula, and observed extinctions, and by analogy to data reported for both alkaline earth and other lanthanide phases. The lattice constants obtained in this investigation agree within standard error with the values reported previously for Eu3O42'3, Eu02’4. Eu304Br35, and EuOBr36. The interplanar d-spacings 67 Table I: Analytical results. wt% Europium wt% Bromine Compound % Observed % Calculated % Observed % Calculated Eu304 87.62 i 0.35 87.67 __ -_ ‘EuO 90.38 i 0.34 90.47 -- —— 'EuBrz 48.76 i 0.13 48.74 51.29 i 0.35 51.26 EuBr3 38.76 i 0.06 38.80 61.33 i 0.13 61.20 Eu304Br 75.96 i 0.10 76.00 13.38 i 0.15 13.32 EuOBr 61.37 i 0.15 61.31 32.73 i 0.30 32.63 Eu3OBr4 57.42* 57.60 —- -— * one analy31s 68 Table II. Powder diffraction results. Phase Symmetry Lat§ice Constants Structure space or deg. Type Group Eu304 orthorhombic a = 10.089 i 0.009 CaFe204 Pnam = 12.056 i 0.009 c = 3.503 r 0.004 EuO cubic a0: 5.144 f 0.002 NaCl Fm3m EuBrz tetragonal a = 11.574 1 0.006 SrBrz P4/n = 7.098 r 0.005 EuBra orthorhombic a = 9.115 i 0.013 PuBr3 Amam b I 12.662 i 0.017 C = 4.013 t 0.005 Eu3O4Br orthorhombic a = 11.978 i 0.004 -— —— b = 11.858 i 0.003 . C = 4.121 i 0.002 EuOBr tetragonal a = 3.926 i 0.003 PbFCl P4/nmm c = 8.019 f 0.008 Eu30Br4 hexagonal a = 9.825 r 0.004 -- —- C = 7.510 i 0.003 EuBr3-6H20 monoclinic a = 10.025 5 0.008 NdCl3-6H20 P2/n b = 6.757 i 0.005 c = 8.164 f 0.007 B = 93.48 i 0.06 EuBrz'Hzo orthorhombic a = 9.196 r 0.011 BaC12°H20 Pmcn = 11.459 i 0.017 c = 4.291 + 0.005 69 and relative intensites of the diffraction lines of previously unreported phases are listed in Appendices I A - I D. 3. Sipgle Crystal and Density Results The vapor transport technique produced dibromide crystals which were spherically or hemispherically shaped. Under polarized light, these crystals exhibited optical properties consistent with tetragonal symmetry, i;§:_two mutually per- pendicular optically active axes, which were subsequently identified by Weissenberg single crystal techniques as the two-fold axes of the tetragonal structure. The flat side of the hemispherically shaped crystals was thereby determined to be coincident with ( 1 0 0). Oscillation photographs obtained about the optically inactive axis gave a lattice spacing (7.1 A) consistent with the c parameter of the indexed powder data. The equi——inclination Weissenberg photo- graphs (0-3 layers) indicated four—fold symmetry about this axis of rotation. From the indexed h00 reflections, a lat- tice parameter (11.7 R), which is also consistent with the powder results, was obtained. Systematic extinctions (h + k = 2n + 1) were observed only in the hk0 reflections. Even though extinctions in 002 could not be determined from the Weissenberg data, the powder indexing indicates that none is present. Only two space groups; P4/n and P4/nmm (Nos. 85 and 129 respectively), are possible85. However, the results of Sass §t_§l. for strontium dibromide25 suggest that No. 85 is the correct space group. 70 The measured density for europium dibromide of 5.51 g/cm3, in combination with X-ray volume of the unit cell (950.85 83), gives Z = 10.1 molecules/unit cell. An-X-ray density of 5.44 g/cm3 is calculated for Z = 10. Direct reaction of europium monoxide monobromide and europium sesquioxide produced single crystals of the tetra- oxide monobromide phase. Two crystalline forms-—rectangular plates and long needles-awere observed. The platelets, which were of suitable size for single crystal studies, ex- hibited one optically active axis colinear with the long axis of the rectangle. Oscillation and Weissenberg data taken about this axis indicate that it is coincident with the body diagonal of the orthorhombic cell. ~However, the crystal could not be alligned on another axis. C. Results of X-Ray Fluorescence Calibration The external calibration curves for the Eu L81 and Br K01 transitions were linear over the concentration ranges of calibration (0-10 ug for Eu and 0-20 ug for Br). The least squares slope and intercept values of the curves employed in the various measurements are presented in Appendix II A. The same Eu and Br calibration curves were employed for the analysis of EuBr2 and Eu3O4Br condensates. Calibration results for gold are also presented in Appendix II A. These data were collected (22; Appendix II B) in experiments coordinated by the National Bureau of Standards for the purpose of establishing primary vapor pressure standards. 71 D. Vaporization Results 1. The Vaporization Mode of Trieuropium Tetraoxide In the temperature range of the investigation, tri- europium tetraoxide was found to vaporize incongruently ac- cording to equation (VI-1). 3Eu304(s) -—> 4Eu203 (s, monoclinic) + Eu(g). (VI-1) This reaction was confirmed by powder X-ray diffraction data which indicated that only Eu304 and B—Eu203 were pre- sent during the vaporization measurements. NO variation in the diffraction patterns was Observed as a function of bulk composition, and no evidence for crucible interaction was detected. Weight-loss measurements yielded 99.2% of the theoretical change for reaction (VI—1). Mass spectrometric studies also confirmed the reaction, since only masses at- tributable to europium (151 and 153) were observed over most Of the temperature range. ~At the maximum temperature (1700°) a faint spectrum of gaseous europium monoxide was Observed. The relative intensity of Eu(g) to EuO(g) was determined to be j_200 at 1700°. The appearance potential of Euf (5.9 eV) is in agreement with the reported value (5.67 eV)8°. 2. The Vaporization Mode of Europium Monoxide For the temperature range of the measurements, the fol- lowing reaction describes the vaporization mode of europium 72 monoxide. 4EuO(s) > Eu3O4(s) + Eu(g). (VI-2) The X-ray powder diffraction data of vaporization residues were assignable only to EuO and Eu3O4. Both weight loss measurements (99.1% of theoretical) and mass spectrometric results (only primary Eu(g)) confirmed the incongruent vaporization described by equation (VI-2). 3. The Vaporization Mode of Europium Dibromide For europium dibromide, congruent vaporization occurs according to reaction (VI-3). EuBr2(£) > EuBr2(g). (VI-3) X-ray diffraction patterns of the condensed phase were in- variant even after 50% sample depletion. Simultaneous fluorescence analyses for Eu and Br indicated that the collected equilibrium vapor contained a Eu:Br ratio of 1:2, while mass spectrometric analysis of dibromide vapor showed the presence of only monomeric europium dibromide. 4. The Vaporization Mode of Trieuropium Tetraoxide Monobromide In the temperature range investigated, trieuropium tetraoxide monobromide vaporized incongruently according to reaction (VI-4). 3Eu304Br(s) —-9 4Eu203(s, monoclinic) + EuBr2(g) + Br(g).(VI-4) 73 A combination of weight loss and X-ray data indicated that molybdenum, tungsten (with and without quartz liners), and thoria-lined graphite reacted with either the solid or vapor phase, or both. Weight losses of 120% of theoretical were observed for MO and W cells, and the solid residues were contaminated with oxides of the cell material. Weight losses of 110% and 105% were observed for quartz—lined metal and thoria-lined graphite cells, respectively. In the latter case, the solid products were contaminated with ThOZ. However, quartz-lined graphite cells were found to be satis- factory, as 99.4% Of theoretical weight loss for equation (VI—4) was observed. Powder X-ray diffraction analysis of the solid vaporization products indicated the presence of only Eu304Br and Eu203. Although the sesquioxide was principally in monoclinic form, traces of the cubic phase were observed. Mass spectrometric analysis of the effusate indicated the presence of Br+ (masses 79,81), EuBr+ (masses 230, 232, 234), Eu+ (masses 151, 153),EuBr2+ (masses 309, 311, 313, 315) and Br2+ (masses 158, 160, 162) in the rela- tive intensities of 1000:100:50:15:5, respectively. The relative intensities of the europium containing species are consistent with the fragmentation pattern observed for EuC12 vapor (EuCl+ : Eu+ : EuC12+ = 100 : 46 : 12)37. The ap- pearance potential measured for EuBr+ (10.4 eV) is consistent with that observed for EuCl+ (10.3 ev)87. In addition, X-ray and chemical analyses of the effusate Obtained in the total collection experiments confirmed that europium dibrom- ide was a vapor species. 74 The results of the various techniques indicate both a Eu:Br ratio of 1:3 and the presence of molecular EuBr2(g) in the equilibrium vapor, but the data do not indicate whether the equilibrium bromine species is the monatomic or the diatomic gas, i;g; should equation (VI-4) have 1/2 Br2(g) or Br(g) as the vaporization product. However, this difficulty may be resolved by consideration of the dissociation equation (VI-5). 1/2 Br2(g) > Br(g). (VI-5) If a is defined as the fraction of dissociation, the partial pressures of the two species (PBr and PBr) may be expressed 2 in terms of the total bromine pressure Pt as follows: PBr2 = [(1 - o)/(1 + a)]Pt. (VI—6) PBr = [Za/(l + 0)]Pt. (VI-7) Substitution of these partial pressure into the expression for the equilibrium constant of the dissociation reaction gives equation (VI-8). l/2 K(VI-5) = Zlet/(l - d2)] . (VI-3) While values for K(VI-5) are readily available69, the mag- nitude of Pt must be estimated from experimental data. The bromine pressure may be Obtained from the europium di- bromide equilibrium by employing the Knudsen equation (III-6) for these vapor species as follows. 75 PEuBr2 = (3.76 X 10_4/SOt)(TMEuBr2)1/2(W/M)EuBr2° (VI-9) PBr = (3'760 X 10‘4/Sot)(TMBr)yg(W/M)Br. (VI-10) If monatomic bromine is produced, the stoichiometry of reac- tion (VI-4) requires that the ratio of moles of EuBrz, (w/M)EuBr2’ to moles or Br, (W/M)Br be unity. Con81deratlon of this requirement and of equations (VI-9) and (VI-10), yields PBr 1n terms of PEuBr2° 1/ PBr PEuBr2(MBr/MEuBr2) 0°50626 PEuBrz' ( I 11) By similar arguments, the analogous expression for the pro- duction of one—half mole of Br2(g) in equation (VI-4) is: p = 0.502 (M 1/2 _ Bra EuBrz /MEuBr2) _ 0'35798 P .(VI-12) Brz EuBrz Therefore, from equations (VI-11) and (VI-12) the total bromine pressure is always of the order of magnitude of the europium dibromide pressure, and experimental values for PEuBrz (9:. VI, F) may be substituted for Pt 1n relatlon- ' _ 0 _. _—__ = shlp (v1 8). At 1600 K, (K(VI 5) 0-496 and PEuBr2 6 x 10-4 atm), a equals 0.995. At the low measurement temperatures (1200°K), K(VI-5) is 0.042, P 7 EuBrz equals 8 x 10- atm, and a is calculated to be 0.999. On the basis of these results, equation (VI-4) adequately describes the incongruent vaporization of Eu304Br. Apparently, the Br2(g) observed in the mass spectrum originated from reac— tion of the monomeric vapor in the mass spectrometer. It should also be noted that the observed relative intensity of Br(g) is more indicative of the bromine pressure in the source region of the mass spectrometer than in the Knudsen cell. 76 5. The Vaporization Mode of Europium Monoxide Monobromide The results of the collection experiment indicated that europium monoxide monobromide vaporizes incongruently according to equation (VI-13). 4EuOBr(s) > Eu304Br(s) + EuBr2(g) + Br(g). (VI-13) X-ray analysis indicated that the solid residue consisted of EuOBr and Eu304Br and that the condensed effusate was the dibromide. By analogy to Eu304Br (pf. VI, D, 4), mon— atomic bromine is assumed to be the second equilibrium vapor species. 6. Pressure—Composition Diagrams In accordance with a previous discussion (2;. III, A. 2, c), the results of vaporization studies may be presented qualitatiVely by a pressure-composition phase diagram. The results of the vaporization investigations are given in Figures 4-6. For the europium-oxygen system, Figure 4 indicates that EuO(s) loses metal vapor to form Eu304(s), which in turn loses gaseous europium to produce congruently vaporizing Eu203(s)15. Likewise, in Figure 5, europium tribromide is seen to lose bromine vapor to form the con- gruently vaporizing dibromide. The existence of the EuBr3- EuBra equilibrium is evidenced by the preparative results; .igg; EuBrz forms at high temperature and low bromine pres— sure, while EuBr3 may be prepared only at relatively low 77 Figure 4. The europium—oxygen pressure—composition phase diagram. E00,,(s) EuO(s) Euzp4(s)E0203(s) Equ(s) + EuO(s) EuO(s) Eusz) + + Eu304 (s) £02036) 2 EuO(s) + Vapor 3 fl 2 E OH + v b u s a L 3 ‘ opor g I .2 \ \\ E0203“) + Vapor n l I l l l 1‘ F__ 0 0.25 0.50 0.75 l.00 [25 I50 (I) 0/Eu Raflo 3/69 78 Figure 5. The eurOpium-bromine pressure-comp081tlon phase diagram. Bra“) EuBr3(s) EuBr2(S) 8'2“) + EuBr3(8) EuBr3(s) + 5085(3) + Vapor EuBrzh) EuBrz(s) + Vapor -_ _ _ _/\/_ 1 1 p l l‘, 0 0.25 0.50 (D Eu/Br Ratio Total Pressure Figure 6. The europium sesquioxide—europium tribromide pseudobinary pressure-composition phase diagram. EuOBr(s) EUSO‘BNS) £02043) EuOBr(s) + EuOBr(s) + Eu3O4Br(s) E0304Br (s) Vapor + Eu,0,8r(s) + Vapor Eu¢O,(s) Toto! Pressure 60103“) + Vapor 1 l l w 2.0 3.0 4.0 V 00 0 Lo . Eu203/Eu8r3 Ra h o 79 temperatures and high bromine pressures. Although phases are not indicated between the di- and tribromide composi~ tions (pf, Figure 5), they are to be anticipated by analogy to the samarium-fluorine system 7%, Figure 6 is a pseudo- binary section of the ternary diagram (pg, VI, A, 1. Figure 3) along the composition line intersecting all stoichiometric phases of trivalent europium. The diagram is treated as a two-component system of Eu203 and EuBr3, and the results are seen to be directly analogous to those of the europium-oxygen binary in that Eu203 is the terminal, congruently vaporizing phase resulting from a series of incongruent vaporizations. Although it is not indicated in the diagram, the vapor phase contains EuBr2(g), the vapor species of the other congruently vaporizing phase. The entire vaporization scheme is indicated by the tie lines in Figure 3. The vaporization products of any condensed phase other than congruently vaporizing Eu203 and EuBrz are indicated by following the tie lines originating at the vaporizing composition. The condensed vaporization product is obtained by following the direction of the arrow to the next composition, while the gaseous vaporization product(s) is/are found at the terminuses of all other lines originat- ing at the vaporizing composition. E. Results of Sticking Coefficient Measurements Results of the bouncing experiment indicate that the sticking coefficient of gaseous EuBrz on liquid-nitrogen— cooled copper targets is nominally unity. The quantity of 80 effusate collected on the target, the lack of any detectable concentration of europium on the back of the disk, and the estimated lower detectable limit of analysis indicate that the sticking coefficient 3.0.95. The measured data have therefore not been corrected. F. Vapor Pressure Equations The temperature and corresponding equilibrium vapor pressure values determined for reactions (VI—1)-(VI-4), are presented in Appendices III A-D, and the least squares equa- tions are presented in Figures 7-10. Since the temperature dependence of only the europium dibromide pressure was determined for equation (VI-4) (Eu304Br vaporization), the least squares equation in Figure 10 does not directly yield second law results for the reaction. The pressure equation (42 independent measurements) for gaseous europium in equi- librium with the tetraoxide and sesquioxide is: log PEu(VI'1) = -(1.8832 1 0.0320 x 104/T) + 6.161 a 0.180, VI-14) for 1604 < T < 2016°K. The equation (34.measurements) for the pressure of gaseous europium in equilibrium with the monoxide and the tetraoxide in the temperature range 1334 < T < 1758°K follows: log pEu(v1-2) = 4(1.6589 r 0.0205 x 104/T) + 6.263 avg;124. The pressure of gaseous europium dibromide (36 data points) in equilibrium with the liquid dibromide for 1185 < T < 1568°K 81 Figure 7. The pressure of Eu(g) in equilibrium with Eu304(s) and Eu203(s), 3.0 4.0 S d3 0 $ 5.0 6.0 _ 82 Figure 8. The pressure of Eu(g) in equilibrium with EuO(s) and Eu304(s). _ u— .— d d - 3.0. .._. 1‘" o I Sf E Mo) am 0 "' LOG (i£)___ ENJN' 8 $5 9300 l 1 1 l l 5.6 6.0 6.4 6.8 7.2 76 I / T x I04 6/68 83 Figure 9. The pressure of EuBr2(g) in equilibrium with EuBr2(£). I T l ' l 3.0,_ __ S — -I ;~4.0_ __ Q? 0 o _ I-1 .1 5.0- ._ RUN Eu Br — ;: z. z - 33 a i 6.0- _. l 1 l . l 6.5 7.5 8.5 '/TX '04 3/69 84 The pressure of EuBr2(g) in equilibrium with Figure 10. Eu304Br(s), Eu203(s) and Br(g). 3.0... (9) atm P (D I 2 “L06 PEuBr .U' C) I 6.0 .— l n l n I 7 5 8.5 6.5 4. l/ T x '0 3/69 85 is given by EuBr (VI-3) = -(1.2733 i 0.0166 x 104/T)+5,032 i 0.123. 2 (VI-16) log P The pressure of europium dibromide (48 measurements) in equi- librium with trieuropium tetraoxide monobromide, europium sesquioxide, and gaseous monatomic bromine in the tempera- ture range 1198 < T < 1600°K is: (VI-4) = —(1.4098 i 0.0172 x 104/T)+5.699 r 0.125. log P EuBr2 (VI-17) G. Thermodynamic Values'Employed in Data Reduction 1. Heat gapcaitquEpthalpy, and Entropy Functions a. Literature Values Measured values were available for Eu203(s)14, Eu(g)88, and Br(g)°9, while estimated functions were employed for EuBr2(s,£)29v31. Values for (H; - H298) and (s; - $398) for the dibromide were obtained by graphical interpolation of the tabulated estimates. b. Approximate Values for Solid Phases lFor the remainder of the condensed phases encountered in this investigation, the heat capacity, enthalpy, and entropy functions were approximated. The heat capacity data for monoclinic Eu203(s)14 and equations (III-29), (III-30), (III—33), and (III-34) were employed to Obtain 0 0 0 . Cp. (HT - H398)’and (ST - $298) equat1ons for Eu3O4(s), 86 EuO(s), Eu3O4Br(s), and EuOBr(s) in the following forms: 3 Cp = a + b x 10- T, (VI-18) 0 o _ -3 2 (HT - H298) _ aT + (b/2) x 10 T - C. (VI-19) (sT - 3398) = a 1n T + b x 10-3T - d. (VI-20) The values of a, b, c, and d for the respective phases are listed in Appendix IVA. c. Approximated Values for Gaseous Phases Europium dibromide is the only gaseous species for which heat capacity, enthalpy, and entropy data are not available. Therefore, in light of the previously discussed trends of metal dibromides (pf, III, E, 4, a, (2)), only the molecular symmetry need be specified for approximation Of these functions. In the molecular beam deflection ex— periments of Buechler, et al.§9 gaseous dihalides of the alkaline earths were found to be both bent (Can and SrClz) and linear (CaClz). On the assumption that a trend, which is apparently dependent upon the cation—anion ratio, con- tinues, strontium and europium dibromides should exhibit linear structures. Therefore the experimental data for gaseous mercuric dibromide69 were selected for the europium species. 87 2. Absolute Entropies a. Approximated Values for Solids In the absence of experimental values, the standard entropies of all the condensed phases were approximated using equations (III-31) and (III-32). Westrum's approxi- mated entropy values17 for Eu203(s) (35.0 eu) and for the lattice contributions to the binary europium oxides (Eu, 14.1 eu; O in Eu3O4, -1 eu; O in EuO, -2 en) were used, while Latimer's71 lattice values (Eu, 14.1 eu; O, 0.5 eu; Br, 10.9 eu) were employed in estimations for oxide bromide phases. The magnetic contributions used for Eu(III) (3.5 eu) and Eu(II)(4.2 eu) were those recommended by Westrum 1%. The results of theSe entropy approximations also appear in Appendix IVA. b. Entropy Values for Gaseous Species Although entropy data are available for Eu(g)88 and Br(g)69, no value appears for EuBr2(g). Therefore, the estimated free energy functions at 298°K for linear gaseous dibromides7° were employed in an entropy approximation. ~Since 8:98 is equal to -fef398 (pf, equation III-22), an estimated value for EuBrz (74.2 eu) was Obtained by graph- ical interpolation according to molecular weight between the fef values for ZnBrz (-67.66 eu), CdBr2(—73.56) and HgBrz (-76.31 eu). Although the $393 value was 2.2 an lower than that for HgBrz, inclusion of a magnetic contri- bution for Eu(II) increased the final estimate to 88 approximately that of the mercury species. Therefore, the entropy value employed for EuBr2(g) (76.3 eu) is that given for HgBr2(g) 69. 3. Free Energy Functions )88 and Free energy functions are available for Eu(s,£,g Br(g)59, but the values for the remainder of the phases were calculated according to equation (III-22) from the experi- mental and approximated data described in sections (VI, G, 1) and (VI, G, 2). The (H; - 3398), (s; - $398), and fef values in the temperature ranges of the measurements are listed in Appendix IVB for Eu203(s), Eu304(s), EuO(s), EuBr2(s,£), Eu3O4Br(s), and EuOBr(s). For reasons which will be dis-, cussed (3:. VII. E, 2), the fef values for EuO(s) were calcu- lated using 8398 = 15.0 eu instead of the estimated 16.3 eu. »Since the estimated heat capacity and standard entropy data for EuBr2(g) are identical to those Of the mercury species, the published fef values for HgBr2(g)69 were employed. ‘The free energy function changes for the various vapor- ization reactions, (VI-1 - VI-4) and (VI-13), were calculated from available°9o88 and estimated (Appendix VIB) functions employing relationship (III—23). These values for Afef of the reactions are listed for the temperature ranges of the measurements in Appendix IVC. Values for Afef at specific intermediate temperatures were obtained by graphical inter- polation of these data. 89 4. Additional Thermochemical Values The additional thermochemical data which were employed in the data reduction (AHO, AGO, 8°, and Do values at 298°K) appear with their sources in Appendix IVD. However, the entropy and free energy of Eu203(s) were estimated as fol— lows. Combination of the 8298 values of Eu(s)88 and 03(9)69 with the estimated entropy of Eu203(s)17 via re- lationship (III-28) yields 28% 298 of Eu203(s) of -77.1 eu. When this value is combined with AH; 298 of Eu203(s) (—393.9 0 kcal/gfw)12, an approximated AG for Eu203(s) of -370.9 f 298 kcal/gfw results. H. Thermodynamic Results 1. Treatment of Trieuropium Tetraoxide Data The least squares pressure equation (VI-14) was employed with relationships (III—11) and (III-12) to give the enthalpy and entropy of vaporization of Eu3O4(s) as follows: 532810 = 86.2 r 1.4 kcal/gfw, and A398,, e 28.20 i 0.82 eu. Reduction of these values to 298°K with the aid of (H; - H398) and (8% - 8298) data (2;, Reference 88 and Ap- pendix IVB) and relationships (III-17) and (III-18) yielded A3298 = 93.5 i 2.5 kcal/gfw and A8298 = 39.4 i 1.7 eu. A value of AGggs = 81.7 i 2.5 kcal/gfw was thereby obtained. From the temperature-pressure data (9;, Appendix IIIA), the corresponding Afef values (pf, Appendix IVC), and equation (III-25), a third law value of 53398 = 92.28 i 0.56 kcal/gfw was obtained (9;, Appendix IIIA). 90 The energetics Of formation of Eu304(s) were Obtained from the second law results. The enthalpy change for re- action (VI-1) was combined with data listed in Appendix IVD according to relationship (III-27) to yield AH; 298 Eu304(s) : -542.4 i 3.6 kcal/gfw. The error limit was obtained gig equation (III-35) by combination of the estimated error in data reduction with the 2.6 kcal discrepancy in the measured enthalpies Of formation of Eu203(s)12.13. .Substitution of the free energy of vaporization and the necessary free energy of formation values from Appendix IVD into equation 0 f 293 of Eu3O4(s) = —510.4 f 3.6 kcal/gfw. (III-27) gives AG An 8293 Eu304(s) value of 48.6 i 2.6 eu resulted from use of the entropy of vaporization and the entropies of Eu303(s) and Eu(g) (pf, Appendix IVD) in relationship (III-20). The quoted error includes a 2.0 eu uncertainty in the Eu203 value. 2. Treatment of Europium Monoxide Data From equation (VI-15), which represents the pressure of europium for reaction (VI—2), the following enthalpy and entropy of vaporization at the median temperature (1546°K) were Obtained: AH2546 = 75.91 i 0.94 kcal/gfw and A83543 = 28.63 i 0.61 eu. By use of tabulated enthalpy and entropy data (pf, Reference 88 and Appendix IVB). these values were reduced (3:. equations (III—17) and (III-18)) to 298°K and yielded 833.. = 80.3 r 2.0 kcal/gfw, 88398 = 33.9 r 1.3 eu, and AGggs = 70.2 i 2.0 kcal/gfw. The measured 91 temperatures and pressures (pf, Appendix IIIB) , the calcu- lated Afef values (pf, Appendix IVC), and equation (III-25) were employed to give the third law'value of 53398 = 80.00 i 0.42 kcal/gfw. NO noticeable temperature trend was observed in the results (2;, Appendix IIIB). The energetics Of formation and the standard entropy were calculated from the second law data with the aid of the Eu304(s) results (2;, VI, H, 1), the data listed in Appendix IVD, and relationships (III-27) and (III-20). -These values are: AH; EuO(s) = —145.2 i 4.1 kcal/gfw, 298' AG; 298 EuO(s) = -136.6 i 4.1 kcal/gfw, and $398 EuO(s) = 15.0 i 3.0 eu. The second law result for Eu3O4(s) (48.6 eu) was employed in the calculation of the standard entropy value. 3. Treatment of_§urppium Dibromide Data The results of the vaporization of liquid europium di- bromide according to reaction (VI-3) were treated in the following way. From the pressure equation (VI—16) (median temperature, 1377°K), values of AH3377 - 58.27 i 0.76 ,kcal/gfw and 58237, = 23.03 i 0.56 eu were obtained, and were reduced to 298°K with data for EuBr2(s,z) (sf, Ap- pendix IVB), that of HgBr2(g)69 (pf, VI, G, 1, C), and relationships (III-17) and (III-18). For the vaporization of EuBr2(s) 23398 = 71.4 i 2.7 kcal/gfw and A8398 = 36.8 i 2.8 eu. The estimated errors were calculated by assuming an error of i20% in the reduction to 298°K. 92 Combination of the measured data and the free energy changes (Appendices IIIC and IVC) yielded a third law 38298 = 69.54 i 0.40 kcal/gfw with no temperature trend in the values (5;. Appendix IIIC) . The energetics of formation were calculated as follows. Combination of the enthalpies of formation of Eu(g)88 and Br(g)69 and the dissociation energy estimated for EuBr33°, gives an estimated AH; 298 EuBr2(g) of -106.6 kcal/gfw. If this value is combined with the enthalpy of vaporization, 0 AHf 298' EuBr2(s) = -178.0 E 3.0 kcal/gfw is obtained. The second law absolute entropy of the dibromide was obtained from the entropy of vaporization, the entropy of EuBr2(g) (pf, Appendix IVA) and relationship (III-20). The resulting value, 8298 EuBr2(s) = 39.5 i 3.0 eu, was subsequently com- bined with the entropies of Eu(s) and Br2(£) (pf, Appendix IVD) in relationship (III-28) to give A82 298 EuBr2(s) = —16.2 i 3.0 eu. From the enthalpy and entropy of formation, 0 AGf 298 EuBr2(s) = -173.2 1 3.0 kcal/gfw was obtained. In addition, 25% 298 EuBr2(g) = 20.6 eu was calculated from ,AS EuBr2(s) and the entropy of vaporization. When 0 f 298 this latter value was combined with the estimated enthalpy 0 f 298 EuBr2(g) = of formation an approximate value of AG -112.8 kcal/gfw was obtained. By extrapolation of pressure equation (VI-16) to one atmosphere, the normal boiling point of EuBr2(£) was calcu- lated to be 2530 i 35°K. The (H; - H398) data for EuBr2(£)31 were graphically extrapolated beyond 1500°K by utilizing 93 the trend established by BBr3(£) data31 to obtain estimated enthalpy functions at 20000 and 2500°K (42 and 49 kcal/gfw, resPectively). From these values, an enthalpy of vaporiza- tion at 2530°K (AH: EuBr2(£) = 52.0 i 3.0 kcal/gfw) was calculated. .Since at the boiling point As: = Aflg/Tb, an entropy of vaporization of As: = 20.6 i 1.9 eu was obtained. 4. Treatment of Trieuropium Tetraoxide Monobromide Data Unlike the previously treated vaporization reactions in which only one gaseous species was observed, the vapori- zation of trieuropium tetraoxide monobromide according to reaction (VI-4) involves two vapor species (EuBr2(g) and Br(g)). However, the equilibrium data described by equation (VI-17) (median temperature 1399°K) give only the dibromide pressure. The equilibrium pressure Of Br(g) was calculated from the dibromide equation by relationship (VI-11) and substituted into the equilibrium constant for the vaporiza- tion reaction to give: K(VI-4) = 0.50626(P )2, or (VI—21) EuBr2 log K(VI-4) = 210g pEuBr2 - 0.29557. (VI-22) By substitution of equation (VI-17) into (VI-22) the tempera- ture dependence (1198° < T s 1600°K) of the equilibrium constant was calculated as: log K(VI-4) = -(2.8195 i 0.0243 x 104/T) +11.101 i(0.177S VI-23 94 For reaction (VI-4), AH2399 = 129.0 i 1.1 kcal/gfw and 052399 = 50.81 i 0.81 eu were Obtained. These results were reduced to 298°K with necessary data (3;, Appendix IVB, Reference 69, and relationships (III-17) and (III—18)), to give 832.. = 137.6 i 2.0 kcal/gfw, AS398 = 64.7 i 2.9 eu, and 33398 = 118.3 f 2.0 kcal/gfw. Point by point substitution of the log P values (pf, Appendix IIID) into relation- EuBrz ship (VI-22) and subsequent combination with Afef values for the reaction (pf, Appendix IVC) and relationship (III—25), yielded a third law AHggs = 139.47 r 0.92 kcal/gfw. .Analysis of the third law values (Appendix IIID) revealed no ap- parent temperature trend. Combination of the second law enthalpy change with the enthalpy of formation of Eu203(s)12, Br(g)°9, and EuBr2(g) (pf, VI, H, 3; Appendix IVD) and relationship (III-27) yielded AH; 298 Eu304Br(s) 3 -597.7 f 5.1 kcal/gfw. Again, the indicated error includes the 2.6 kcal discrepancy in the measured enthalpies of the sesquioxide12.13. Use of the free energy of vaporization and the free energies of formation of the products in equation (III-27) gave AG; 298 Eu304Br(s) = -565.0 i 5.1 kcal/gfw. The entropy of vaporization was combined with necessary data (2;..Appendix IVD and Reference 69) according to equation (III-20) to yield 8:93 Eu304Br(s) = 64.5 i 3.1 eu. 95 5. ,Estimation of Thermodynamic Data for Europium Monoxide Monobromide (Although the vaporization reaction for europium monoxide monobromide (3;. equation (VI-13)) has been determined, no equilibrium pressure measurements have been made; however, combination of thermodynamic arguments and vaporization data from europium dibromide and trieuropium tetraoxide mono- bromide allows estimation of the equilibrium pressure equa- tion for the vaporization, and hence, estimation of thermo- dynamic values for EuOBr(s). The activity of EuBr2(g), igg, its pressure, must be less than that in equilibrium with the condensed EuBr2 phase, but greater than that in equilibrium with Eu304Br(s). Knowledge about the entropy of the vapori- zation reaction when combined with these pressure limits, allows estimation of a pressure equation. Since the vapori- zation reactions of both Eu3O4Br(s) and EuOBr(s) involve 0 T' should be approximately equal to As; Eu304Br(s). An alter- two solid phases and identical vapor species, AS EuOBr(s) nate approach involves estimation of the entropy Of vapori- zation at 298°K from approximated values of the standard entropies Of reactants and products (pf, Appendix IVA) gig relationship (III-19). If the A8398 value so Obtained (65.92 eu) is corrected to the median temperature (14000K) of the EuBr2 and Eu304Br vaporization measurements with the aid of tabulated data (pf, Appendix IVB, and Reference 69), a Asg4oo = 56.65 eu is obtained. When this entropy Change is converted into an intercept term, its value (5.89) agrees 96 with that observed for the Eu304Br vaporization (5.699). -If an intermediate pressure selected from equations (VI-16) and (VI-17) is combined with the estimated intercept, the following pressure equation is obtained. log 9 (IV-13) = —(1.403 x 104/T) + 5.89. (VI—24) EUBI‘Z When this equation is treated in a manner directly an- alogous to that employed for Eu304Br(s) (3;, VI, H, 4), the following values are obtained for the enthalpy of vaporization: 852,00 = 128.5 kcal/gfw and AHggs = 135.5 kcal/gfw. Substitution of the approximated enthalpy change at 298°K and the enthalpies of formation of the products of equation (VI—13) (pf, VI, H, 4) into relationship (III-27) gives AH; 298 EuOBr(s) = -203.3 f 6.5 kcal/gfw. The error reflects the deviations in the enthalpies of formation of Eu304Br(s) (i5.1 kcal) and EuBr2(g) ($3.1 kcal), and the difference in enthalpies of formation calculated for EuOBr(s) using the slopes of the EuBr2(£) and Eu304Br(s) pressure equations (pf, equations (VI-16) and (VI-17)) as limiting values for obtaining the enthalpy of vaporization of EuOBr. . . 0 _ 0 For the EuBr2(£) 11m1t, AH298 - 123.5 kcal/gfw and AHf 298 3EuOBr(s) = -200.2 kcal/gfw, while for the Eu304Br(s) 0 o _ boundary, on... = 136.0 kcal/gfw, and AHf 293 - -203.4 kcal/gfw. The small difference in the enthalpies of forma- tion (3.2]«al/gfw) arises because of the large value of Vj (equation III-27). From the estimated 08398 of 97 vaporization and free energies of formation of the vaporiza- 0 tion products, AGf EuOBr(s) = -193.4 f 6.5 kcal/gfw. 298 6. Compilation of Thermodynamic Results The thermodynamic results obtained in the preceeding calculations are tabulated for median vaporization tempera- tures in Table III and for 298°K in Table IV. Estimated values appear in parentheses. In Table V, thermodynamic values at the boiling point of europium dibromide are presented. 98 Anm.oov An.mmav Aooeav AmHIH>V Anvumosm Hmo a Hmoo H.H a o.oma some Awue>v Ahvaneoosm on.o a ao.mm as.o hem.oo heme Anna>v Amvaumsm Ho.o a oo.mm .o.o hao.os own“ AmnH>v Anvosm am.o a o~.om ..H n a.om came AauH>v Amv.0nsm so 3mm Hmux mm>9v A mm>9 v Axev coauommm wmmnm om< and B GMHCOS sOwumuflnomm> .musumummfimu usaEmHSmMOE GMHUOE um muadmmn GOHDMNHHOQM> Baa Usoowm. .HHH wanna 99 a.H a o.om o.m a o.no on 5 cans > > D Asmv 6mg A3mm\amoxv and 3ma can Azev B .ocaom msaeaoa on» no moaaoun rat Esflmonsm UHSUAH How muHSmmH OHEmcmpOsumna .> wanna Am.nHHv Ao.ooev Am.osv -u- -n- nu- onanmsm Aa.o a..moav Aa.o an.nomv Ao.omv Amo.oov -r- An.ooav Anvumosm a.n ao.noo a.n as.aoo a.m “3.36 o.m as.so aozo esv.ona o.m Ho.sma onum4055m o.m ha.msa o.m a o.wsa o.m en.om o.m ao.om oe.o heo.oo s.m a..as Ahvanmsm a.c no.oma a.c Ha.oca o.m Ho.oa a.a no.mm av.o noo.om o.m ho.om Anvosm o.n a..oan 6.» u..mco o.m no.wv ..H a..om on.o www.mo a.m an.mm Anveoasm A3mm\amoxv A3mm\amuxv Asmv msov A3m0\amoxv Azmm\amuxv .m m m> mm> mm> soon one- on one one one whose 3ma 5mm, Spa CGN .Meme an muadmmu UHEmsmposnmze .>H.wanme CHAPTER VII DISCUSSION A. The Phase Diagram 1. Phases in thp_§uropium—Oxyqepggromine System A general formula was given (Sf. III, A, 1) for all possible stoichiometric oxide, bromide, and oxide bromide phases of europium; however, few of these have been Observed (2;. VI. A, 1 and Figure 3). Several interesting observa- tions are evident in the preparative results. All the anticipated phases in the ternary system must fall on or between the lines connecting EuO with EuBrz and Eu203 with EuBr3. Of the eight phases observed, only one composition, Eu304, falls between the limiting lines, iggL, contains both di- and trivalent europium. This observation is not meant to imply that mixed valent bromides and oxide bromides are nonexistent, but, instead, indicates that the mixed- valent region of the phase diagram.has not been investigated. Only the europium-oxygen binary and the ternary section for trivalent europium, igg;, stoichiometries on the line con- necting Eu203 and EuBr3, have been investigated thoroughly. The present vaporization studies have transversed the Eu-O binary from EuO to Eu203 and most of the trivalent, ternary 100 1 ill III)! III! III .III I I) )I l [‘5' ll .1] III) II [III 1' 101 line. The region from EuBr3 to EuOBr has been investigated by combination of the 4:1 (tribromide to sesquioxide) stoi- chiometry, which yielded a mixture of EuOBr and EuBra. Therefore, the existence of a europium analog of the LnZOBr4 phases which were observed thermogravimetrically for the heavy lanthanides (Gd-Lu)19 is doubtful. Compositions along the divalent line have been only partly investigated,and the results suggest that phases other than Eu30Br4 exist. No attempt has been made to prepare mixed-valent oxide bromides, which could probably be attained by reacting EuBra-Eugoa, EuBra-EuO, EuBrz-Eu304, or EuBra—Eu304 mixtures. 2. Discrepancies Between the Present Results and the Literature a. On the Crystal Structure of Europium Dibromide One unsuccessful attempt22 (5;, II. B, 1, a) to char- acterize the crystal structure of europium dibromide appears in the literature. In addition, an incorrect crystal sym- metry (orthorhombic) is listed for the phase in a recent review of the lanthanide halides9°. Obviously the measure— ment for strontium dibromide monohydrate is the source of this error, but propagation of this inaccuracy only compli— cates and hinders further investigation. The present powder and single crystal X-ray diffraction data indicate that the tetragonal structure recently described for strontium di- bromide35, which is isostructural with EuBrz, is correct. The diffraction pattern reported by Doell and Klemm22 agrees 102 with that observed for the tetragonal phase and suggests that they indeed prepared the pure dibromide. Since pure samples of europium dibromide monohydrate were not Obtained, the X-ray diffractlon results were employed for its identification. Sass et al.25 analyzed a sample of strontium dibromide monohydrate and Suggested that it was the phase examined by Kammermans23. The structure reported for the barium dichloride and dibromide monohydrates84 displays the same symmetry, space group, systematic extinc- tions, number of molecules per unit cell,and heavy atom (metal and halide) coordinates as the structure described by Kammermans. Since the X-ray data for the initial hydrol- ysis products of europium dibromide also exhibit the same symmetry and systematic extinctions as these alkaline earth dihalide monohydrates, the phase is obviously the dibromidev monohydrate. b. On the Preparation of Europium Tribromide and Tri— iodide Although attainment of europium tribromide by direct dehydration of the tribromide hexahydrates19r2° would not be expected to be a useful preparative procedure, dehydra- tion of an ammonium bromide—tribromide hexahydrate matrix18 would appear feasible. However, numerous attempts to repeat the latter technique were unsuccessful. In every case, the products exhibited the same physical characteristics (light grey color and clear water solution) described by Taylor 103 and Carter, but chemical analysis (2:. Table I) clearly in- dicated the dibromide composition. In addition, the products were all isostructural with strontium dibromide. -Since the europium dibromide product obtained by vapor transport (vacuum reduction)ues clear and white, the greyish color apparently arose from minor contamination by the incompletely reduced, chocolate-colored phase of unknown composition Ob- served by Doell and Klemm21. Although the tribromide was successfully prepared at temperatures of 110° and 12 atm of bromine, the product was not attained at 60° and 1 atm. Therefore, preparation of the phase by the matrix technique under vacuum at high temperatures (350°) is most unlikely. This observed thermal instability of the tribromide is entirely consistent with the estimated free energies of formation of the di— and trihalides31. ~Although the tri- bromide is more stable than the dibromide at room tempera- ture, the free energy curves cross at approximately 110- 115°. Above the crossover temperature, the dibromide be- comes increasingly more stable than the tribromide, and in the absence of a high bromine pressure, preparative attempts have little chance of success. The free energy estimates for the europium iodine sys- tem31 indicate that the diiodide is 17 kcal/gfw more stable than the triiodide at 25°. This approximation is also con- sistent with the results of Asprey 2E_§l,91 who were unable to prepare europium triiodide under rigorous conditions (Eu metal under 100 atm I2 at 600°). 104 As with the crystallographic data, much of the reference material on the lanthanide halides is filled with sweeping generalities which do not apply to those elements, europium in particular, which exhibit divalent Character. The impli- cation is given that all LnX3 phases are readily prepared. For example, the preparative method suggested by Cotton and Wilkinson24 for EuBrz or EuIz is the thermal decomposition of the trihalide. Because of the stringent conditions necessary to attain even the tribromide, any previously re— ported preparation of the triiodide must be questioned. C. On the Composition of the Hexagonal Oxide Bromide Previous discussions of the structures of europium phases have indicated that the chemistry of europium is Often very similar to that of the heavier alkaline earth elements (Ca, Sr, Ba). The hexagonal oxide bromide phase appears to be isostructural with a phase recently reported for the oxide halides of strontium and barium92.93. The lattice constants for the europium phase (a = 9.825 i 0.001 R, c = 7.510 r 0.004 R) are almost identical to those reported for the strontium analog (a = 9.82 i 0.01 A , c = 7.51 i 0.01 R), for which a composition (M4OX6), apparently based on miscibility observations and X-ray data, is given. In the present investigation excess dibromide is found in the Eu0:53EuBr2 product. The analytical data are also consis- tent with the Eu30Br4 composition. 105 3. The Stabilities of Phases a. Elucidation of the Vaporization Process Examination of the vaporization reactions observed in the europium-oxygen-bromine system suggests definite trends in the modes of vaporization for the different phases. Of the various factors determining the mode of vaporization, Gilles44 lists first the stability of the gaseous species and second that of the condensed phase. These factors are readily applicable to the present system, but possibly in reverse order of importance. The stability of the sesqui- oxide is apparently the overriding factor in the vaporiza- tion of all oxygen containing phases, while that of the dibromide appears to determine the vaporization mode of the europium-bromine binary system. Obviously the stabilities of gaseous europium and europium dibromide are also of im- portance, but to a lesser extent. For all the oxides or oxide bromides, the flow of reaction is successively toward a more oxygen-rich condensed phase, until the congruently vaporizing sesquioxide is obtained. Likewise, in the Eu-Br binary, the stoichiometry shifts to that of the congruently vaporizing dibromide. In each case, the stoichiometry of the vapor is fixed by the composition change of the solid phase. For the oxide bromides, the stability of gaseous di- bromide determines that the dibromide and bromine vapor species are observed instead of the gaseous tribromide. Characterization of the vaporization mode of Eu3OBr4 would 106 be an interesting investigation, but again, little freedom is possible. Gaseous dibromide and a second condensed Eu(II) phase (oxide bromide or oxide) is anticipated. Since vaporization of either the purely divalent or trivalent oxide bromide places an oxidation-reduction restriction on the system, the vaporization behavior of a mixed-valent oxide bromide might be more informative. The present investigation has established general guide- lines for the elucidation of the vaporization process of ternary phases containing one metallic component, ipggj MXY. Unless the phases of the two metal—anion binary systems are of comparable volatility, the composition of a vaporizing ternary will shift toward the less volatile binary system and finally to a congruently vaporizing composition within that binary. The composition of the vapor will be determined by shifts in the composition of the solid, but the gaseous species will be determined by the vaporization behavior of the more volatile metal-anion binary. If the vaporization modes (temperatures, pressures, and species) of the binary systems are first determined, the vaporization behavior of any ternary involving these anions may be readily predicted. In the elucidation of the vaporization mode of a congruently vaporizing binary, the stability of the gaseous species does assume the determining role. Only if the metal binary sys- tems are of comparable volatility does the possibility of a congruently vaporizing ternary exist. 107 b. Disproportionation of the Oxide Bromides The cooling curve data of Baev and Novikov43 indicate that the monoxide monochlorides of lanthanum and neodymium melt with decomposition to form the sesquioxide and a melt of unspecified composition at 934° and 791°, respectively, but the data given are insufficient to determine if decompo— sition is actually occurring. Since an oxide bromide is expected to be less stable than the corresponding oxide chloride phase, disproportionation would be anticipated. However, at temperatures approximately 100° higher than the disproportionation point reported for LaOCl, EuOBr(s) was found to be in equilibrium with Eu3O4Br(s) according to re- action (VI-13). An argument might be presented that the oxide bromide does disproportionate (in this case into EuBr3~xEu203(£) and Eu304Br(s)) and on cooling forms the EuOBr(s)-Eu304Br(s) mixture observed by X-ray diffraction. However, if disproportionation did occur, the tribromide product would instantly decompose into dibromide and gaseous bromine which would escape from the effusion cell and change the composition such that EuBrz and Eu304Br would be present on cooling. It is therefore apparent that the Russian workers have either erroneously interpreted a phase change as a melting point, or misinterpreted their decomposition products. Thermodynamic instability (disproportionation) of both EuOBr and Eu304Br is expected at temperatures higher than those attained in the present equilibrium studies. A 108 consideration of the equilibrium pressure equations (VI—16), (VI-17) and (VI-24) for the gaseous dibromide indicates that they must cross at some temperature above the range of measurements. For Eu304Br(s) and EuBr2(£) (Equations VI-17 and VI-16) the calculated crossing temperature is 2040°K, while for EuOBr(s) and EuBr2(£) (Equations VI-24 and VI-16) the estimated crossover point is 1512°K. At temperatures above these respective values, the activity of EuBr2(g) in equilibrium with EuBr2(£) is lower than that in equilib- rium with solid oxide bromide, and therefore, disproportiona— tion according to equations (VII-1) and (VII-2) is antici- pated. 3 Eu304Br(S) ——> 4 Eu203(s) + EuBr2(£) + Br(g). (VII-1) 4 EuOBr(s) -—> Eu304Br(s) + EuBr2(£) + Br(g). (VII-2) By combining the appropriate enthalpies of formation, the estimated free energy functions at high temperatures (2;. Appendix VL,and relationship (III-24), third law calculations have been effected at various elevated temperatures. These calculations indicate positive free energy changes for the reactions at temperatures above the anticipated dispropor- tionation points. For reaction (VII-1) at 2500°K, 362500 = 0.74 kcal/gfw. This positive value appears to negate the pressure boundary argument used in approximating equation (VI-24) (pf, VI, H, 5), but the use of approximated free energy functions at such high temperatures is obviously not 109 an exact method. For example, if the calculation for re- action (VII-1) at 2500°K is effected with 5398 Eu203 = 36 eu (instead of 35 eu),AGgsoo - -9.26 kcal/gfw. Thus7even though thermodynamic calculations are unable to verify the disproportionation of the oxide bromides at the calculated crossover temperatures, these higher temperatures are more accurate than those previously proposed for disproportiona— tion of the oxide chlorides43. B. The X-Ray Fluorescence Technique The X-ray fluorescence technique has proven satisfac- tory for target collection analysis. Its most Obvious ad- vantage is that the procedure provides a rapid, direct, microanalytical procedure. The problems associated with quantitative removal of the effusate for spectrophotometric or spectrographic analysis or with the availability of neu- tron sources for activation analysis are eliminated. The scanning procedure removes the difficulties of accurate alignment on the spectral maximum and of shifts in the maxi- mum arising from the Chemical environment of the analyzed element or from temperature effects on the analyzing crys- tal. The disadvantages of the technique are the low ratio of characteristic to background counts obtained in the scanning procedure and the difficulty of accurately repro- ducing the conditions necessary for external standardization. The availability of a precision spectrometer would eliminate the unfavorable statistics by allowing the use of a fixed 110 angle procedure, while the necessity for reproduction of conditions appears to have been adequately eliminated by the control procedure. The phenomena of enhancement and suppression should be considered in the selection of x-ray tubes and of materials for collection targets. If an element being analyzed has an X-ray absorption edge at a slightly longer wave length than a characteristic energy of the primary beam, the fluor- escence spectrum of the element will be enhanced. Likewise, if the target material has its characteristic radiation in the same relationship to the absorption edge, the same ef- fect will be Observed. The problem of suppression arises for the reverse situation in the case of matrix analysis and Occurs because an absorption edge of a second element in the matrix absorbs the characteristic radiation of in- terest. In this latter case, increased concentration of the second element decreases the observed quantity of character- istic radiation. The selection of X-ray tubes is controlled primarily by monetary considerations, but the choice of target material allows for more possibilities. In the pres- ent investigation the Eu Lad, transition was found to be more intense than the L04. because of selective enhancement of the B transition by the secondary a radiation of the cop— per target. Problems with suppression do not arise in the present technique because Of the superficial nature of the sample. 111 Although the accuracy of this fluorescence procedure has not been confirmed by independent analysis, the measure- ment of the vapor pressure of gold (pf, Appendix IIB) and the simultaneous analysis for both europium and bromine provide a basis for evaluation of the technique. Since a complete set of free energy functions is not available for any of the reactions studied in this investigation, the use— fulness of third law values is only in checking the consis- tency of the thermodynamic approximations. In the case of gold, agreement of second and third law enthalpies is a Check on the accuracy of the analytical method. The agree- ment obtained between the second law (88.7 i 1.4 kcal/gfw) and third law (88.00i 0.56 kcal/gfw) enthalpies is indica- tive of the accuracy of the technique. These values are in agreement with the 88.84 kcal/gfw Knudsen effusion result Obtained by Ward94, the 88.3 kcal/gfw torsion effusion value of Hildebrand and Hall95 and the 87.3 kcal/gfw value recom- mended by Hultgren gp_§l.9°. In addition, the collection of EuBrz effusate in both the Eu3O4Br and EuBr2 vaporization experiments allowed an internal check from simultaneous analysis of the two components. The agreement of the two analytical results is evidenced by the data in Figures 9 and 10, in which the pressures calculated from Eu and Br analy- tical data are seen to agree within experimental error. The standard deviations in the slopes of the various calibration curves (pf, Appendix IIA) indicate that the sensitivity and precision of the technique vary from 112 measurement to measurement. These various values result primarily from the use of different X—ray generators and analyzing crystals during the course of the investigation. For the gold calibration, a representative case for the technique, the precision is found to be i0.1 ug at the 95% confidence level. This reproducibility suggests that second law enthalpy data could be Obtained without calibration of the spectrometer for absolute pressure measurements. C. The Target Collection Knudsen Effusion Technique 1. The Attainment of Knudsen Conditions The attainment of Knudsen conditions (Sin III, B, 2) in the present experimental procedures is evidenced by con— sideration of the trends and limits discussed previously (pf, III, B, 3). The temperature-pressure data indicate that inconsistencies and trends in the pressures are not observed either upon six to eight-fold variations Of orifice areas (pf, Figures 7-10) or with successively increasing and decreasing temperatures (SE: Appendices IIIA-IIID for data in chronological order of collection). The third law enthalpies also exhibit no trend with temperature. These observations suggest that difficulties stemming from sam- pling and non—equilibrium problems are insignificant. Even though the pressures and orifice sizes are within the region of validity of the cosine law determined by Mayer57 (pf, III, B, 3, b), the ratio of mean free path to orifice 113 radius has been calculated for a representative system by use of the relationship given by Dushman56; L = 1/(2)1/2vn02. The mean free path of the molecule, L, is a function of the number of molecules/cm3, n, and the molecular diameter, 0. Values for n were calculated from the measured pressures by invoking the ideal gas assumption. For the vaporization of Eu304(s), the highest pressure, 7.4 x 10-4 atm, was ob- served at 2016°K with an orifice of radius 0.015 cm, while 6 atm, was measured at 1605°K with the lowest value,3.3 x 10- an orifice of radius 0.042 cm. If 0 Eu(g) = 4.0 R97, these data points, which correspond to L/R ratios of 3.5 and 42, respectively, are well within the region of molecular flow (L/R.i 1) set by Dushman55. 2. Temperature Gradients The most troublesome difficulty encountered in the tar- get collection experiments is the presence Of a temperature gradient across the cell. Since asymmetric-type Cells ex- hibit a much greater tendency for surface gradients than symmetric types, the problem appears to result from heating by induction. Although comparisons of sample and optical cavity temperatures for both cell designs indicate that the difference was never greater than i5°, samples of europium dibromide were consistently found on the crucible lid after vaporization measurements. The only explanation for this behavior is that it resulted from a temperature gradient within the sample cavity. The effect of this gradient on 114 the pressure measurements is unknown, but the results of Ward“9 show that the cosine law is obeyed in the forward direction only when the sample is on the surface directly opposite the orifice. For a solid sample, the effect of a small gradient is therefore not expected to be great, but complete transport of the sample to the lid requires that most of the effusate in the forward direction comes from re-evaporation off the bottom and walls of the cell. The low vapor pressure of the dibromide in the temperature range investigated indicates that complete transport of the sample could not have occurred during the exposure time of the first target, or even of the first few targets. However, the lack of a noticeable trend in the pressure values with chronological order of exposure suggests that the presence of a temperature gradient has not greatly affected the pres- sure measurements for europium dibromide. 3. Crucible Materials Any involvement of the crucible material in the equi- librium is also important. Weight loss measurements indi- cate the selected crucible materials are suitable. Since 'molybdenum was a noninteracting container material for grow- ing single crystals of europium monoxide from the melt at temperatures ZOO-300° above the maximum temperature of the trieuropium tetraoxide measurements98, no difficulties with either Eu3O4 or EuO are to be anticipated. Graphite, which has previously been employed in Knudsen effusion measurements 115 on SrC1299, appears to be both inert and impervious to both gaseous and condensed europium dibromide. The normally refractory metals (Mo and W) cannot be used in the presence of gaseous bromine or the condensed oxide bromide because of the stability and volatility of the gaseous halides of these elementleQ The volatility of molybdenum dibromide in the temperature range studied easily accounts for weight losses of greater than 100% of theoretical. In studies of the oxide bromides, the condensed phase must be separated from the graphite crucible to prevent reduction of the oxide by carbon. D. Evaluation of Thermodypamic Approximations 1. Heat Capacity Approximations For all condensed phases other than europium sesqui- oxide and europium dibromide, relationships (III-29) and (III-30) have been employed in approximation of the heat capacity equations. Other than the second—third law enthalpy agreement (pf, Table IV), which serves as a check on the consistency of heat capacity and entropy approximations, little evidence for their accuracy exists. Equation (III-29) has been tested for systems in which measured sets of data are available1°1. Use of the heat capacity equation for y-Fe203(s) to calculate a value for B-Fe304(s) at 1500°K yields 48.4 cal/deg gfw versus the reported 48.0 cal/deg gfw. At 1500°K, the heat capacity of Cu20(s) (26.98 cal/deg gfw), 116 which is estimated from CuO(s) data, agrees with the experi- mental value (23.45 cal/deg gfw) within 15%; at 298°K, the estimated and experimental values agree within 7%. These results are well within the 120% error limits assumed for second law data reduction. If the heat capacity approxi- mations from either binary phase yia_equation (III-308 is valid (2;, III, E, 4, a), then the approximation from one binary to the second binary should also be valid. Since experimental data for Eu203(s)14 and Brewer's enthalpy and entropy function approximations for EuBr2(£f?are available, a check on the internal consistency of the-present approxi- mations is possible. If the heat capacity data of Eu203(s) is converted gig equation (III-30) to an expression for that of EuOBr(s), the value should be the same as that which would be approximated for EuBr2(s) since the cation to anion ratio is the same. In order to compare the results with Brewer's approximations, (H; — H298) and (s; - 8393) were calculated for EuBr2(s) at 1400°K (22,330 cal/gfw and 30.91 eu, respec— tively). Addition of the enthalpy (6,000 cal/gfw) and en— tropy of fusion (6.3 eu) for EuBr2(s) yields (H; - H398) = 28,330 cal/gfw and (s; - S398) = 37.2 eu for EuBr2(£). These results compare favorably with Brewer's values of 29,600 cal/gfw and 37.5 eu, and are well within his r20% limits of accuracy. These results suggest that the method might be employed to estimate heat content functions for any metal-anion binary if data for a similar binary are available. 117 The theoretical basis for equations (III-29) and (III—30) is very simple. The method assumes that the metal in an ionic lattice is the major contributor to the heat capacity function, and that its contribution in a second lattice may be approximated by employing the known heat capacity of any similar phase of the metal. The anion contribution is as- sumed to obey Kopp's rule65 which is employed to adjust the heat capacity to the correct metal-anion stoichiometry. Such an approach should give an internally consistent set of heat capacities, and, hence, should result in reasonably accurate second law reductions, especially for incongruent vaporiza- tions, i.e. those having a solid as reactant and as product. 2. Entropy Approximations Since several discussions of the theoretical basis for Latimer's method are available 17.71.72, a comparison of the estimated and experimental (second law) entropy values Obtained in this investigation is probably most instructive. The estimated values (9:. VI, G, 2, a) and the calculated second law results, which are based on experimental data and the independently approximated heat capacities, appear in Table VI. The agreement is indicative of the consistency of the heat capacity and entropy approximations and suggests that in the absence of necessary lattice or magnetic contri— butions to the entropy, the second law results may be em- ployed for the calculation of free energy functions. 118 Table VI. Comparison of estimated and experimental $298. Estimated Second Law Phase $298 (eu) 8398 (eu) Eu304(s) 49.0 48.6 i 2.6 EuO(s) 16.3 15.0 i 3.0 EuBr2(s) 40.1 39.5 r 3.0 Eu3O4Br(s) 63.8 64.5 i 3.1 E. -Evaluation of Vaporization and Thermodynamic Results 1. Trieuropiumfigetraoxide Data In light of the vaporization results for Eu203(s)?5, the presence of gaseous europium monoxide should be antici— pated for Eu304(s) at the higher temperatures. The sesqui— oxide vaporizes congruently by two competing modes to produce in one case Eu(g) and 0(9) and in the other EuO(g) and 0(9). These two equilibria and reaction (VI-1) are all subject to the gas phase equilibrium described by equa- tion (VII-3). Eu0(9) = Eu(g) + 0(g)- (VII-3) Use of pressures reported by Panish15 for Eu(g) and EuO(g) at 2000°K permits an approximation of the equilibrium ' constant for reaction (VII—3). If the congruent vaporiza- tion of Eu203 to Eu(g) and 0(9) is assumed to be the domin- ), the pressure of monatomic ant mode (P > P EU(9) EuO(g) 119 oxygen can be calculated from the Observed europium pressure by taking cognizance of their mass differences. A value for K(VII-3) = 2.6 x 10.7 atm is thereby obtained. If the oxygen pressure calculated at the extremum dictated by the two vaporization modes is combined with the experimental pressure of Eu(g) at 2000°K, the anticipated upper and lower limits of EuO(g) pressure can be set for the Eu304- EUan system to be 2 x 10.6 i PEuo atm i.7 x 10-5. The value observed mass spectrometrically is 5,3 x 10-6. Thus, the contribution of europium monoxide to the target collec- tion measurements is inconsequential, and the data have not been corrected for it. Consistency of the enthalpy and entropy values with other thermochemical data is evident. The enthalpy of form- ation of Eu3O4(s) (-542.4 kcal/gfw) would be expected to be more negative than the sum of the enthalpies of formation of EuO and Eu20312 (-539.1 kcal/gfw). Likewise, the en- thalpies of formation of the europium oxides should become increasingly negative with increasing oxygen content, as 0 EuO(s) .-. 445.2 kcal/gfw, AHf 298 follows: AH Eu01.33(s) 0 f 298 = -180.8 kcal/gfw, and AH; 298 Eu01.50(s) : -196.9 kcal/gfw. -The entropy of formation of Eu304(s) (-107.3 eu) is of the magnitude observed for other M304 phases1°2: Fe3O4 (—82.5 eu), Mn3O4 (—85.2 eu), and Pb304 (-94.0 eu). Consideration of the formation reaction indicates that the more negative value arises for the europium phase because of the large entropy of elemental europium. Although the absolute entropy 120 is also difficult to evaluate because of the magnetic nature of europium, 5398 = 48.6 eu is consistent with values for Mn304 (35.5 eu), Fe3O4 (35.0 eu), and Pb304 (50.5 eu) in light of the mass differences of the metals1°2. 2. Europium Monoxide Data -Even though the similarities of the divalent lanthanides and the alkaline earths are numerous, an important differ? ence between the two is the existence of the trivalent lanthanide oxidation state. ‘The vaporization behavior of strontium or barium monoxide1°3.1°4 indicates that EuO(s) should vaporize principally to the gaseous monoxide. How- ever the stability of the Eu3O4(s) phase, which has gaseous europium as the principle Species in the Eu304-Eu203 two- phase region, forces europium to be the only gaseous product in the EuO-Eu3O4 composition range. The argument is presented (2;, VI, H, 5) that a close correspondence should be observed between the AS; values for two vaporization processes which both involve a solid as product and reactant in equilibrium with the same vapor. The Eu304-Eu203 and EuO-Eu304 equilibria should provide a test for this reasoning. The entropy changes observed at the median measurement temperature of reactions (VI-1) and (VI-2) (28.2 eu and 28.7 eu respectively) substantiate the validity of the argument. The third law enthalpy calculations for vaporization equation (VI-2) provide a critical test of the entropy value ll’lll 121 of EuO(s). According to Westrum's estimate17, the sum of lattice and magnetic contributions to the entropy of EuO is 16.3 eu, while the second law result is 15.0 i 3.0 eu. These values agree within standard deviation, but the 3.0 eu un- certainty arises mainly from a large error (i 2.0 eu) assumed for the approximated entropy of Euzoa and may not reflect a true uncertainty. Although the discrepancy does not appear to be great, the coefficients of reaction (VI-2) are such that a 1.3 eu difference in $298 of EuO gives rise to a 8.0 kcal difference in the third law enthalpy. The third law result (72.64 i 0.59 kcal/gfw) obtained by using free energy functions based on $398 EuO(s) = 16.3 eu is several kilo— calories less than the second law value (75.9 kcal/gfw) at the median temperature (1546°K). The value of 298°K must be larger than the value at the elevated temperature because of the lower heat capacity of the gaseous product. However, the third law enthalpy (80.00 i 0.42 eu) obtained by using free energy functions calculated with 5393 = 15.0 eu agrees within 0.3 kcal/ng'with second law value. This result sug- gests that, relative to the 35.0 eu entropy of Eu203(s), the entropy of EuO(s) should be 1 eu lower than approximated. Perhaps Westrum's17 estimate of 4.2 eu for the magnetic contribution of divalent europium is too large since the use Of this value to approximate the contribution Of Eu(II) in Eu304 again results in a $398 value in excess of the second law result. 122 The consistency Of the present thermodynamics data with previous measurement is evident. The enthalpy of formation agrees exactly with the calorimetric value of Burnett and Cunningham7 and fits well into a correlation of ionic radii of the divalent alkaline earths with their enthalpies of formation102 presented in Table VII. The ionic radii are calculated from the experimental lattice parameters of the NaCl-type monoxides78 using a 1.40 R radius for the oxide ion97. The entropy of formation (-28.8 eu) is in agreement with the values reported for other MO phases1°2; SrO (-24.5 eu), SnO (-23.2 eu), and PbO (-25.8 eu); however, the value again reflects the large entropy of elemental europium. Similarly, the $398 value for EuO is consistent with that of other monoxide phases”2 when their mass differences are con- sidered: SrO (13.0 eu), SnO (13.5 eu), EuO (15.0 eu), and PbO (16.1 eu). Table\n15 Correlation of the divalent radii and enthalpies Of formation of metal monoxides. MO M+2 Radius (R) AH; 298 (kcal/gfw) CaO 1.00 -151.9 EuO 1.17 -145.2 SrO 1.17 -141.1 BaO 1.35 -133.5 123 3. Europium Dibromide Data The vaporization and thermodynamic results for europium dibromide are consistent with the various estimated values. The equilibrium pressure equation is well within the limits set by Brewerzs. Although the Observed vapor pressure is lower than the estimated median value, the boiling point is higher. The enthalpy of vaporization at 298°K (71.4 kcal/gfw) is in excellent agreement with the 72 kcal/gfw value esti- mated by Feber3°. Since the approximated dissociation energy recommended by Feber has been employed in the data reduction, the remaining thermodynamic values are also in agreement. The enthalpy of vaporization at the boiling point (52.0 kcal/gfw) agrees with Brewer's approximated value (50 kcal/gfw)28; the entropy of vaporization at the boiling point (20.6 eu) is in good agreement with Trouton's rule. 4. Trieuropium Tetraoxide Monobromide and Europium Monoxide Monobromide Data Since no previous vaporization or thermodynamic measure- ments have been made for any lanthanide oxide bromide, evalu— ation of the data is difficult. Although gaseous niobium monoxide tribromide (NbOBr3) species are reported”5 and might be anticipated for transition group VB elements, none was observed for europium. The stabilities of europium ses— quioxide and dibromide (SE: VII, A, 3, a) probably prevent the formation of these phases. The thermodynamic values 124 may be compared with those obtained for the LnOCl phases43. The estimated enthalpy of formation of EuOBr (-203.3 kcal/gfw) is consistent with the more negative values (-230 to -245 kcal/gfw) observed for the monoxide monochlorides. The en- thalpy Of bromination of a divalent europium oxide phase should be essentially constant, and the difference between the enthalpies of formation of Eu304(s) and Eu304Br(s) and those of EuO(s) and EuOBr(s) are 55.1 kcal/gfw and 58.1 kcal/gfw, respectively. F. On the Existence of Lower Oxides of Ytterbium Although the lower oxides of europium are easily ob— tained, prepartive procedures for the corresponding phases of other lanthanides have been unsuccessful. Brauer gp_§l.1°6 indicate that attempts to prepare LnO and Ln304 (Ln = Nd. Sm, Yb) by the reduction of the oxide bromides with lithium hydride and by combination of the metals with their sesqui- oxides have been unsuccessful. The results of Felmlee and Eyringl°7 and of Butherus and Eick”8 indicate that the previously reported monoxides are either oxide—nitride or oxide—carbide phases with NaCl-type lattices. The experi- mental results of the present investigation should be help- ful in determining if, and in what temperature range, the existence of other lower lanthanide oxides is to be antici- pated. To effect third law calculations on the reactions of interest, certain thermodynamic data must be approximated. 125 Estimated entropies were obtained by using the schemes of Westrum17 and Latimer71 for oxide and oxide bromide phases, respectively, in conjunction with the measured entropy of Yb303(s) (31.8 eu)17. Since Yb(II) is isoelectronic with Lu(III), for which no magnetic anomolies have been observed, a magnetic contribution was not included in the 11.1 eu value approximated for 8398 of Yb0(s). The entropies of Yb304(s) and Yb304Br(s) were estimated by summing the en— tropies of szoa and YbO and correcting the results for anionic lattice contributions. In a similar manner, the 8398 value for YbOBr is obtained from the YbO entropy. The free energy functions for ytterbium oxide and oxide bromide phases were calculated at various temperatures from the fef of the corresponding europium phase by subtracting $298 of the europium compound and adding $298 of the ytterbium phase. The enthalpies of formation of ytterbium oxides and oxide bromides may be estimated because of general trends in the lanthanide series. The enthalpies of formation of lanthanide monoxide monochlorides increase linearly (£;2;I become more positive) across the series43. The effect of this trend appears in the decreasing thermal decomposition temperaturesl°9r11° of the oxide chlorides with increasing molecular weight. Since an identical decomposition trend is observed for the oxide bromidesl9, an enthalpy of forma- tion of YbOBr (-195 kcal/gfw) may be estimated from that of EuOBr and the trend set by the measured oxide chloride 126 enthalpies. The enthalpy change for bromination of Eu(II) in EuO(s) (-58 kcal/gfw) must be corrected for the differ- ence in bond strength of the Eu(III)-Br and Yb(III)-Br bonds. This difference may be obtained from the estimated enthalpies of formation of EuBr3 and YbBr33°, which give values of -66 and -61 kcal/gfw per bromine bond, respectively. This 5 kcal difference implies that the enthalpy of bromina— tion of YbO(s) should be -53 kcal/gfw. Use of this value gives an? YbO(s) = -142 kcal/gfw. »The enthalpy of formation of the metal monoxides also may be calculated gig a Born-Haber cycle. The enthalpy of formation of a monoxide phase is given by the following equation: 0 AHf 298 = AH: + 1/2 D0 + IP — EA - U. (VII-4) where AH: and IP represent the enthalpy of vaporization and the ionization potential Ofthe metal, respectively, Do and EA the dissociation energy and electron affinity of oxygen, and U the lattice energy. For an isostructural series of compounds, the common steps in the cycle (Do, EA, and U) may be expressed in terms of a constant and the variable r, the equilibrium separation of nearest-neighbor ions in the lattice. Therefore, the enthalpy of formation of EuO(s) may be used to calculate a general equation which is a func— tion of AHg, IP, r, and constants. Values for the second ionization potentials111 and enthalpies of vaporization88 are available for europium and ytterbium. The value for 127 r (2.58 R) is readily calculated from the lattice constant of EuO. rSince no experimental data are available for YbO, the Yb(II) radius may be estimated from the radius of Eu(II) and Eu(111)112 (1.17 X/o.95 8). Combination of this 1.25 ratio with the 0.85 R radius of Yb(111)112 gives a Yb(II) radius of 1.06 R, which in turn yields r = 2.46 X for YbO(s). Use of this distance in the Born-Haber equation gives 1. AHO f 293 Of Yb0(3) = -144 kcal/gfw. The average value (—143 kcal/gfw) between this result and the previous estimate has been selected for the thermodynamic calculations. It The enthalpy of formation of ytterbium tetraoxide may also be approximated by analogy to the europium data. The enthalpy of formation of Eu304 is observed to be 3.3 kcal more negative than the sum of the enthalpies of EuO and Eu203. Addition of this difference to the sum of the Yb203 and YbO values gives AH? 298 for Yb304 of -580 kcal/gfw. Combination of this tetraoxide value with the difference in enthalpies of formation of Eu304 and Eu304Br and inclusion of the 5 kcal/gfw correction for the Yb-Br bond yields a AH; 298 of -630 kcal/gfw for Yb304Br. These values are presented in Appendix V with other approximated data and values from the literature. Third law calculations have been used to obtain the free energy changes for the lithium hydride reduction of the oxide bromides of europium and ytterbium (equations VII-5 - VII-8). 128 3LnOBr(s) + 3LiH(£) ——e 3LnO(s) + 3LiBr(£) + 3/2 H2(g)(VII-5) 3LnOBr(s) + 3LiH(£) -> Ln203(s) + Ln(s) + 3LiBr(£) + 3/2H2(g). (VII-6) 3Ln3O4Br + 3LiH(£) —> 3Ln304(s) + 3LiBr(£) +.3/2H2(g).(VII-7) 3Ln304Br(s) + 3LiH(£) -> 4Ln203(s) + Ln(s) + 3LiBr(£) + 3/2H2(g). ~ VII-8 Since the melting point of LiH (960°K) appears to mark the onset of rapid reduction, 1000°K has been selected for the calculations. The liquid state is assumed for LiBr because long heating is required to volatilize the phase after the reduction is apparently complete. The results listed in Table VIII clearly exhibit the differences observed experi- mentally; namely, that the lower oxides of europium are readily attained by hydride reduction, while those of ytter- bium are not because sesquioxide formation is favored. Since ytterbium hydride is actually observed instead of the free meta11°6, reactions (VII-6) and (VII—8) are even more favored than indicated. Since attempts to prepare ytterbium monoxide by reduc- tion of the sesquioxide with the metal according to reaction (VII—9) have also been unsuccessfu11°°, an examination of the energetics of this reaction for Ln ='Eu and Yb is of interest. Ln(s,£,g) + Ln203(s) > 3LnO(s). (VII-9) The data given in Appendix V have again been employed in third law calculations of the free energy changes. The 129 Table VIII. Free energy changes calculated for the reduction of europium and ytterbium oxide bromides with lithium hydride. Lanthanide AGO at 1000°K(kcal/gfw) Reaction Products Eu Yb 3 LnO(s) -54 -74 Ln203(S) + Ln(s) -21 -91 3 Ln304(s) -61 —71 4 Ln203(s) + Ln(s) —17 -81 Table IX. Free energy changes for the reaction of europium and ytterbium with their ses- quioxides at various temperatures. AGU(kcal/gfw) Ln 298°K 1003K 1400°K 2000°K Eu —39 —33 -30 -- Yb 8 16 21 114 130 results listed in Table IX indicate that the preparation of YbO at elevated temperatures is impossible because of the disproportionation reaction to the metal and the sesquioxide. However, the trend in AG; is such that the phase might be stabilized at low temperatures if it were prepared by con- densation Of the gaseous monoxide. In order for YbO to be thermodynamically stable, i.e., AG0 :.0 for reaction VII-9, —— T its AH; 298 1 -148.5 kcal/gfw. Although the question of why no lower oxides other than those of europium appear to exist has not been answered di- rectly, the free energy calculations for reactions (VII-5) - (VII-9) give an indication. With the exception of the euro- pium and ytterbium sesquioxide values (—394 and -434 kcal/gfw, respectively), the enthalpies of formation of the lanthanide sesquioxides vary in a monotonically decreasing manner from lanthanum to lutetium (-428 to -449 kcal/gfw)17. The anoma- lously high enthalpy of formation of Eu203, which deviates from the trend by 40 kcal/gfw, allows its lower oxides to be stable. The stability of ytterbium sesquioxide, with a de- viation of only 14 kcal/gfw, prevents the attainment of di- valent oxides. Gschneidner113 has recently explained the deviations of the enthalpies of formation of the europium and ytterbium sesquioxides in terms of the promotional energy re- quired to overcome the divalent electronic configuration and form the trivalent configuration present in the sesquioxides. If this enthalpy deviation, which appears to measure divalent tendencies of the metals, is a valid indicator, the possibil— ity of preparing the lower oxides of samarium and other lanth— anides, which show no deviation, i.e. divalent tendency, is indeed unlikely. CHAPTER VIII SUGGESTIONS FOR FUTURE INVESTIGATIONS The europium-oxygen-bromine ternary has proved to be an interesting chemical system, but numerous possibilities for continued investigation are apparent. The phase diagram in the region EuBrz-EuBr3 probably contains stoichiometric and nonstoichiometric phases, while the preparative possibili- ties of the oxide bromides have not yet been exhausted. Certainly the composition of the hexagonal oxide bromide should be determined. Absolute equilibrium pressures of bromine could be determined for the EuBrz-EuBra region by use of a controlled-temperature, visible-spectrometer cell with calibration of the instrument with bromine. This pro— cedure could simultaneously provide thermodynamic and phase data for this composition range. The crystal structure in— vestigations of EuBrz and Eu3O4Br, both of which appear to be new structure types, should be completed. As better values become available for the enthalpy and entropy of formation of Eu203(s) and the entropy of Eu(s), the thermo- dynamic calculations for Eu3O4(s), EuO(s), Eu3O4Br(s), and EuOBr(s) should be reevaluated. 131 REFERENCES 10) 11) 12) 13) 14) 15) REFERENCES K. A. Gschneidner, Jr.,”Rare Earth Alloys", D. Van Nostrand Company, Inc., New York, 1961, pp 239-251. R. C. Rau, "Rare Earth Research II, Proceedings of the Third Conference on Rare Earth Research", K. S. Vorres, Ed., Gordon and Breach, New York, N.Y., 1964, pp 117- 134. H. Baernighausen, J. Prakt. Chem., 34( ), 1 (1966). H. A. Eick, N. Baenzinger, and L. Eyring, J. Amer. Chem. Soc.. 18’ 5147 (1956). I J. C. Achard, C. R. Acad. Sci. Paris, 245, 1064 (1957). B. T. Mathais, R. M. Bozorth, and J. H. Van Vleck, Phy . Rev. Lett” 1, 160 (1961). J. L. Burnett and B. B. Cunningham. AEC Report UCRL- 11126, Berkeley, Calif., Feb. 1964. J. C. Achardjand M. G. Chaudron, C. R. Acad. Sci. Paris, 250. 3025 (1960). H. Baernighausen and G. Brauer, Acta Crystallogr., LE' 1059 (1962). R. c. Rau, ibid., 2g, 716 (1966). H. Baernighausen, Z. Anorg. Allg. Chem., 349.280 (1967). E. J. Huber, Jr., G. C. Fitzgibbon, and C. E. Holley, Jr., J. Phys. Chem., 32x 2720 (1964). J. M. Stuve. U.S. Bureau of Mines Report of Investiga- tion 6640. Reno. Nev.. Oct. 1964. L. B. Pankratz, E. G. King, and K. K. Kelley, ibid., 6033, Washington, D.C., Jan. 1962. M. B. Panish. J. Chem. Phys., 34/ 1079 (1961). 132 16) 17) 18) 25) 26) 27) 28) 29) 30) 31) 32) 133 C. F. Guerci, and U. L. Moruzzi, Bull. Amer. Phys. Soc., 2, 225 (1964). E. F. Westrum. Jr., "Advances in Chemistry Series 71. Lanthanide/Actenide Chemistry". R. F. Gould, Ed., American Chemical Society, Washington, D.C., 1967, pp 25-50. M. D. Taylor and C. P. Carter, J. Inorg. Nucl. Chem., 22, 387 (1962). I. Mayer and S. Zolotov, ibid., 21x 1905 (1965). D. Brown, S. Fletcher, and D. G. Holah, J. Chem. Soc., A, 1968, 1889 (1968). W. Klemm and W. Doell, Z. Armg.Allg.'dI-3m., 241, 233 (1939). W. Doell and W. Klemm, ibid., 241 239 (1939). M. A. Kammermans, Z. Kristallogr., 101, 406 (1939). F. A. Cotton and G. Wilkinson, "Advanced Inorganic Chemistry", 2nd ed, John Wiley and Sons, Inc., New York, N.Y., 1966. PP 1070-1071. R. L. Sass, T. Brackett, and E. Brackett, J. Phys. Chem., 61, 2862 (1963). M. D. Taylor, Chem. Rev., 62, 503 (1962). G. I. Novikov and O. G. Polyachenok, Usp. Khim., 33” 732 (1964): Russ. Chem. Rev.. fig, 342 (1964). L. Brewer. "Chemistry and Metallurgy of Miscellaneous Materials: Thermodynamics", L. L. Quill, Ed., McGraw— Hill Book CO., Inc., New York, N.Y., 1950, paper 7. L. Brewer, L. A. Bromley, P. W. Gilles, and N. L. Lofgren, ibid., paper 6. R. C. Feber, AEC Report LA-3164, Los Alamos, N.M., 1965. C. E. Widks and F. E. Block, "Thermodynamic Properties of 65 Elements--Their Oxides, Halides, Carbides, and Nitrides", U.S. Department of Interior, Bureau of Mines Bulletin 605, U.S. Government Printing Office, Washing- ton, D.C., 1963. A. Carrington and D. H. Leavy, J. Chem. Phys., 22: 1298 (1966). 33) 34) 35) 36) 37) 38) 45) 46) 47) 48) 49) 50) 134 H. Grenbaut, G. Pannetier, and P. Goudmand, Bull. Soc. Chem. Fr., 1962, 80 (1962). A. Pflugemacher, H. Rabben, and H. Dahmen, Z. Anorg. Allg. Chem., 279, 313 (1955). A. J. Arivia, P. J. Aymonino, and H. J. Schumacher, ibid., 298, 1 (1959). H. Baernighausen, G. Brauer, and N. Schultz, ibid., 338, 250 (1965). W. H. Zachariasen, Acta Crystallogr., Ex 388 (1949). N. Schultz and G. Reiter, Naturwissenschaften, 54, 469 (1967 . C. W. Koch, A. Broido, and B. B. Cunningham, J. Amer. Chem. Soc., 14, 2349 (1952). C. W. Koch and B. B. Cunningham, ibid., ZE/ 796 (1953). C. W. Koch and B. B. Cunningham, ibid., 76, 1471 (1954). F. Weigel and H. Hang, Chem. Ber., 94/ 1548 (1961). A. K. Baev and G. I. Novikov, Zh. Neorg. Khim., 10, 2457 (1965); Russ. J. rnorg. Chem., lg, 1337 (1965). P. W. Gilles. "The Application of Fundamental Thermo- dynamics to Metallurgical Processes", Gordon and Breach. New York, N.Y., 1967. PP 281—298. J. L. Margrave, "Physiochemical Measurements at High Temperature", J. Bockris, J. White, and J. Mackenzie, Eds., Academic Press, Inc., New York, N.Y., 1959, Chap- ter 10. M. Knudsen, Ann. Phys., 28” 75 (1909); English Trans- lation by L. Venters, Argonne National Laboratory (1958). M. Knudsen, ibid., 28, 999 (1909); English Translation by K. D. Carlson andfiE. D. Cater. Argonne National Laboratory (1958). R. J. Ackermann, AEC Report ANL—5482, Lemont, Ill., Sept. 1955. J. W. Ward, AEC Report LA-3509, Los Alamos, N.M., Jan. 1966. P. Clausing, Physica, 9, 65 (1929). 51) 52) 53) 54) 55) 56) 57) 58) 59) 60) 61) 62) 63) 64) 65) 66) 135 W. G. Pollard and R. D. Present, Phys. Rev., 73, 762 (1948). A. R. Miller, J. Chem. Phys., 42, 3734 (1965). A. R. Miller, "The Fraction of Effusing Molecules Striking a Collector Plate over a Circular Capillary", Aerojet-General Nucleonics Report AN-1328, San Ramon, Calif., Dec. 1964. R. P. Iczkowski, J. L. Margrave, and S. M. Robinson, J. Phys. Chem.. fiz, 229 (1963). R. A. Kent, Ph.D. Thesis, Michigan State University, East Lansing, Mi., 1963. S. Dushman, "Scientific Foundations of Vacuum Tech— nique", John Wiley and Sons, Inc., New York, N.Y., 1949, Chapter 2. H. Mayer, Z. Phys., 58, 373 (1929); English Translation by K. D. Carlson, Argonne National Laboratory (1958). K. D. Carlson, P. W. Gilles, and R. T. Thorn, J. Chem. Phys.. 38, 2064 (1963). R. J. Ackermann, R. J. Thorn, and G. H. Winslow, Abstracts, 135th National Meeting of the American Chem- ical Society, Boston, Mass., April 1959. G. M. Rosenblatt, P. Lee, and M. B. Dowell, J. Chem. £hys., 42, 3454 (1966). G. M. Rosenblatt, J. Phys. Chem., 71, 1327 (1967). G. H. Stout and L. H. Jensen, "X-Ray Structure Determina- tion-eA Practicaeruide", The Macmillan Co., New York, N.Y., 1968. W. Parrish, "Advances in X-Ray Diffraction", Centurex Publishing Company, Eindhoven, 1962. J. L. Margrave, "Physiochemical Measurements at High Temperature", J. Bockris, J. White, and J. Mackenzie, Eds., Academic Press, Inc., New York, N.Y., 1959, Chapter 2. G. N. Lewis and M. Randall, "Thermodynamics", Revised by K. S. Pitzer and L. Brewer, McGraw-Hill Book Co., Inc., New York, N.Y., 1961. D. Cubicciotti, J. Phys. Chem., 29, 2410 (1966). III]: I'll! II e7) 68) 69) 70) 71) 72) 73) 74) 75) 76) 77) 78) 79) 80) 81) 82) 83) 136 P. A. Pilato, Ph.D. Thesis, Michigan State University, East Lansing, Mi., 1968. J. M. Haschke and H. A. Eick, J. Phys. Chem., 22, 1697 (1968). "JANAF Interim Thermochemical Tables", D. R. Stull, Project Director, Dow Chemical Co., Midland, Mi., 1960 and Supplements. L. Brewer, G. R. Somayajulu, and E. Brackett, Chem. Rev., 63, 111 (1963). W. M. Latimer, "Oxidation Potentials", 2nd ed, Prentice Hall, Englewood Cliffs, N. J., 1952, Appendix III. F. Grenwold and E. F. Westrum, Jr., Inorg. Chem., 1, 36 (1962). J. W. Youden, "Statistical Methods for Chemists", John Wiley and Sons, Inc., New York, N.Y., 1951. W. Feller. "An Introduction to Probability Theory and Its Applications", 2nd ed. John Wiley and Sons, Inc., New York, N.Y., 1960, pp 115-116. J. J. Stezowski, Ph.D. Thesis, Michigan State University, East Lansing, Mi., 1968. H. Diehl and G. F. Smith, ”Quantitative Analysis", John Wiley and Sons, Inc., New York, N.Y., 1955, p 113. P. G. Hambling, Acta Crystallogr., 6, 98 (1953). J. D. H. Donnay, Ed., "Crystal Data Determinative Tables", 2n ed, American Crystallographic Assn., Washington, D.C., 1963, p. 841. O. Lindquist and F. Wengelin, Ark. Kemi, 28, 179 (1967). M. J. Buerger, "X-Ray Crystallography", John Wiley and Sons, Inc., New York, N.Y., 1942. M. C. Powers, "X-Ray Fluorescent Spectrometer Conver- sion Tables", Philips Electronic Instruments, Mt. Vernon, N.Y., 1960. H. J. Neff, Arch. Eisenhuettenw., 34, 903 (1963); Siemens Pamphlet Eg 4/10e, Aug. 19632 M. Marezio, H. A. Plettinger and W. H. Zachariasen, Acta Crystallogr., 14, 234 (1961). 84) 85) 86) 87) 88) 89) 90) 91) 92) 93) 94) 95) 96) 97) 98) 137 B. A. Vajnstejn and Z. G. Pinsker, Zh. Fiz. Khim., 24, 432 (1950); A. J. C. Wilson, Ed., "Structure Reports~ for 1950", Volume 13, International Union of Crystal- lography, Oosthoek's Uitgevers Mij, Utrecht, Netherland, 1954, pp 209-210. N. F. M. Henry and K. Lonsdale, Eds., "International Tables for x-Ray Crystallography", Volume I, Interna- tional Union of Crystallography, Kynoch Press, Birming- ham, England, 1952. R. W. Kiser, "Introduction to Mass Spectrometry and Its Applications", Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. J. W. Hastie, P. Ficalora, and J. L. Margrave, J. Less- Common Metals, 14, 83 (1968). R. Hultgren, R. L. Orr, P. D. Anderson, and K. K. Kelley, "Supplement of Selected Values of Thermodynamic Properties of Metals and Alloys", private communication, R. Hultgren. A. Buechler, J. Stauffer, and W. Klemperer, J. Chem. Phys., 32, 3471 (1964). R. E. Thoma, "Progress and Science and Technology of the Rare Earths", Volume 2, L. Eyring, Ed., Pergamon Press, New York, N.Y., 1962, pp 90-122. L. B. Asprey, T. K. Keenan, and F. H. Kruse, Inorg. Chem., 3” 1137 (1964). B. Frit, B. Tanguy, and P. Hagenmuller, Bull. Soc. Chem. Fr., 1966, 2190 (1966). B. Frit, M. M. Chbany, and P. Hagenmuller, ibid., 1968, 127 (1968). J. W. Ward, J. Chem. Phys., 41/ 4030 (1967). D. L. Hildebrand and W. F. Hall, J. Phys. Chem., 62, 754 (1962). 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, N.Y., 1963. L. Pauling, "The Nature of the Chemical Bond", 3rd ed, Cornell University Press, 1960. C. F. Guerci and M. W. Shafer, J. Appl. Phys., 31, 1406 (1966). 99) 100) 101) 102) 103) 104) 105) 106) 107) 108) 109) 110) 111) 112) 113) 138 R. E. Loehman, R. A. Kent, and J. L. Margrave, J. Chem. Eng. Data, 12, 296 (1965). L. Brewer, L. A. Bromley, P. W. Gilles, and N. L. Lofgren, "The Chemistry and Metallurgy of Miscellaneous Materials: Thermodynamics", L. L. Quill, Ed., Mc- Graw-Hill Book Co., Inc., New York, N.Y., 1950, paper 8. K. K. Kelley, U.S. Bureau of Mines Bulletin 584, U.S. Government Printing Office, Washington, D.C., 1960. F. D. Rossini, D. D. Wagman, W. H. Evans, S. Levine, and I.Jaffe, Circular 500, National Bureau of Standards U.S. Government Printing Office, Washington, D.C., 1952. R. F. Porter, W. A. Chupka, Phys., 22, 1347 (1955). M. G. Inghram, W. A. Chupka, 22, 2159 (1955). and M. G. Inghram, J. Chem. and R. F. Porter, ibid., C. 0. Schulz and F. E. Stafford, J. Phys. Chem., $2, 4686 (1968). G. Brauer, H. Baernighausen, and N. Schultz, Z. Anorg. Allg. Chem., 356, 46 (1967). T. L. Felmlee and L. Eyring, Inorg. Chem., Z, 660 (1968). A. D. Butherus and H. A. Eick, J. Amer. Chem. 90,1715 (1968). Soc., W. W. Wendlandt, J. Inorg. Nucl. Chem., 2/ 118 (1957). W. W. Wendlandt, ibid., 2x 136 (1959). A. Eucken, Ed., Landolt—Boernstein, vol. I(1),Springer Verlag, Berlin, Germany, 1950, pp 211-212. D. H. Templeton and C. H. Dauben, J. Amer. Chem. Soc., IQ, 5237 (1954). K. A. Gschneidner, Jr., J. Less—Common Metals, 11, 13 (1969). APPENDICES llil' APPENDIX I: Appendix IA: Observed Sinze (l d-Values Tetragonal EuBr2 1.54051 R) and Interplanar Rela- d value Rela- d value tive hkl sin29 tlve hkl sinze Inten- (R) Inten- (R) sity sity vw 110 .00891 8.160 s 321 .06953 2.921 w 001 .01184 7.079 w-m 330 .07986 2.726 w-m 101 .01630 6.033 s 302 .08716 2.609 w 111 .02078 5.343 m-s 420 .08876 2.585 vw 201 .02974 4.466 m-s «312 .09159 2.545 s 211 .03412 4.170 m 421 .10067 2.528 vw 220 .03570 4.077 w-m 322 .10469 2.381 w 310 .04451 3.651 w-m 402 .11792 2.243 w 002 .04723 3.544 w-m 501 .12268 2.199 w-m 102 .05166 3.389 m 520 .12841 2.149 m-s 311 .05624 3.248 m 521 .14045 2.055 m 202 .06501 3.021 w 313 .15051 1.985 Appendix IB: Orthorhombic EuBrz'HZO w 110 .01186 7.073 s 230 .06902 2.932 m 020 .01810 5.725 m 040 .07242 2.862 w-m 210 .03259 4.267 w 301 .09545 2.493 w-m 101 .03966 3.868 s 231 .10104 2.423 w 111 .04379 3.681 m-s 041 .10485 2.379 w 130 .04721 3.545 m 400 .11236 2.298 w 021 .05042 3.430 m-s 002 .12891 2.145 vs 211 .06498 3.022 139 III III Ill] 1' I I.IIIIII [I 'II. 140 Appendix IC: Orthorhombic EuBr3 Rela- Rela-‘ tive hkl s' 29 d value tive hkl sinze d value Inten- 1“ (R) Inten-‘ (R) SitY sity s 020 .01466 6.362 s 320 .07881 2.744 m 200 .02872 4.561 m-s 240 .08727 2.607 vw 001 .03629 4.043 m 231 .09819 2.458 vw 011 .04035 3.835 s 311 .10450 2.383 w 220 .04313 3.709 w 400 .11411 2.280 w 111 .04768 3.527 w 420 .12866 2.147 w 121 .05865 3.181 m 060 .13369 2.107 w 201 .06573 3.004 m 151 .13557 2.092 s 211 .06892 2.934 m-s 002 .14708 2.008 m-s 031 .06978 2.916 vw 102 .15456 1.959 vs 131 .07676 2.780 m 341 .16035 1.924 Appendix ID: Monoclinic EuBr3'6H20 w 010 .01304 6.745 w 012 .04862 3.493 m 101 .01397 6.515 vw 020 .05202 3.377 m 101 .01575 6.138 w 120 .05798 3.199 w 110 .01895 5.595 w 301 .06480 3.026 m 011 .02196 5.198 w 310 .06635 2.990 m 200 .02375 4.998 w 212 .06892 2.934 m 111 .02696 4.691 vw 212 .07603 2.793 m 111 .02871 4.546 w 311 .07813 2.756 s 002 .03577 4.073 w 221 .08276 2.677 vw 210 .03697 4.006 w 221 .08618 2.624 s 211 .04376 3.682 w 022 .08787 2.598 m 211 .04729 3.542 w 122 .09195 2.540 a. 1': III I!“ l t . ’Iul'llulul! 411v ‘ APPENDIX II: X—Ray Fluorescence Appendix IIA: Linear calibration curves for X-ray fluores- cence giggiiiigg Element (CountS/ug 4 min) b Eu304(3) Eu 87 i 23 54 EuO(s) Eu 113 i 13 13 EuBr2(£)\ Eu 540 i 24 42 EuBr2(£) Br 858 i 22 -33 Au(£) Au 202 i 11 8 Appendix IIB: The Vapor Pressure of Gold Introduction In cooperation with the National Bureau of Standards in an attempt to establish vapor pressure standards, the vapor pressure of gold has been measured by the target collection Knudsen effusion technique. -The results of such an investi- gation should also be useful for evaluation of the X—ray fluorescence technique. Experimental The gold sample employed in this investigation (99.999% purity, NBS Standard Reference Material #685, 60 mil wire from spool #13—1-60) was provided by the National Bureau of 141 142. Standards. The 0.15—0.50 g portions employed in the measure- ments were prepared by metal fatigue and placed in molybdenum cells of the assymmetric design (g§.IV, K). wThree orifice 4, 21.6 x 10-4, and 7.0 x 10-4 cm2) were sizes (58.5 x 10- used in the target collection experiments (22: V, H) which extended over the temperature range 1598-19259K. The quantity of effusate collected was analyzed by the X—ray fluorescence technique (2;, V, G). The linear calibration curve (Appendix IIA) was obtained for the Lal line of gold by weighing onto copper targets 0.02-0.10 g quantities of standard solutions which were prepared by dissolving weighed samples of 24k gold (Engelhard Industries, Inc., Newark, N.J.) and HAuC14°3H20 (49.1% assay, J. T. Baker Chemical Co.) in 3 ml of aqua regia and in water, respectively, and di- luting. Results The following calculations were made under the assump— tion that monatomic gold is the only vapor species. A linear least squares equation describing the 30 data points (9;, Appendix IIC) obtained in 5 independent vaporization experiments is: 1109 9 = -(1.8176 1 0.0304 x 104/T) + 5.937 i 0.176. From this equation, the following thermodynamic data have been obtained for the vaporization of gold at the median temperature: AH2762 = 83.2 i 1.4 kcal/gfw and ASg762 27.17 i 0.81 eu. These values have been reduced to 298°K 143 with published enthalpy and entropy functions96 to give 88298 = 88.7 i 1.4 kcal/gfw and 88398 = 32.46 i 0.81 eu. A third law value of 83398 = 88.00: 0.42 kcal/gfw (9;. Appendix IIC) was obtained through use of published free energy functions95. These values are in excellent agree— ment with the second law value of 88.84 i 0.55 kcal/gfw obtained by Ward94, the heat of formation value of 88.3 kcal/gfw given by Hildebrand and Hall95 and the value of Hultgren gt_§l.9° of 87.3 kcal/gfw. Appendix IIC: Equilibrium pressures and third law enthal- pies for Au AH“ AH" T“°K) ‘1°9 P (kcai73fw> T (°K’ ‘1°9 P (kcai73fw) 1676 4.956 88.411 1925 3.451 87.421 1722 4.706 88.678 1843 3.847 87.277 1778 4.309 88.154 1772 4.411 88.701 1819 4.134 88.602 1672 4.896 87.724 1869 3.850 88.459 1640 5.128 87.885 1898 3.706 88.486 1853 3.842 87.690 1858 3.904 88.435 1910 3.562 87.767 1791 4.250 88.279 1688 4.839 88.056 1745 4.486 88.036 1725 4.552 87.617 1701 4.748 87.991 1674 4.899 87.759 1687 4.825 87.912 1650 5.036 87.693 1737 4.429 87.196 1613 5.316 87.907 1802 4.108 87.761 1598 5.462 88.205 1863 3.734 87.205 1710 4.686 87.955 1898 3.606 87.617 1774 4.332 88.160 APPENDIX III: Equilibrium Pressures and Third Law Enthalpies Appendix IIIA: Trieuropium tetraoxide vaporization U -log P AHV‘ o 298 o '109 P AH T ( K) (atm) (kcal/gfw) T ( K) (atm) (kca17gfw) 1700 4.847 91.79 1939 3.545 92.13 1765 4.464 91.99 1916 3.772 93.12 1854 3.997 92.28 1888 3.911 93.08 1824 4.141 92.10 1736 4.669 92.18 1793 4.357 92.43 1799 4.276 92.05 1736 4.698 92.43 1826 4.234 92.97 1722 4.663 91.46 1769 4.581 93.09 1754 4.527 91.91 1726 4.846 93.08 1805 4.301 92.53 1700 4.932 92.45 1867 3.941 92.39 1662 5.529 93.02 1927 3.491 91.14 1604 5.480 91.59 1899 3.781 92.45 1665 5.090 91.88 1842 4.043 92.11 1661 5.166 92.26 1788 4.463 93.06 1715 4.822 92.35 1738 4.784 93.20 1715 4.751 91.79 1664 5.087 91.80 1743 4.680 92.63 1888 3.748 91.67 1743 4.714 92.89 1950 3.459 91.86 1691 5.060 92.98 2016 3.131 91.63 1694 5.025 92.86 1972 3.348 92.11 1639 5.218 91.49 2014 3.105 91.32 1639 5.313 92.20 Appendix IIIB: Europium monoxide vaporization 1510 4.702 80.47 1661 3.697 80.39 1565 4.459 81.48 1713 3.384 80.27 1602 4.207 81.45 1758 3.116 80.08 1639 3.896 80.88 1756 3.118 80.00 1395 5.544 80.02 1728 3.312 80.36 1430 5.279 80.19 1687 3.508 80.11 1453 5.110 80.30 1636 3.859 80.48 1495 4.831 80.59 1452 5.122 80.33 1545 4.541 181.08 1500 4.774 80.46 1598 4.175 581.03 1534 4.643 81.25 1633 3.940 80.93 1473 5.035 80.84 1581 4.267 80.89 1474 5.072 81.10 1519 4.702 80.92 1423 5.403 80.62 1485 4.922 80.84 1421. 5.406 80.54 1499 4.732 80.05 1392 5.654 80.58 1547 4.437 80.45 1369 5.854 80.54 1597 4.069 80.20 1334 6.141 80.32 144 ; .IIJII \I] ill 4' 1| II II [II-Elli! Appendix IIIC: 145 Europium dibromide vaporization 0 -log P AHggs 0 -log P AHo T (K ) (atm (kcal/gfw) T ( K) (atm) (kca17gfw) 1237 5.326 69.77 1412 3.951 69.33 1278 4.978 69.65 1367 4.260 69.31 1304 4.655 68.92 1318 4.633 69.40 1331 4.465 68.99 1345 4.481 69.71 1352 4.285 68.80 1383 4.193 69.61 1237 5.328 69.78 1439 3.930 70.38 1278 4.905 69.23 1511 3.411 70.05 1304 4.739 69.42 1568 3.119 70.47 1331 4.548 69.50 1476 3.598 69.82 1352 4.301 68.90 1445 3.790 69.71 1318 4.628 69.36 1412 4.006 69.69 1345 4.504 69.85 1367 4.352 69.89 1383 4.145 69.30 1185 5.654 69.15 1439 3.868 69.98 1228 5.324 69.33 1511 3.384 69.86 1246 5.128 69.05 1568 3.034 69.86 1185 5.674 69.26 1476 3.587 69.75 1228 5.403 69.77 1445 69.96 1246 5.234 69.66 34676 Appendix IIID: Trieuropium tetraoxide monobromide vapori- zation '1219 5.860 139.11 1275 5.403 139.85 1261 5.462 139.07 1226 5.842 139.67 1331 4.846 138.87 1198 6.091 138.31 1331 4.890 139.42 1240 5.645 138.96 1367 4.582 139.11 1303 5.112 139.27 1219 6.000 140.67 1341 4.838 139.76 1261 5.514 139.63 1275 5.308 138.74 1331 4.809 138.44 1389 4.521 140.44 1331 4.816 138.52 1441 4.232 141.56 1367 4.504 138.13 1520 3.592 138.97 1407 4.313 139.47 1537 3.551 140.81 1352 4.611 138.03 1600 3.064 139.04 1423 4.170 139.10 1565 3.403 141.07 1505 3.602 138.78 1485 3.702 138.41 1455 4.068 140.68 1414 4.394 141.23 1407 4.366 140.16 1389 4.398 138.89 1352 4.611 138.03 1441 4.136 140.29 1423 4.244 140.06 1520 3.564 139.53 1505 3.682 139.88 1537 3.413 138.85 1455 4.101 141.12 1600 3.071 139.14 1198 6.100 139.45 1565 3.427 141.41 1240 5.685 139.40 1485 3.753 139.11 1303 5.072 138.79 1414 4.206 138.74 1341 4.861 140.05 1466 3.821 138.36 APPENDIX IV: Thermodynamic Values for Data Reduction Appendix IVA: Approximated heat capacity, enthalpy and entropy values Phase a b c d Estimated S298 eu Eu304(s) 43.61 6.24 13,270 250.31 49.0 EuO(s) 12.54 2.08 3,830 72.60 16.3 Eu3O4Br(s) 49.57 6.24 15,050 284.26 63.8 EuOBr(s) 18.50 2.08 5,610 106.02 29.0 EuBr2(s) --— -- --- --- 40.1 EuBr2(g) -—— —- -—- --- 76.3 Appendix IVB: Enthalpy, entropy and free energy functions 0- Eu203 (s, monoclinic)(I-IT 0 H393),(S;-S298) values from refer- ence 14. o 0 0 o T (OK) (HT-H298) cal/gfw (Sg‘sg98) eu ‘(GT‘sts)/T eu 1100 26,840 42.75 53.35 1200 30,430 45.88 55.52 1300 34,070 48.79 57.58 1400 37,750 51.52 59.55 1500 41,470 54.08 61.43 1600 45,220 56.50 63.24 1700 48,990 58.79 64.97 1800 52,780 60.96 66.64 1900 56,590 63.02 68.24 2000 60,140 64.98 69.78 Continued on next page 146 147 Appendix IVB: (Continued) 0 0 L 0 0 T (0K) (HT-H298) cal/gfw (sTészgs) eu -(G;-Hggs)/T eu Eu304(s) 1300 48,700 70.49 82.30 1400 53,900 74.35 84.85 1500 59,170 77.98 87.53 1600 64,490 81.42 90.11 1700 69,880 84.69 92.58 1800 75,340 87.80 94.94 1900 80,850 90.78 97.22 2000 86,430 93.65 99.44 EuO(s) 1300 14,230 20.56 24.61 1400 15,760 21.69 25.43 1500 17,320 22.78 26.23 1600 18,900 23.79 26.98 1700 20,490 24.75 27.70 1800 22,110 25.69 28.41 0 EuBr2(s.E) (Hg-H298) and (s;- S398) values from References 29 and 30 by graphical interpolation 1000 20,000 29.00 49.10 1100 22,400 31.50 51.20 1200 24,800 34.00 53.40 1300 27,200 36.00 55.20 1400 29,600 37.50 56.50 1500 32,000 39.00 57.80 1600 34,400 40.00 58.60 Eu304Br(s) 1100 43,250 69.75 94.43 1200 48,930 74.68 97.91 1300 54,660 79.27 101.22 1400 60,460 83.57 104.38 1500 66,330 87.62 107.40 1600 72,250 91.44 110.28 EuOBr(s) 1400 22,330 30.91 43.96 148 Appendix IVC: Free energy function changes for the vapori- zation reactions Phase Eu304(s) EuO(s) EuBr2(£) Eu304Br(s) T°K —Afef(VI-1) —Afef(VI-2) -Afef(VI-3) —Afef(VI-4) 1000 34.86 1100 33.77 59.76 1200 32.55 59.21 1300 31.77 31.52 58.79 1400 31.60 31.17 58.32 1500 31.35 30.68 57.88 1600 32.03 31.19 30.56 57.52 1700 31.79 31.03 1800 31.62 30.78 1900 31.41 2000 31.14 Appendix IVD: Thermodynamic functions from the literature Phase FEE::?ggy2:m2980x Value Reference Eu(g) AH; kcal/gfw 41.9 i 0.2 88 Eu203(s) -393.9 i 0.9 12 Br(g) 26.740 69 Eu(g) AG; kcal/gfw 34.212 88 Eu203(s) " (-370.9) (est) Br(g) " 19.700 69 Eu(g) S° eu 45.097 88 .Eu203(s) " (35.0) 17 Br(g) " 41.850 69 Eu(s) " 19.31 88 Br2(£) " 36.38 69 ,EuBr2(9) no kcal/gfw (202) 30 APPENDIX V: Data for Thermodynamic Calculations -AH° 829 7(ég/figés77T (eu) -Phase (kcaf/§%3) (eu 10009R’ 14009K 2000°K 2500°K LiH(£) 15.10a 16.37a LiBr(£) 80.97a 26.28a 32(9) 0 34.76a Eu203(s) 393.9b 35.0b 51.08 59.55 69.8 77.9 Eu3O4(s) 542.6 49.0 72.72 Eu304Br(s) 597.7 , 63.7 90.56 120.4 131.5 .EuO(s) 145.2 15.0 21.89 25.43? 29.72 EuOBr(s) 203.3 29.0 38.92 50.0 54.1 Eu(s) 0 19.31C 22.85C 25.29C Yb203(s) 433.68b 31.8b 47.88 56.25 66.58 Yb304(s) 580 40.9 64.72 Yb304Br(s) 630 57.3 84.16 YbO(s) 143 11.1 17.99 21.53 25.82 YbOBr(s) 195 24.4 34.42 Yb(s,£) 0 . 14.30c 17.82c 20.17c Yb(g) -36.35c 47.40c EuBr2(s,£) 178.0 40.1 49.1 56.50 58.3 61.0 Br(g) -26.74a 41.81a 44.34a 47.10a 48.11a aReference 69 bReference '17 CReference 88 149 71W 9941 mmmmlmmm' W1... ) ununmnu)