THE VAPORIZATION AND SUBLIMA-TI’ON THERMODYNAMICS 0F SELECTED LANTHANIDE FLUORIDES . Dissertation for the Degree of Ph. D. r MICHIGAN STATE UNIVERSITY ' ROBERT MALCOLM BIEFELD : 1974 “‘z E L Mkia ‘ E ’5, University a . x -W W. IBRARY hgnSmw ‘ 4 ..4 'v, ABSTRACT THE VAPORIZATION AND SUBLIMATION THERMODYNAMICS OF SELECTED LANTHANIDE FLUORTDES By Robert Malcolm Biefeld The vaporization and sublimation reactions for the samarium, thulium and ytterbium fluoride systems have been investigated at high temperatures. Mass loss, X-ray powder diffraction and elemental analyses were used to determine the high temperature reactions in these systems. The ytterbium fluoride system was also examined by mass spectrometry. The appearance potentials and fragmentation patterns + + , for the gaseous ions Yb+, YbF and YbF2 were determined from the effusates of: (l) a condensed ytterbium fluoride with a composition that varied between YbF to YbF 2.00 (2) YbF and (3) YbF 2.40’ 2.40 3.00' Both SmFZ.00 and YbF2.00 decompose when heated to give metal rich vapors and metal deficient residues until residues of the compo- sitions Ssz 40 and YbF2 40 are reached. Thulium partially reduced TmF3, but a reduced thulium fluoride was not isolated. Partially reduced TmF3 decomposes when heated to a metal rich vapor and a TmF 3 enriched residue. The following equilibrium vaporization and sub- limation reactions were established: nF2.40(s,£) = (0.60) LnF2(g) + (0.40) LnF3Cg). (1) an F3. 00(s, z) = (0. 05) LnF2. 40(s,£) + (0.95) LnF3(g) + (0.03) F(g). (2) for Ln = Sm and Yb; and mF3 00(5, £)= TmF3(g). (3) A target collection Knudsen effusion method was used to obtain eqllilibrium vapor pressures for these reactions over the temperature Robert Malcolm Biefeld ranges of: 1369-1791 K for SmF2.40, 1452-1742 K for YbF2.40, 1353- 1342-1794 K for YbF and 1348-1809 K for 1746 K for SmF3.OO, 3.00 TmF3.00° The following second-law enthalpy and entropy changes with associated standard deviations were derived at the median temperatures: _ + . 1580 (37.2 ‘ 1 4) 1 _ 1.1) kcal mol and A81597 - + . _ 2 O) kcal (90. i 2.2) kcal mol“1 and A30 ”2. 40’ “1580" -1-1 cal mol K ; YbF 5 40, AH0 = (96. 2.1597 9+ - -1-1 + o _ 0.67) cal mol K , SmF3.OO(s), AH1462— O -1 -1 i 1.4) Cal mol K ; Sm F3. 00(2), AH1669: -l -1 = (34.8 +2. 8) cal mol K ; (36.8 - (95. 3 -1 mol and A51462- (42.8 (83. i 4.7) kcal mol-1 and A80 1669 -1 O i 0.41) kcal mol and A31568— 8 = (86.24 i 0.48) kcal mol"1 and 2 bF3.00 1568 9 -1 cal mol-1K ; and TmF 0, AH° 3.0 1579 ASiS79= (34.95 i 0.32) cal mol ”1K 1. Estimated and reported thermo- dynamic functions were employed to reduce the thermodynamic values to 298 K. The following values with estimated uncertainties were derived by the 2' method: SmF (s), AH398 = (100. i 3.4) kcal mol-1 2.40 2 and A8398 = (46.2 i 2.8) cal mol ”1K 1; YbF2.40(s), AH298 = (110.7 i 2.3) kcal mol.1 and A8398 = (50.8 i 2.1) cal mol-1K 1; SmF3.OO(s), ‘AH398 = (101.7 i 2.0) kcal mol"1 and A8398 = (52.5 i 1.7) cal mol-lK-l; YbF3.OO(S)' AH298 = (111.1 i 1.3) kcal mol.1 and A8398 = (56.2 i 1.3) cal mol'lx‘lg and TmF3.00(s), AH298= (108.2 i 1.5) kcal mol-1 and A8398 = (55.4 i 1.3) cal mol ”1K 1. The following AH298 values with estimated uncertainties were derived by the third-law procedure: -1 . + . ' SmF2.40(s), (104 3 0) kcal mol , YbF 4 _ -1 mol , SmF3.OO(s), (101.7 -1 3.5) kcal mol , and TmF3.OO(S)’ (107 (S)! (1090 i 204) kcal 8 (s), (107. 2.40 i 2.6) kcal mol-1; YbF + 3.00 0 - '1 + Robert Malcolm Biefeld The derived thermodynamic values were used with estimated and reported values for the enthalpies of formation and standard entropies 5398’ to calculate the enthalpies and entropies for the hypothetical congruent sublimation reactions of SmF2(s), SmF3(s), YbF2(s) and o O = .+.. YbF3(s) at 298 K. Values are as follows. SmF2(s), AH298 (99.S _ 1 _. _1 -1 O O 9.3) kcal mol , A5298 9 i 6.8) cal mol K and AH298(3rd law) -1 -l + 0 O : , + , , 5 _ 9.1) kcal mol , SmF3(s), AH298 (101 2 _ 2 S) kcal mol 1 _1 - o = + O = . + . A8298 (54.1 _ 1.9) cal mol K and AH298(3rd law) (101 2 _ 3 2 -1 o -1 0 : + O = . + kcal mol , YbF2(s), AH298 (109.O _ 8.4) kcal mol , A8298 (46 0 _ 1 -1 - o -1 = + ' 6.1) cal mol K and AH298(3rd law) (111 _ 10) kcal mol , and -1 o = . + . ’ o YbF3(s), AH298 (113 3 _ l 8) kcal mol AS cal mol-lK-l and AH398(3rd law) = (109. = (40. = (106. ) = + 298 (58'1 - 1'4) -1 + . . 0 _ 4 1) kcal mol Boiling points and the associated enthalpies of congruent vaporization were derived for SmF 40(2), SmF2(£), SmF3(£), YbF (fi), 2. 2.40 YbF2(£), YbF3(£) and TmF3(£). Calculations with estimated thermodynamic values for EuF 3.00(S) indicated that it should sublime in a manner analogous to those of SmF3.OO(s) and YbF3_OO(s). The thermodynamic values derived for the hypothetical congruent vaporization and sublimation of the lanthanide fluorides are compared with previously reported values for the alkaline earth difluorides and selected lanthanide fluorides. The differences and similarities are discussed. The trifluoride thermodynamics are similar to those reported by some investigators but not others. The difluoride therm- dynamics are similar to those of europium(II) and strontium(II) fluorides. THE VAPORIZATION AND SUBLIMATION THERMODYNAMICS OF SELECTED LANTHANIDE FLUORIDES By Robert Malcolm Biefeld A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry ACKNOWLEDGEMENTS It would be impossible to mention all of the people who have contributed to the completion of the research for this dissertation in a short space. However, I wish to thank all of the past and present members of Dr. Harry A. Eick's research group and the faculty and staff of the Chemistry Department at Michigan State University. Special thanks must be given to Dr. A. V. Hariharan for his help with the experimental techniques which were used and to Dr. Harry A. Eick for his helpful suggestions and guidance. I wish to thank my wife, Dr. Carol G. Biefeld, without whose encouragement, understanding and hours of effort this dissertation might not have been completed. The financial support of the Chemistry Department at Michigan State University and the U. S. Atomic Energy Commission is acknowledged gratefully. ii TABLE OF CONTENTS Chapter Page 1. Introduction 1 2. Previous Investigations of Lanthanide Fluoride Systems 3 2.1. Preparation of Lanthanide Fluorides 3 2.2. Structural Determinations 4 2.3. Thermochemical Measurements on Lanthanide Halides 7 2.4. Molecular Geometry and Infrared Spectra of Gaseous Lanthanide Fluorides 11 2.5. Electronic Structures of the Gaseous Lanthanide Fluorides l3 3. Theoretical Considerations 15 3.1. The Phase Rule and Vaporization 15 3.2. Determination of Vapor Pressure -- The Knudsen Effusion Method 16 3.3. Temperature Measurement 22 3.4. Mass Spectrometric Measurements 23 3.5. X-Ray Fluorescence Analysis 26 3.6. Thermodynamic Calculations 27 4. Experimental Materials, Equipment and Procedures 34 4.1. Materials 34 4.2. Preparative Procedures and Equipment 35 4.3. X-Ray Powder Diffraction Analysis 37 4.4. Metal Analysis 37 4.5. Mass Spectrometric Procedures 38 4.6. Target Collection Procedures 38 4.7. X-Ray Fluorescence Analysis 41 4.8. Film Thickness Monitor 43 4.9. Distillation Experiments 44 4.10. Mass Loss Experiments 44 5. Results 46 5.1. Preparations 46 5.2. Mass Loss Results 49 5.3. Mass Spectrometric Results 53 iii TABLE OF CONTENTS (cont'd.) 5.4. Distillation Results 5.5. Knudsen Effusion Results 6. Discussion 6.1. Evaluation of Experimental Procedures 6.2. Evaluation of Thermochemical Data and Estimates 6.3. Pressure-Composition Diagrams and Stability Relationships 6.4. Conclusions and Suggestions for Future Investigations References Appendices iv 66 67 92 92 94 102 111 113 121 10. 11. 12. 13. 14. 15. LIST OF TABLES Structural Data of Selected Lanthanide(III) Fluorides Phase Regions Observed in the LnFZ-LnF3 System for Ln = Eu and Sm X-Ray Fluorescence Spectrometer Conditions Metal Analytical Results for Selected Lanthanide Fluorides X-Ray Diffraction Results for Selected Lanthanide Fluorides Structures of Selected Reduced Lanthanide Fluorides Results of Mass Loss Experiments for Ytterbium Fluoride Samples Confined in M0 Results of Mass Loss Experiments for Samarium and Thulium Fluoride Samples Confined in Mo Appearance Potentials of the Ions Detected in the Ytterbium Fluoride System Fragmentation Patterns for Selected Lanthanide Halides Experimental Conditions for Vaporization Runs in the Ytterbium Fluoride System Results of Linear Least-Squares Analyses of Vaporization Reactions in the Ytterbium Fluoride System Lower Limits of Knudsen Numbers Comparison Between the Sublimation Thermodynamics of Selected Lanthanide(III) Fluorides at 298 K for Incongruent and Congruent Reactions Thermodynamic Values for the Congruent Sublimation of Selected Lanthanide(III) Fluorides Page 42 47 47 48 50 52 62 68 70 93 96 97 LIST OF TABLES (cont'd.) 16. 17. 18. 19. Comparison of Pressures Observed by Various Investigators for Gaseous Lanthanide Fluorides at Median Temperatures 98 Thermodynamic Values for the Congruent Sublimation of the Intermediate Fluorides Ssz.40 and YbF2.40 According to the Reaction LnF2 40(5) = (0.6) LnF2(g) + (0.4) LnF3(g) 100 Thermodynamics for the Congruent Sublimation of Selected Meta1(II) Fluorides lOl Thermodynamic Values for the Congruent Vaporization of Selected Metal Fluorides at their Boiling Points 103 vi 10. 11. 12. 13. LIST OF FIGURES Page Distillation Assembly 45 Intensity of Yb+ from YbF (0.00 < x < 0.40) Confined . . 2+x -— in Mo XE} Time 54 + Ionization Efficiency Curve of Yb from YbF2+X (0.00‘5 x < 0.40) Confined in M0 56 Intensity of Yb+ from YbF (0.00 < x < 0.40) Confined . . 2+x —- ‘— in M0 XE} Time 57 . . . + + + Fractional Ion IntenSities of Yb , YbF and YbF2 from YbF (0.00 f_x S_0.40) Confined in M0 vs, Time 58 2+X . . . . + + + Ionization Effic1ency Curves for Yb , YbF and YbF2 from YbF2+x (0.00 5.x < 0.40) Confined in M0 60 Ionization Efficiency Curves for Yb+, YbF+ and YbFz+ from YbF Confined in M0 61 2.40 . . . . + + + Ionization EffiCiency Curves for Yb , YbF and YbF2 from YbF3 Confined in Mo 63 Natural Logarithm of the Equilibrium Constant for the Congruent Vaporization of YbF2 40 and the Pressure of Yb(g) from YbF2+x (0.00 f_x < 0.40) vs. Reciprocal Temperature 71 Rate of Deposition of Yb(g) from YbF2+x (0.01 Slx < 0.40) Confined in M0 vs. Time 72 Natural Logarithm of the Equilibrium Partial Pressure of YbF3(g) from YbF3(s,£) Kg, Reciprocal Temperature 76 Rate of Deposition for Sm(g) from SmF2+x (0. 00 <’x < 0. 40) Confined in M0 vs. Time 80 Natural Logarithm of the Equilibrium Constant for the Congruent Vaporization of SmF2 0 and the Pressures of Sm(g) from SmFZ+x (0. 00 uwmao mcowwmm mmmnm .N wanmh ’.:. to? ...-. - ‘ u n.- @- .a.... .. ‘ A...-L.. . . 0} f - ' n‘.. \. ‘4- - f‘ 9 and Gibbs free energy of formation for yttrium(III) fluoride, often considered one of the rare earths, have been measured by fluorine bomb calorimetry [AH‘%(298 x) = —(410.7 1- 0.8) and AG‘%(298 K) = -(393. i 1.0) kcal mol-'1].32 6 2.3.1.2. Lanthanide(II) Fluorides No data are available for the lanthanide(II) fluorides. The estimative technique of Hariharan,S which is to use the values reported for the alkaline earth fluorides, is probably the best alternative. 2.3.1.3. Other Selected Lanthanide Halides Enthalpy increments have been reported for certain lanthanide(III) chlorides, bromides, and iodides,33"35 but no experimental data are available for any corresponding lanthanide(II) compounds. The enthalpies 236’37 and YbClz38 have been measured. 2.3.2. High Temperature Sublimation and Vaporization Studies of formation of EuCl 2.3.2.1. Lanthanide(III) Fluorides Recently there has been a resurging interest in the sublimation and vaporization properties of the lanthanide(III) fluorides. Searcy and coworkers characterized the high temperature behavior of LaF 3, CeF3 and PrF3 by a combination of torsion-effusion and torsion-Lang- muir techniques.39-41 By using high temperature mass spectrometric methods, these workers have also demonstrated the existence of La2F6(g) and Ce2F6(g) and have determined the stabilities and partial pressures of these species in equilibrium with LaF3 and CeF3.42’43 spectrometric studies have been made on the sublimation reactions of all of the lanthanide(III) fluorides except promethium.44 The bond Mass dissociation energies and stabilities of the gaseous mono- and difluorides of all the lanthanides except promethium were derived 10 . . . . . . 44 from ionization potentials determined by the electron-impact method. The sublimation thermodynamics and vapor pressures of all the lanthanide(III) fluorides except promethium, samarium, europium and ytterbium were redetermined by simultaneous mass effusion and mass . 8 5 spectrometric measurements. ’4 ’46 This latter series of measurements was effected as part of a study on the role of the correlation of entropy and enthalpy in the error analysis for vaporization and sub- limation thermodynamics. 2.3.2.2. Lanthanide(II) Fluorides The vapor pressure and the sublimation and vaporization thermo- dynamics study on EuF by Petzel and Greis47 with mass effusion methods 2 is the only determination reported for a lanthanide(II) fluoride. 2.3.2.3. Other Lanthanide Halides Of particular interest to this dissertation are the thermochemical values reported for the halides of samarium, europium, thulium and 3,48 SmClz, EuC13, TmCl3 and YbClBAg were measured by the mass effusion method. A boiling ytterbium. The vapor pressures of the halides SmBr point method was used to measure the vapor pressures of SmClz, EuCl and YbClz.SO The dissociation pressures of SmCl3, EuCl3 and YbCl3 were determined by the measurement of chlorine pressures with a quartz 2 membrane.51 The decomposition of EuBr3 to EuBr2 and bromine has 52 also been investigated. Recently the vaporization and sublimation thermodynamics of europium(II) halides have been studied systematically and correlated by mass spectrometry and Knudsen effusion methods.5’47’53-SS A close correspondence in the thermochemical properties was reported between the dihalides of europium and the heavier alkaline earths (Ca, Sr 11 and Ba), especially with those of Sr. Another important observation concerned the constant entropy of congruent sublimation at 298 K for europium(II) halides.S From the above observations the thermo- chemical properties of other lanthanide(II) halides might be expected to correspond to properties of the heavier alkaline earths and the entropy change for the congruent sublimation at 298 K for the di- halides of a particular lanthanide should be constant. The vaporization and sublimation of EuCl2 and EuCl3 were inves- tigated zia_mass spectrometry by Hastie g£_al,56 A target collection technique in conjunction with mass spectro- metry was used to study YbC12.57 The vaporization thermodynamics of YbCl2 corresponded closely with those of EuCl2 and SrClz. None of the other dihalide systems has been investigated. 2.3.3. Galvanic Cell Measurements The solid electrolyte galvanic cell technique was used to deter- mine the free energies of the displacement reactions for selected metals and their fluorides.58 The free energies of formation as a function of temperature were reported for YF3, NdF3, GdF3, DyF3, ErF3 and LuF3. 2.4. Mblecular Geometry and Infrared Spectra of Gaseous Lanthanide Fluorides A variety of methods have been used to investigate the molecular geometry of the lanthanide fluorides. These methods include electron diffraction of molecular beams, infrared and Raman spectra of the gaseous fluorides isolated in low temperature, inert gas matrices and electric quadrupole deflection of molecular beams in inhomogeneous electric fields. The information arising from such investigations, 12 although sometimes contradictory, has been an invaluable aid in estimating the thermodynamic functions of the gaseous lanthanide fluorides. 2.4.1. Lanthanide(III) Fluorides An unresolved controversy exists over the structures of some gaseous lanthanide(III) fluorides. The trifluorides can assume a planar, D3h’ or a non-planar, C3v’ structure. Of the fluorides of interest to this dissertation, SmF3, EuF3, TmF3 and YbF3, only SmF3(g) 59,60 However, SmF3 was not investigated by Hauge g£_§1.61 who assigned a non-planar configuration has consistently been reported as planar. for EuF3(g) and YbF3(g) while Wesley and DeKock6O assigned a planar configuration to these molecules. The results obtained by Kaiser 32 21.59 from their electric deflection experimetns were inconclusive for SmF3(g), EuF3(g) and YbF3(g) due to reduction of the samples by the nickel oven. The F-Ln-F angle used by Hauge gt 31.,61 117°, indicates that any distortion from a planar configuration, 120°, for the gaseous lanthanide(III) fluorides is small. The use of Raman measurements resolved the controversy for PrF3(g), and it is considered planar.62 However, no other trifluoride was investigated in this manner. The reported reduction of YF 63 3 be used to explain the spectra observed by Hauge gtual.61 for EuF3Cg) by tantalum containers cannot or YbF3(g) since the spectra did not correspond to those reported for EuF2(g)64'65 and YbF2(g).65 The incorrect choice of configuration for the gaseous trifluorides changes the calculated entropy and free energy function values by R 2n 2 (R = 1.98717 cal mol-1K-1) (cf. Section 3.6.6.3.). 13 Electron diffraction studies have yielded Ln-F distances for YF3(8)- LaF3Cg) and NdF3(g).66 2.4.2. Lanthanide(II) Fluorides . . . 5 Both electric deflection59 and infrared matrix isolation64’6 experiments are in complete agreement in so far as the structures of SmF2(g), EuF2(g) and YbF2(g) are concerned. The gaseous difluorides have a non-linear structure with a F-Ln-F angle of (110 i 15)° for SmF2(g) and EuF2(g) and an angle of (140 i 10)° for YbF2(g). Neither electron diffraction nor Raman matrix isolation studies have been carried out on the difluorides. 2.5. Electronic Structures of the Gaseous Lanthanide Fluorides 2.5.1. Lanthanide(III) Fluorides In the absence of experimental data, an accepted practice for calculating the electronic contribution to the statistical entropy 60,67,68 has been to use the data available for the free ion. Values have been reported for the trivalent lanthanide ions of interest to this dissertation (Sm+3, Eu+3, Tm+3 and Yb+3).69-71 2.5.2. Lanthanide(II) Fluorides The same lack of experimental information exists for the gaseous lanthanide(II) fluorides. The ground states of the lanthanide(II) ions are assumed to be those described by Sugar and Reader72 (1.3,, an fN configuration). The electronic energy levels of the lanthan- ide(II) ions are taken to be the same as the (Ln + l)+3 levels. For example the reported electronic energy levels for europium(III)70 were used to estimate the levels for samarium(II). The scarcity of thermochemical measurements for lanthanide binary compounds requires the use of many estimates in investigations such 14 as the one reported in this dissertation. Because of this scarcity the thermodynamic values presented herein are deemed to be a small but valuable contribution to the thermodynamic data presently avail- able for the lanthanide halides. CHAPTER 3 THEORETICAL CONSIDERATIONS 3.1. The Phase Rule and Vaporization High temperature vaporization and sublimation reactions can be classified broadly as either congruent or incongruent. Congruency requires that the vapor and condensed phases have identical composi- tions. Conversely, incongruency requires nonidentical compositions for the vapor and condensed phases. The application of the Phase Rule, (3-1), in which for each system F is the number of degrees F=C-P+2 (3-1) of freedom (1.3., the number of parameters that must be specified to establish the state of a system73), C the number of independent chemical variables or components and P the number of phases present, further characterizes vaporization reactions at equilibrium. For a congruent reaction in a binary (333., two component) system, the number of phases, P, is two (1.3., vapor and solid or liquid). However, the congruency constraint requires that the composition of both of these phases be equal, and the number of independent components, C, is one. Thus, according to the Phase Rule, for a congruent reaction in a binary system only one parameter, 235! the temperature, needs to be specified to define the pressure of the system (1.3., the system is univariant). For an incongruent reaction in a binary system, the number of independent components, C, is two. 15 .—.. v. 16 If in addition to the vapor, two condensed phases are present, the state of the system is again defined completely by specifying one parameter. However, if in an incongruent reaction the condensed phase is a solid solution or a solid whose composition can vary within limits, the pressure of the system is not defined completely by fixing the temperature (1.3,, the system is bivariant). The qualitative aspects of vaporization and sublimation reactions in a binary system can be represented in the form of a constant temperature diagram of pressure vs. composition. The composition range of the phases and their vaporization reactions are readily defined from such a diagram. More complete discussions of the Phase Rule, pressure-composition diagrams, and heterogeneous equilibria can be found elsewhere.73"75 3.2. Determination of Vapor Pressure -- The Knudsen Effusion Method 3.2.1. The Kinetic Theory of Gases . . 76 A variety of methods can be used to determine vapor pressures. The Knudsen effusion method, which was used in the research for this 10 5 dissertation, is applicable in the pressure range 10- to 10.3 atm. In the Knudsen effusion method the flux of molecules through an orifice in an isothermal cell is determined. Under certain ideal conditions (discussed below) the equilibrium vapor pressure within the container can be calculated from this flux and from the kinetic theory of ideal gases.77 The appropriate expression for the flux of molecules, dJ, which strike or leave an area, da, in the solid angle, dw, for an ideal gas in equilibrium with its surroundings is given by (3-2). dJ = (06/41:) cose dw da (3-2) 1“ (3~2) 9 is the angle of the normal to da and the line of direction .,.. H.- 17 defined by dw, v is the molecular density and E is the average molecular thermal speed. Equation (3-2) is called the cosine distri- bution law. Integration of (3-2) yields the total molecular flux, J, which strikes an area, a, J = avE/4. (3-3) Use of (3-3) in combination with the ideal gas law, pV = NkT, and E = (8kT/n1fifi, where k is the Boltzmann constant, T is the absolute temperature, N and m are the number and mass of the molecules, respectively, yields the Hertz-Knudsen equation (3-4),78’79 p = (w/at)(2flkT/m)%, (3—4) in which w is the mass of the vapor which strikes an area, a, in a given time, t. If the molecules are allowed to escape through an infinitely thin orifice of area, a, into a vacuum, the above expression remains unchanged provided the rate of molecular escape does not change the equilibrium vapor pressure in the cell. 3.2.2. The Target Collection Technique One of a variety of methods used to determine the rate at which molecules effuse through an orifice is target collection. In this method a fraction of the effusing gases is collected by condensation on a target located coaxially with and parallel to the orifice. If the orifice and target are circular, and the orifice radius, R0, is Eflnall compared to that of the target radius, R, and to the target to (xrifice distance, C, application of the cosine distribution law 6 for the fraction of the effusate, F, Yields an expression, (3-5),7 F = 1(2/((:2 + R2) (3—5) Striking the target. Combination of (3-4) and (3-5) and substitution (If? nunnerical values for the appropriate constants leads to equation .. 18 23 -1 (3-6). The following values were used: N = 6.0225 x 10 mol , l p(atm) = (w/44.33 at)(T/M)6(1/F) (3-6) ~16 -l _ 6 -2 k = 1.3805 x 10 erg K , 1 atm — 1.0133 x 10 dynes cm , and n = 3.1416. In (3-6) M is the molecular wight of the effusing gas in amu, and the quantities w, a, t, T, M, and F are experimentally determinable. By application of equation (3-6) to a univariant binary system, the equilibrium vapor pressures can, in theory, be determined. 3.2.3. Underlying Assumptions and Limitations of the Knudsen Effusion Method 3.2.3.1. Kinetic Theory of Ideal Gases Many assumptions are made in the derivation of the equations used in the Knudsen effusion method. The most basic of these is that the vapor species behave as ideal gases. An ideal gas is an isotropic vapor of identical non-interacting point masses with a Phxwellian velocity distribution. Since most gases approach ideality at low pressures,80 their behavior in the pressure regions measured by the Knudsen method should approximate ideality.77“8O 3.2.3.2. Experimental Limitations In the Knudsen effusion method, an attempt is made to approxi- mate ideal conditions so that a physical measurement of the equili- brilnn vapor pressure of a system can be made. The Knudsen cell must be impervious and inert. Chemical reaction between the cell material and the substance under investigation could alter the activities of the substance and change the corresponding vapor pressures.80 Ward .e_t :23 have reported the effect which vapor loss by interactions with the cell wall through collisions can have on the measured vapor 19 18 pressures, ’ 2 and have demonstrated that these effects can be significant. Since a real orifice cannot be infinitely thin, the ideal ori- fice is often approximated with a knife-edged orifice (Lo/R0 8‘ 0, L0 is the length of the orifice and R0 its radius). However, the orifice will always be of finite thickness and the molecular flux from the cell will be altered. Corrections for this effect have . . . 8 been calculated for various types of orifices 3’ 4 and are termed Clausing transmission factors because of his original treatment of 7,88 angular distributions from Knudsen cells.85’86 Hirth and coworkers have extended these calculations to include surface diffusion along the orifice walls and the cell lid. Their calculations involve Parameters that are dependent on the cell material and the effusing Species. Fortunately, the correction factors for the angular dis- bu': ions commonly encountered in the target collection method are not Significantly different from unity. Ward 25 11.81’82’89 have cal- culat ed and measured severe deviations from the cosine law at large angles, but observed only minor effects at the small angles used in the target collection technique. They reported a marked effect, independent of the compound involved, for cell geometry. These effecnm can be minimized by use of a small orifice area as compared to the interior cross sectional area of the cell and by use of a collection technique which employs only small angles. Other reports incliciate that only minor deviations from ideal behavior occur for kn~ 11:‘e-edge orifices or for non-ideal orifices when Clausing trans- m' . - 18SlLon factors are used.90 93 0‘.- .4 .y- ..- u out! no I I ub- . I45. nit 'u. ...' 20 The Knudsen cell must be maintained at a uniform temperature to insure equilibrium conditions. The complete elimination of a temperature gradient in a cell is very difficult experimentally, and a small but constant temperature gradient of 5 to 10° has been shown to have little effect on the resulting experimental values.5’94 However, a small variation in the gradient over the temperature range can have a marked effect upon the derived thermodynamic values. The minimization of the effects of temperature gradients has been discussed by Storms.9 Additional experimental limitations to the target collection method involve the condensation of the effusing vapor as it strikes the target and the interference from molecular collisions between 5,96 the effusing vapor and residual gases. Previous investigators Who employed the same experimental systems that were used for the 1‘‘-?Search done for this dissertation have found no evidence that the lanthanides or the lanthanide halides do not condense when they im- pinge on a chilled target. If residual pressures are maintained two to three orders of magnitude below those of the effusing vapors, 1rlterference from collisions with the residual gases would be limited. 3.2.3.3. Equilibrium in the Knudsen Cell If a system is at equilibrium the rate of the forward reaction, e . . vaporation, must equal the rate of the reverse reaction, condensa- t ’ . . . . 1011. Introduction of an orifice into the cell dictates that a net 1 088 of vapor occurs and that a steady state situation exists. An 7 . which relates the measured pressure, (3-7) e xpt‘ession (3-7) has been derived9 pe = pm[l + f(l/a + l/wA - 2)] pm, to the equilibrium pressure, pe. In this expression f = Waa/A, L11 0.. --. .r‘ 21 a is the orifice area, A is the sample surface area, Na and WA are the Clausing transmission factors for the orifice and the cell body, respectively, and a is the evaporation and/or condensation coefficient. The evaporation coefficient, av, is defined as the observed rate of evaporation divided by the equilibrium rate of molecules striking the sample surface. The condensation coefficient, ac, is defined as the number of molecules which condense divided by the total number of molecules which strike the sample surface. For commonly used Knudsen cells WA 8 0.5. If a z 1, a/A = 0.01, and W8 = 1, then % pm(l + 0.01). The most common experimental indication of a De non-unity vaporization/condensation coefficient is a change in the observed pressure for orifices of different areas. If a differs Significantly from unity, a plot of pIn .‘E‘ pmf for orifices of differ- ent size should be linear and from this plot one can determine p63 and 0.. Lack of any observable orifice effect on the measured pressures ' . . . 8 18 a good indication that pm a: pe. Paule and Margrave have separa- ted the evaporation and condensation coefficients and derived equation (3‘8) . However, experimental determination of av and ac cannot be p9 = pmac/avfi + f(l/o-C + l/wA - 2)] (3-8) effected unequivocally. Recent and more complete discussions of t . O 0 hese coefficients and their determination are available.99’100 3.2.3.4. Molecular Flow Pressure Limits Equilibrium pressure determinations from Knudsen effusion ex- DeI‘T'Lments are reliable only in the pressure range in which the be- h - avlor of the vapor species can be described by the kinetic theory of gases, the molecular flow region. An upper limit for molecular flow has been observed when the mean free path, A, of the vapor 22 . . . lOl . became small compared to the orifice diameter, 2R0. When this . . . . . 101 condition is approached, collisions occur within the orifice region. Various workers have reported the onset of hydrodynamic flow for Knudsen numbers, K= A/ZRO, between 0.05 and 10 for ideal and near- ideal orifices.39’m)’101-105 A lower pressure limit for molecular flow has not been observed experimentally. 3.3. Temperature Measurements The range of temperatures ( Z 1000 K) encountered in the Vaporization reactions for the binary lanthanide compounds are con- veniently measured with a disappearing filament optical pyrometer.106 Temperatures are measured by comparing the intensity of the filament at a given visible wavelength, A z 650 nm, to the brightness of the radiation from a cavity in the Knudsen cell. The intensity of the filament is varied by changing the current passed through it. This current is then matched by means of a shunt resistance to the e°m-f. of a standard cell and the instrument acts as a zero-current potentiometer. Usually the radiation from the cell cavity is observed throngh several optical interfaces from outside the vacuum chamber. To Correct for optical absorption, the temperature of a constant radiation tungsten strip lamp is determined with the optical inter- faces, To, and without them, T. Equation (3-9) relates the actual ' 0 = (l/T - l/To) (3-9) tel“I'lerature, T, and the observed temperature, To, to D which is Q outinonly known as the Wien's Law correction factor.5’106 This cor- ): - . th lion factor may be expressed in terms of the wavelength, 1, the e - . . a , . Inlsswity of the cell caVity at that wavelength, 6, the transmittance 23 of the optical elements, 1, and Planck's second radiation constant, Over the temperature range of C = 0.438 cm K by equation (3-10). (3—10) 2 D = (X/C2)£n(€'7) interest, D is essentially constant for the optical elements used. Temperatures measured by the optical pyrometers were corrected by intercomparison with another pyrometer that had been calibrated at the National Bureau of Standards to the International Practical Temperature Scale of 1948 (IPTS - 1948). On January 1, 1969, a new scale, IPTS - 1968, became effective. No attempt was made to convert the observed temperatures to the more recent scale; only a very 107 small change 2*: (2-5)° would result from such a conversion. 3 .4. Mass Spectrometric Measurements The importance of identifying the molecular species which effuse from the Knudsen cell cannot be overemphasized. Without knowing the molecular composition of the gas in equilibrium with the condensed Phase or phases, one cannot be sure that the vaporization reaction postulated is correct. Because of this uncertainty, the equilibrium pressures and the corresponding thermodynamic values will remain 11" doubt. A time-of-flight mass spectrometer equipped with a high temperature I(rilldsen cell inlet was used for this investigation. Ionization of the molecular beam from the Knudsen cell was accomplished by eleCitron bombardment. In a time-of-flight instrument, the ions are accelerated in pulses and separation occurs in a field-free flight region. Mass identification of the ions is based on velocity selection or time-of—flight in this field-free region. The neutral precursors of the ions (_i_-_e_-. the molecules effusing from the Knudsen cell) 24 can be identified from the fragmentation patterns (1.3., the masses of the ions observed and their relative intensities at a given ion- ization energy) and the ions' ionization efficiency curves and appear- ance potentials.108’111 Appearance potentials can be determined by a variety of techniques,112 such as the linear extrapolation procedure of ion intensity .‘E' electron ionizing energy which was used in this study. This method is known to yield results that are 0.1-0.3 V too high, but use of the known appearance potential for a standard, 3.5. Hg, whose ionization efficiency curve is related closely to that of the ions of interest, helps to reduce uncertainties. If two ion formation processes contribute to an observed ion current, the resultant ionization efficiency curve of that ion can exhibit a distinct break.108 The potential at this distinct break is equal 44,108 to the appearance potential for the second formation process. The absolute pressure of a molecular precursor, pi, is related 8 to the intensity, Ii’ observed for that ion by equation (3-11).10 (3-11) IiT = piOiYiA In (3-11) Oi is the ionization cross-section for the fragmentation prOCess which produces the ion at a given electron energy, Yi is the multiplier gain, and A is a function related to the instrumental so‘-11‘(:e configuration, ionizing energy and transmission factors. Calibration of the instrument by use of a substance of known vapor IDressure and ionization cross-section (_e_._g_. Ag) during each experi- ment allows one to determine A for equation (3-11). However, even if the instrument is calibrated in this manner the lack of t he(Tiretical or experimental data on ionization cross-sections and i I O o . nStrument senSitiVity for most molecules render questionable absolute 25 pressure data obtained from mass spectrometric investigation of these molecules. Ionization cross-sections can be approximated by the 112 additivity principle from published values for the elements or by the calculations of Mann,113 but use of these procedures has been questioned extensively (3.5. see 109). Because of the uncertainties introduced by estimating the quanti- ties in equation (3-11), ion intensities were not used to determine absolute vapor pressures in this dissertation. These uncertainties can be overcome by simultaneous determination of the absolute vapor pressures with an alternate method. Appearance potentials can also be used to obtain bond dissociation . . . . 108,109 or atomization energies of the efquing molecules. If the lienatral precursors and their relative contributions to an ion's intensity can be determined, if the fragmentation processes that prOduce the ion can be identified, and if the appearance potential fTDI‘ each process is determined, the atomization energies for the helltral precursors can be determined from thermochemical cycles. jrl‘ef large uncertainties in the appearance potentials, the kinetic ene‘rgies of the ions, and the separation and identification of frag- mentation processes often render the error limits large and the de- teI‘mination of marginal value. Without extensive calibration procedures, the use of ion intensities and ionization efficiency (harves would yield questionable thermochemical values. However, the lack of extensive calibration will not affect the identification of the composition of the gas which effuses from the Knudsen cell. 26 3.5. X-Ray Fluorescence Analysis When electromagnetic radiation of sufficient energy interacts with a neutral atom an electron is ejected from an inner atomic or- bital. Fluorescent radiation results if an electron from an outer atomic orbital fills the inner vacancy. The energy of the fluores- cent radiation is dependent on the energy separation of the inner and outer levels. If these atomic levels are unaffected by chemical bonding, the energy of the fluorescent radiation will be independent of its environment. X-Ray fluorescence spectrometry is the measure- ment of the energy and intensity of this characteristic fluorescent radiation. Discussions of this method of non-destructive analysis are available (3.5. see 115, 116). Both energy and wavelength dis- Pe‘rsive fluorescence methods have been devised. The wavelength dis- Persive method used in this investigation effects analysis of the fluorescent radiation by diffraction of the beam with a crystal of fiXed interplanar d-spacings. The radiation is detected at a given angle, 28, with respect to the incident beam. By use of the Bragg e(vacation, (3-12) one can determine the theta, 9, values characteristic nk = 2d sine (3-12) 0 . . . . f fluorescent radiation for each element. The intenSity of the f1'~-‘l(>rescent radiation depends upon the characteristic energy chosen, incident tube intensity, and matrix absorption or enhancement effects. The proper choice of detector depends on the resolution of the analyzing crystal and the energy of the fluorescent radiation. It181::‘rumental factors and matrix effects require calibration for each e:Le‘l‘luent before a quantitative anaylsis can be carried out. The 09‘ t ‘ . . linization procedure used for each instrumental parameter is described 27 by Neff.117 His analyses indicate that to discriminate between small differences in concentration, R(I), defined in (3-13), should 1 = 6 _ 3-13 R(I) (r1) /(r1 r0) ( ) be minimized, whereas to extend the detection limits to very low concentration, R(II), defined in (3-14), should be minimized. In R(II) = (ro)%/(r1 - to) (3-14) these equations rO and r1 are the pulse rates for the background and a standard, respectively. 3.6 . Thermodynamic Calculations 3.6.1. The Equilibrium Constant and Standard States The formalism used to represent the equilibrium constant for the reactions studied in this investigation is represented in equation (3-15), where K is the equilibrium constant, v.1 and vj are the K = n(a.)Vi/n(a.)vj (3-15) . i . J 1 J StOichiometric coefficients and a.1 and aj are the activities of the pI‘Oducts and reactants, respectively. Throughout this dissertation the activities of all solid or liquid phases are assumed to be unity. Slnce in a Knudsen effusion experiment the vapors are treated as Ideal, all gaseous activities are considered equal to their partial pressures. The standard state for each gas is taken as the ideal gas at one atmosphere. Because the pressures studied are very low, t . . . . he ideal gas assumption is valid. However, the assumption about the activity of the condensed phases is somewhat arbitrary. The use of Knudsen cells of different materials can help to identify an effect of the cell material on the activities of the condensed phases.118 Examination of the Knudsen effusion residues by X-ray diffraction can give indications of contamination or changes in the crystal 28 lattice. In the absence of any experimentally observable interaction between the condensed phase and the Knudsen cell, the condensed phases are assumed to remain in their standard states (133., the pure sub- stance). The equilibrium constant, K, for a chemical reaction at constant temperature, T, is related to the change in free energy, AG°, by equation (3-16).119 The symbol A is used to represent the sum of A0}; = - RT£n K (3—16) an extensive thermodynamic property, X, for the products of a reaction minus the sum for the reactants, i,e., AXL= 2 v.X. - 2 v.X. (3’17) . i i . J J 1 J At a given temperature 0 = O .. O - ACT AHT TAST. (3 18) When the identities (3-16) and (3-18) are equated, (3-19) results. - Run K = on; - TASS} (3-19) 3.6.2. The Slope-Intercept Method If AH° and AS° are assumed constant over the experimental temper- ature range, a plot of En K.y§, 1/T will be linear with slope fiAH°lR and intercept AS°/R. This method is often referred to as the second- law method. The resultant values of AS° and.AH° are usually equated, not Unannaiguously,120 with the median temperature of the experimental range, T1. These values for AH}! and A85}. can then be reduced to a 1 1 refeltence temperature, T, by the following equations: T O = O o _ AHT AHT1 + J'Tl Acp dT, (3 20) As; = ASSI’. + I; (AC IT) or. (3-21) 1 l p 29 Also, corrections must be made for any condensed phase transitions. Throughout this dissertation 298 K is used as the reference temper- ature . 3.6.3. The Sigma Methods The 2- and 2'-methods use analytical expressions for the heat capactities or thermodynamic functions, respectively, in combination with individual vapor pressure-temperature data points.80’121 Use of these methods eliminates the assumption that.AH° and AS° do not vary with temperature. Since the thermodynamic functions for the lanthanide trifluorides have been reported,7’18 the E'-method of Cubicciotti121 is used in this work. The term 2' is defined as . = -. .. O _ O O _ 0 Z Rfin K A(HT H298)/T + A(ST 8298) = o - o - AH298/T A8298. (3 22) A plot of E. XE! 1/T is linear with a slope and an intercept that give directly AH398 and A8398. The Z and 2' methods are more exact than the slope-intercept method only to the extent that the heat Capacities or thermodynamic functions are known. 3.6.4. The Third-Law Method If the absolute entropies, 3398’ of the reactants and products are known or can be estimated, another independent method of data rEduction is available. The name, third-law method, derives from the use (bf the absolute entropies. The free energy function,8 FEET = (a; - H398)/T = (H; - H398)/T - S°, (3-23) 1nV61ves the absolute entropy and the enthalpy function for a given phase . For any reaction, AFEFT = A(G,‘I’. - H398)“. = - RZn KT - AH398/T (3-24) I - - nleldual values of AH‘2’98 result from the combination of AFEF and 30 in K at each temperature, 0.14398 = - T(AFEF + Rzn K). (3-25) The individual values ofAHg98 derived by the third-law method may be examined to identify temperature or chronological trends. A systematic error in the pressure or temperature determination or in the estimated free energy function change for the reaction may be reflected by a temperature trend. 3.6.5. Comparison of Second- and Third-Law Methods Comparison of the values for AH398 calculated by the two methods is a commonly used check on the experimental measurements and formula- tion of the vaporization reaction. Large discrepancies in the second- and third-law values can indicate experimental errors, choice of an incorrect reaction, nonequilibrium conditions and/or the use of incorrectly estimated thermodynamic functions. Close agreement of these values is support for the correct assignment of the above Parameters. If measured free energy functions are available, dis- agreement of the second- and third-law methods can be used readily to identify experimental errors. Thorn122 has discussed the use of second- and third-law values for the identification of systematic and random errors. He recommends that for a more meaningful measure of data.consistency than just a comparison of only two calculated enthalpies, comparison be made of the £n p _v_s_. l/T intercept (ASE?) f9? (each experiment with the (estimated) absolute entropy change 0N$;,, third-law). Thorn also describes in the same paper122 a method of Statistically correlating the second-law slopes and intercepts f O . C . or SeVeral experiments, a method that yields information about the r ' I o p 0bability of the correctness of the derived thermodynamic values. 31 3.6.6. Estimation of Thermodynamic Functions 3.6.6.1. Solid and Liquid Heat Capacities Since the heat capacities, C3, and the thermodynamic functions for many substances have not been determined, it is often necessary to estimate their values to carry out the data reductions described above. A number of estimative techniques have been developed (33g. see 5, 80, 123, and 124). Also, estimated values for the lanthanide halides have been reported.23 The heat capacities of the solid lanthanide difluorides were estimated at 298 K from the values for the isostructural alkaline earth difluorides by use of the Neumann-Kopp rule, CB(MX2) = CB(M'X2) - CB(M') + CB(M). (3-26) Values for G; at the melting point were estimated gig Kubaschewski's approximation123 that close to the transition point, C° for a solid is 7 to 7.25 cal K.1 g atom-1. Similarly, the heat capacity, C°, P 0f a liquid was estimated to be the same as that found for the alkaline earth difluorides. These values are close to those estimated123 for inorganic liquids, c; e 8-8.75 calK"1 g atom"1 [24-26.25 cal K-l mol"1 for nx2(2)]. 3.6.6.2. Standard Entrppies for Solids Latimer's additivity method125 is used commonly to estimate the Stankflard entropy, 8398’ of solid ionic compounds. This method, which takes into account the mass, size, and charge of the ions involved, yields values within 2 to 4 cal K”1 mol.1 of measured values. Recent reviSions of Latimer's numberslza’126 Cal Kulmol-1 improve the accuracy to l to 2 . Of special interest to this dissertation are the 32 . . 127 . improved values compiled by Westrum. These values allow conSider- ation of the magnetic contribution of the lanthanide ions. 3.6.6.3. Ideal Gas Statistical Calculation of Thermodynamic Functions If ideal gas behavior is assumed, thermodynamic functions may be calculated from experimental spectroscopic data by the use of 5'124’128 The theory involves the formulation statistical mechanics. of a system partition function, Q, in terms of a molecular partition function, q, for N ideal gas molecules satisfying the condition that the number of available molecular states is much greater than N, Q = qN/N!. (3-27) If it is assumed that the translational, rotational, vibrational and electronic contributions to the molecular partition function are independent, q can be expressed as a product of the independent terms, q(V.T) = qt(V,T)qr(T)qv(T)qe(T)- (3-28) These independent partition functions, qi, can be calculated if Spectroscopic data have been determined experimentally or estimated. Also, thermodynamic functions can be derived in terms of these Partition functions. The reader is referred elsewhere for the ana- 1ytical functions and the assumptions used to derive them.5'124’128 3.6.7. Error Analysis A least-squares refinement with associated error analysis was “SGT! to derive the second-law enthalpy and entropy values.129 The accompanying uncertainties are reported as i- o’. No attempt has been In . . . . ade to aSSign to the resultant thermodynamic values uncertainties due . . t3<> errors in temperature measurements, vapor pressure eqUipment 33 constants, Knudsen cell orifice area or X-ray fluorescence analysis. Estimated uncertainties in the thermodynamic functions are included in the thermodynamic values reported at 298 K. An uncertainty in the free energy functions has been estimated, and was included with the standard deviation in the uncertainty of the reported third-law derived enthalpy values. The overall uncertainties in the derived thermochemical values have been based on additivity. The use of additivity is consistent with the representation of the estimated uncertainties as determinate errors rather than indeterminant errors and represents a more liberal uncertainty than the treatment for indeterminate errors.129’13o CHAPTER 4 EXPERIMENTAL MATERIALS, EQUIPMENT AND PROCEDURES 4.1. Materials The following chemicals were used: ytterbium metal (99.92 distilled metal, lot#YbM 3-082D, Research Chemical Co., Phoenix, Ariz.), ytterbium sesquioxide (99.92, code#1202, LT1114, American Potash and Chemical Corp., W.Chicago, Ill., and 99.99%, lot#YbO 4-008, Research Chemcial Co., Phoenix, Ariz.), samarium metal (99.9%, PSO#2716, lot#Sm-6ll-M, Michigan Chemical Corp., St. Louis, Mi.), samarium sesquioxide (99.9%, PSO#4056, lot#Sm-102-O, Michigan Chemical Corp., St. Louis, Mi.), thulium metal (99.92, distilled metal, lot#TmM 3-085D, Research Chemical Co., Phoenix, Ariz., and 99.92, PSO#6092, lot#Tm-587-M, Michigan Chemical Corp., St. Louis, Mi.), thulium sesquioxide (99.99%, lot#TmO 4-003, Research Chemical Co., Phoenix, Ariz.), hydrofluoric acid (48%, aqueous reagent grade, Matheson, Coleman and Bell, Norwood, Ohio), and reagent grade NH F and HN03(aq), (- from various sources. Materials used included: graphite stock (Becker Brothers Carbon Co.,, Cicero, 111.), molybdenum rod and 302 tungsten-molybdenum stock (KUIite Tungsten Corp., Ridgefield, N.J-). platinum (J. 31811013 and Co. o Malvern, Pa.), copper stock (McMaster Carr Supply Co., Chicago- 111 - ) .9 vitreous carbon crucibles (Beckwith Carbon Corp., Van NuyS- Cal- ) .9 quartz boats (Thermal Syndicate, Ltd., England), quartz tubing 34 -v ..- -¢ ~- 35 (Engelhard Industries, Inc., Hillside, N.J.), and seamless tantalum tubing (Fansteel Corp., North Chicago, 111.). 4.2. Preparative Procedures and Equipment 4.2.1. Preparatory Apparatus The preparatory apparatus used was similar to that described by Hariharan.S The set-up consisted of a 66 cm long by 3 cm inner diameter Vycor reaction tube located in a Lindberg Hevi-Duty tube furnace. The inlet end of the reaction tube was connected by means of a ground glass joint with a vacuum stopcock and rubber tubing to a liquid nitrogen trap, through which the sweep gases, He and H2, entered the system. A gas-handling manifold with a palladium catalyst and an auxillary inlet line of copper tubing were connected to the liquid nitrogen trap by rubber tubing. The exit side of the reaction tube was connected by means of a ground glass joint to a safety trap. The safety trap was connected by rubber tubing to a gas bubbler. During a typical dehydration reaction (see below) a flow of He and H2, at rates as estimated from observation of the gas bubbler of 10 to 1, respectively, was maintained over the system. The temperature of the furnace was controlled by a temperature controller (model TPC-I/3, Weather Measure Corp., Sacramento, Cal.). 4.2.2. Lanthanide(III) Fluorides Lanthanide(III) fluoride samples were prepared by dehydration of the precipitated trifluoride. The sesquioxide was dissolved in hot concentrated nitric acid. This hot solution was transferred to a,polyethylene beaker and while the solution was stirred by use of? a teflon rod, a 242 hydrofluoric acid solution was added dropwise until precipitation was complete. The resulting solution was allowed 36 to digest and cool. A drop or two of the 242 hydrofluoric acid solution was added to the supernatant liquid to test for complete precipitation. The liquid was decanted and the precipitate washed with a 52 hydrofluoric acid solution, water and finally, ethanol. The precipitate was centrifuged in polyethylene test tubes, placed in a platinum boat and dried at 383 K for 10-12 h. The dried pre- cipitate was then mixed intimately with at least a six molar excess of NHAF and placed in a platinum boat which was heated in the Vycor apparatus described above. The temperature of the Vycor apparatus was increased over a period of 4-6 h to a maximum of 973 K and held at that temperature for 2 h. A subsequent heating under high vacuum (less than 10.5 torr) was necessary to remove traces of NHAF. 4.2.3. Lanthanide(II) and Mixed Valence Fluorides All reduced lanthanide fluoride specimens were prepared by the method of Stezowski and Eick13’131 from the metal and the trifluoride. Appropriate amounts of the metal and the trifluoride were sealed into outgassed tantalum thimbles by arc welding in a zirconium-gettered argon atmosphere. The welds were examined for discoloration, indica- tive of oxidation or reaction between the sample and the thimble, and for faults in the seal. If the weld appeared clean, the sealed thimbles were heated under high vacuum (less than 10.5 torr) to 1700-1900 K, held at that temperature for 5-30 min and cooled slowly (2-3 h) to room temperature. If the thimble expanded, a tight weld was indicated. The sample was discarded if the thimble did not expand. 4.2.4. Storage of Samples All of the lanthanide metals and the prepared fluorides were stored in a controlled atomosphere glove box which has been described 37 . 5,131 preViously, or in a vacuum desiccator. The glove box atomos- phere was circulated by a permanently sealed bellows pump (model #MB-ISO, Metal Bellows Corp., Sharon, Mass.). The purification man- ifolds contained Linde Molecular Sieve pellets to remove moisture and BASF catalytic oxygen remover R 3-11. An open tray of reagent grade phosphorus pentoxide was maintained in the glove box to aid in the removal of water. 4.3. X-Ray Powder Diffraction Analysis X-Ray powder diffraction photographs were obtained for all samples and experimental residues with a Haegg type Guinier forward-focussing camera (80 mm radius) and Cu Kal radiation, la = 0.154051 nm,132 T = (297 i 5) K. The fine focus X-ray tube was powered by a Picker 809 B generator. Sample preparation, film measurement and Guinier techniques have been discussed extensively elsewhere.5’131’133'134 In this work, platinum powder served as an internal standard [2_= O.39237(3) nm].135 The X-ray diffraction photographs were used to identify the number and purity of the phases present and for the determination of the lattice parameters of freshly prepared samples, effusion residues and sesquioxide residues from the analytical procedure. 4.4. Metal Analysis Pyrohydrolysis was used to convert fluoride samples to the sesquioxide for the purpose of metal analysis according to the method of Stezowski and Eick.13’131 A weighed sample (0.05 to 0.20 g) was placed in a constant-weight platinum boat. This boat, contained in a larger quartz boat, was heated for 3-12 h at 1275 K in a Vycor tube through which water was distilled at a rate of approximately 38 40 ml/h. The temperature of the sample was then decreased to 1175 K and maintained at that temperature for 3-12 h under a static atmos- phere of air to remove adsorbed carbon dioxide. 4.5. Mass Spectrometric Procedures A Bendix Model 12-107 time-of-flight mass spectrometer equipped 110’136 was used to with a high temperature Knudsen source inlet obtain several spectra in the Yb-F system (2:. Section 3.4.). A Keithley 417 K electrometer was used in lieu of the instrument electro- meter to increase the sensitivity. A single cavity Knudsen cell with a conical orifice136 was heated by radiation and electron bombardment. The instrument was operated in pulse ionization mode with an ioniza- tion energy of (45 i 5) V to obtain spectra over a temperature range of 1075-1825 K. Ion currents derived from the molecular beam were identified by their shutterability. Assignment of masses to ion currents observed in the spectra was accomplished by use of known isotopic distributions and relative time-of-flights as compared with Hg. Ion intensities were taken as the peak height over the recorder's base line. Appearance potentials of the observed ions were obtained as discussed previously (pf. Section 3.4.). Tempera- tures were measured with a Leeds and Northrup optical pyrometer by sighting directly into the sample cavity. Temperature corrections were made for the optical interfaces and by intercomparison with an NBS calibrated (IPTS - 1948) instrument (sf. Section 3.3.). 4.6. Target Collection Procedures 4.6.1. Tapget Collection Apparatus Two different target collection set-ups were employed. An all Vycor apparatus, similar to that described by Ackermann et a1.102 39 and Kent,137 with a demountable pyrex section between the water-cooled heating chamber and the liquid nitrogen-cooled target magazine was used only for some measurements on the Yb-F system. The Vycor system was pumped with a 5 cm mercury diffusion pump. Residual pressures were maintained between 10-7-10-5 torr. An all metal system designed by Seiver133 was used to study all the lanthanide fluoride systems. The metal apparatus was pumped directly with a 10 cm oil diffusion pump and residual pressures varied between 10-8-10-6 torr. The targets were contained in a water cooled circular holder rotated by means of a Wilson type O-ring seal. 4.6.2. Target Materials Two types of targets were used to collect the effusing gases. The copper targets were 2.65 cm in diameter and 0.42 cm thick with a 2.14 x 0.23 cm cylindrical recession on the collection side. The platinum targets were constructed of an aluminum backing of similar dimensions as the copper targets with a 2.10 x 0.005 cm platinum disk inserted into the cylindrical recession. The platinum disk was held in place by an iron wire (5.5 x 0.08 cm) coiled so as to form a spring. The copper targets were cleaned before each experiment by washing in dilute nitric acid and water and drying in air. The platinum disks were cleaned in concentrated nitric acid and water and oven-dried at 383 K. 4.6.3. Knudsen Effusion Cells The graphite or molybdenum effusion cells were designed with two cavities and converging conical orifices with an apex angle of 138 . . . x 90°. Orifice areas were determined before and after each 40 experiment from photomicrographs (x 80, x 100, and x 200: Bausch and Lomb Dynazoom Metallograph) by measuring the enlarged orifice area with a compensating polar planimeter (Keuffel and Esser Co.). The planimeter was standardized by measuring a known area. The effusion cells were outgassed before use for 2-3 h (x 10.6 torr) at 1900-2000 K. 4.6.4. Distance Meausrements The target to Knudsen cell orifice distance was determined by use of either a precision cathetometer (Gaertner Scientific Co., 1 0.005 cm) in the Vycor apparatus or precision vernier calipers (Helias, i 0.05 cm) in the metal line. The distance varied for each experiment and ranged from a 9-11 cm for the metal line and 8 12-13 cm for the Vycor line (see Appendix 5). 4.6.5. Heating A high frequency induction generator (Thermonic, push-pull type, 250 kHz, 20 kVa) was used to heat the Knudsen cells. Direct coupling of the induction coil with molybdenum cells was used for five of the experiments performed on an intermediate ytterbium fluoride composition. In all of the other experiments the Knudsen cell was heated indirectly by radiation from an inductively heated 302 W-Mo oven. Hariharan5 has measured the vapor pressure of Ag with this heating arrangement and found the oven to be suitable for use in Knudsen effusion investigations. 4.6.6. Temperature Measurement Temperatures were measured by use of disappearing filament optical pyrometers (Leeds and Northrup: Micro Optical) by sighting the orifice of the bottom cavity of the Knudsen cells. The 41 temperatures were corrected as described previously (2.2. Section 3.3.). In the metal line the absence of a temperature gradient C< 10 K) across the Knudsen cell, in all experiments but one, was confirmed by monitoring the temperature of the top and bottom cavities. In the glass line the apparent surface temperature of the oven was measured at the top and the bottom. If any temperature gradient was present the induction coil was adjusted to compensate for it. 6.6.7. General Target Collection Procedure The general target collection procedure has been described previously by several investigators (33g. see 5, 130, 131). Samples of z 0.1-2.0 g were used for each different vaporization experiment. No precautions were necessary to avoid hydrolysis while the sample was transferred to the effusion line. Ten targets were usually collected at both increasing and decreasing temperatures. A mini- mum of 10 min was allowed for equilibrium to be reached within the Knudsen cell after each temperature change. When temperature drifts of'more than i 10° were observed, the target was not used in the data reduction. Target exposure times were measured with a Lab-chron timer Ct 0.01 min). Approximately 4-20 ug of the lanthanide metal was collected on each target for analysis by X-ray fluorescence after the vaporization experiment. 4.7. X-Ray Fluorescence Analysis A four position Norelco Universal Vacuum spectrograph was used in conjunction with a broad focus tungsten tube powered by a Norelco XRG-SOOO X-ray generator. Analysis for the lanthanide metals (Sm, Tm or Yb) was carried out by use of a graphite monochromator 42 (d = 0.3354 nm: (002) plane) and a NaI (Tl) scintillation counter. The spectrometer instrument settings are presented in Table 3. In this table the discriminator settings E and AE refer to the detector pulse height and channel width and were chosen by use of the pro- 112 cedure of Neff’ tx>maximize the count rate, equation (3-13), for small differences in concentration (Eff Section 3.5.). Table 3. X-Ray Fluorescence Spectrometer Conditions Element Collector Discriminator 29(h11) Counts/ug/min Target Setting E AE Sm Cu 2.25 V 4.75 V 38.3° 2066 i 258 Tm Pt 2.00 6.50 29.8 5410 i 364 Yb Pt 1.80 5.90 28.8 3828 i 366 Calibration for each element was achieved by evaporating onto each of ten targets 50 ul of different standard solutions prepared by dissolving weighed amounts of a lanthanide sesquioxide in a volume of dilute nitric acid. Five different amounts in the range of 4-16 ug of lanthanide metal were deposited onto ten targets so that duplicates of each amount were produced. The targets were prepared by depositing and evaporating to dryness 15-20 small droplets to obtain a uniform surface. The target surface exposed to the energizing X-ray beam was defined by a circular 45° beveled insert inside of which the standard was deposited. For the copper and platinum targets the radii of the exposed areas, R, were found to be 0.795(5) and 0.833(5) cm as measured by vernier calipers, respectively. The errors in I. 43 the count rates reported in Table 3 are the standard deviations from the means for the ten standard targets. The normalization method of Hariharan5 was used in this work to insure precision by counting a control blank and standard before and after every five targets. For additional discussions of the X-ray fluorescence analysis procedures see Hariharan,5 Work99 and/or Haschke.138 4.8 . Film Thickness Monitor A film thickness monitor (model#21900l, Granville-Phillips Co., Boulder, Col.) was utilized to record the rate of deposition of mat erial onto the targets in the metal vaporization apparatus. The instrument uses the change in the frequency of oscillation of a CIlia-rtz crystal to determine the mass of a coating deposited on its surface. The film thickness changes were recorded during the target collection periods. The rate of deposition indicated by the thin film monitor was found to be directly proportional to the mol- ecular flux from the Knudsen cell as determined by the target collection procedure. The ratio of film thickness to pg of lanthanide metal deposited on a target during a given time period was determined for each target. The mean of these numbers was then used to cal- culate vapor pressures for temperatures at which the deposition rate was monitored, but no target collected. For a given crystal over a temperature range of 481° the thickness to ug ratio for an inter- mediate samarium fluoride varied an average of i 32 with no temper- ature or chronological trend indicated (see Appendix 5). The life- time of the crystal varied from one to several effusion experiments “1C1 is dependent upon the amount of material deposited on the crystal. 44 The film thickness monitor was used to expand the number of data points obtained from a single Knudsen effusion experiment. 4.9. Distillation Experiments Distillation experiments were performed by completely evaporating and condensing SmF3 and YbF3. The distillation assembly is depicted in Figure l. A cylindrical molybdenum apparatus was used for SmF3 and a graphite apparatus for YbF3. A temperature gradient was intro- duced along the edge of the assembly by positioning the induction coil so that the lid extended beyond the top of the coil. The majority of the effusate condensed on the lid. 4.10. Mass Loss Experiments In the mass loss experiments a sample which contained a pre- determined percentage of lanthanide metal was placed in a molybdenum Knudsen cell. The cell was then heated in high vacuum for a given time period. After the effusion experiment the mass loss, percent metal and the X-ray diffraction pattern of the residue were determined. Some samples were vaporized completely (1,3,, the Knudsen cell was heated to constant weight) to test for any major sample-cell inter- action by mass loss of the Knudsen cell. Figure l. 45 LL] Distillation Assembly CHAPTER 5 RESULTS 5.1. Preparations The metal analytical results for the lanthanide(III) fluoride preparations (SmF3, TmF and YbF3) are presented in Table 4. The 3 preparative procedure yielded a white powder in each of the three cases. The X-ray powder diffraction results for the trifluorides, presented in Table 5, are in agreement with those previously re- 4’17'18 Also listed in Table 4 are the metal analytical ported. results for three reduced ytterbium fluorides. Since the metal contents calculated from the molar ratios in which the samples were mixed agreed with the contents determined by analyses for these three separate preparations, analyses were not undertaken for other reduced fluoride preparations. A total of five reduced fluorides were prepared in the ytterbium fluoride system. Their compositions and the symmetry assigned to the observed diffraction patterns are presented in Table 6. Also presented in Table 6 are data on the two reduced fluorides prepared in the samarium fluoride system and the results of the attempted preparation of TmF The relative in- 2. tensities, d-spacings and assigned Miller indices of the observed reflections are reproduced in Appendix 1. The tetragonal and hexagonal symmetry assignments for the ytterbium fluoride system are identical to those observed in the 46 47 Table 4. Metal Analytical Results for Selected Lanthanide Fluorides Compound Calculated Found1 YbF3 75.2 2 75.2 i . 2 SmF3 72.5 72.5 i . TmF3 74.8 74.3 i + YbF2.00 82.0 81.9 _ . + YbF2.41 79.1 78.9 _ I + YbF2.51 78.4 78.43 _ 0.01 l . . Errors are standard deViations for analyses Table 5. X-Ray Diffraction Results for Selected Lanthanide Fluorides Com ound Structure Space Lattice Parameters1 p Type Group a(nm) b(nm) C(nm) YbF3 Orthorhombic ana 0.6207(8) 0.6788(4) 0.4439(6) (YF3) SmF3 Orthorhombic ana 0.6671(4) 0.7063(7) 0.4402(1) (YF3) SmF3 Hexagonal P3cl 0.698(2) ----- 0.703(5) (LaF3) TmF3 Orthorhombic ana 0.6276(7) 0.6812(1) 0.4412(4) (YF3) l . . . . Errors are calculated standard deViations in the least-squares fit 48 Table 6. Structures of Selected Reduced Lanthanide Fluorides ' r eters Compound Structure(s) Lattice Pa am a(nm) b(nm) c(nm) YbFz.01 Cubic 0.5600(1)2 ------------ YbF2 19 Cubic 0.5585(1) ------------ YbF2 29 Tetragonal + U1 0.3925(2) ------ 0.5587(2) YbF2 41 Hexagonal + 01 0.3926(4) ------ 1.940(2) YbF2 51 Hexagonal + U'1 + (same phase as in YbF2 41) ' Orthorhombic YbF3 (see Table 5) ' YbF2 6O Hexagonal + U'1 + (same phase as in YbF2 41) ° Orthorhombic YbF3 (see Table 5) ' Ssz.00 Cubic 0.5872(1) ------------ SmF2 44 Hexagonal 0.4086(1) ------ 2.0189(7) TmFx Hexagonal +U"1 + 0.3953(1) ------ 1.937(1) Orthorhombic TmF + gsee Table 5) 3 Tetragonal Tm304P6 0.5513(2) ----- 0.5355(2) 1 O O O C U, U' and U" = unidentified lines (superstructure) 2 . C I Vaporization reSidue 3Reference 139 49 13,131 samarium and europium16 fluoride systems. The symmetry changes were explained by distortions of the cubic fluorite lattice. The distortions have been attributed to interstitial anions and cation substitution which results in contraction of the unit cell and an increased density (sf. Section 2.2.3.). Although the distortions of the cubic unit cell cause the tetragonal and hexagonal reflections, the presence of unidentified lines (superstructure) indicates that the actual unit cell is of symmetry lower than the one chosen. The physical appearances of reduced europium, ytterbium and 13-16,131 samarium fluorides have been described previously. The following color-composition changes were noted during this investi- gation. Ytterbium fluoride changes from black-green (YbF ) to 2.01 green-brown (YbF Samarium fluoride changes from dark purple 2.50)' (SmF ) to red (SmF ). The reduced thulium fluoride of unknown 2.00 2.44 composition was tan. Incomplete reduction of TmF3 was indicated by the presence of reflections assignable to orthorhombic TmF3 in the X-ray powder diffraction photograph of the partially reduced product (see Appendix 1). A small amount of oxide fluoride contam- inant (TmAO ) was found in the reduced thulium fluoride preparation. 3F6 A similar contaminant (SmAO3F6 or Yb403F6) was also observed in some of the samarium and ytterbium fluoride preparations, but these pre- parations were discarded. 5.2. Mass Loss Results The results of a series of mass loss experiments, effected with molybdenum cells and undertaken to determine what changes, if any, would occur in the ytterbium fluoride residues during vapori- zation are presented in Table 7. Vaporization of reduced ytterbium 50 Honduosuuwuodswv mmcHH cmHmHucochs u :D cam.D .D .mmnw oHnEonuocuuo u o .Hmcowaos n m .Hmcowmuumu u H .oHnso H cm «0.0 H mH coHuHmOQEoo :H Houpo owmwo> N H coHumNHuomm> wouw¢ mo wusuwpodEoH coHumNHuomm> whomom 0: 2H cochcoo medEwm mcHwosHm EdHnwwuu> pom mucoEHpmdxm mmoH mmmz mo wuHDmom .n oHan 51 fluorides with compositions in the region YbF2+x (0.00 E_x < 0.40) resulted in a decrease in the percentage of ytterbium in the residue. Vaporization of ytterbium fluoride samples with compositions in the region YbF (0.40 < x S_0.60) resulted in an increase in the 2+x percentage of ytterbium in the residue. No significant change in the composition or X-ray powder diffraction pattern was found for the vaporization of YbF These results indicated that in the 2.40. region YbF (0.00 S;x $LO°°0) all compositions, except that of the 2+x pseudo-hexagonal phase, YbF 0’ undergo incongruent vaporization. 2.4 When YbF3 was vaporized from a molybdenum cell, the percentage of ytterbium metal in the residue increased slightly. The X-ray powder diffraction photographs of these residues indicated the pre- sence of the congruently vaporizing pseudo-hexagonal phase, YbF2.40' Results such as these can be explained only by the incongruent vaporization of YbF or by a fluoride-cell interaction. To determine 3 if any fluoride-cell interaction was present, three samples of YbF3 (0.28, 0.34 and 0.36 g) were vaporized completely at 1800 K. The resulting average mass loss, (100.1 i 0.3) 2, indicated no significant fluoride-cell interaction. Also, three samples of YbF2 (0.42, 1.58 and 2.25 g) were evaporated completely with an average mass loss of (99.8 i 0.8) 2. The absence of any significant fluoride-cell interaction and the presence of two phases in the residue can be explained only by the incongruent vaporization of YbF3. Mass loss experiments were also carried out on the samarium and thulium fluoride systems. The results of these experiments are presented in Table 8. The samarium fluoride system vaporized in the same manner as the ytterbium fluoride system with a congruently 52 Amwauospum-uodomv mocHH conHucmchs u D .mmEH Ho mmEm oHnEonuocuwo u 0 .Hmcommxw: u : .Hmcowmuuou u H .oHnsu u 0N «0.0 H mH coHuHmooEoo :H Houwm wwmuo> N H :0HumNHwomm> wwum< mo chaumwodeoh :oHumuHummw> owomwm 0: CH cmchcoo moHdEmm mchosHm ESHHDLH cam EdemEmm pom mucwEHponm mmoH mmmz mo muHmem .w anwH 53 vaporizing composition of SmF Total mass loss experiments for 2.40. the samarium fluoride system, three samples of SmF3 (0.73, 0.91 and 0.72 g) and two samples of SmF2 (0.28 and 0.47 g), resulted in mass losses of (99.8 i 0.2) 2 for SmF and (99.8 i 0.3) 2 for 2 SmF3 and indicated no fluoride-cell interaction. The thulium fluoride system exhibited vaporization behavior different from the samarium and ytterbium fluoride systems. Mass loss experiments performed on the reduced thulium fluoride preparations indicated the disappearance of the reduced fluoride phases. The intensities of lines assignable to the orthorhombic trifluoride were stronger in the X-ray diffraction photographs of the residue than in that of the reactant. The TmF3 samples vaporized congruently with no apparent change in composition or X-ray diffraction pattern. A single total mass loss experiment conducted with a molybdenum cell and 1.0 g TmF3 resulted in a 99.9 2 mass loss. 5.3. Mass Spectrometric Results The vapors effusing from molybdenum Knudsen cells which contained Yb and YbF were examined by mass spectrometry to determine F2.01 3.00 their molecular structure and their behavior with respect to time and temperature. Mass spectrometric analysis of the effusate from YbF2.01 at temperatures lower than 1477 K indicated only the presence of Yb+. No other ion had an intensity greater than 1 2 of the intensity of Yb+. When the temperature of the sample was elevated, the Yb+ in- tensity increased: but, with time, the Yb+ intensity decreased and, consequently, was not reproducible with temperature (Figure 2). The ionization efflCiency curve for Yb , recorded during the initial 54 15y- 10 » ION INTENSITY (arbitrary units) p- L- 1 J 1 TIME (hours) Figure 2. Intensity of Yb+ from YbF2_._,x (0.00 f_x < 0.40) Confined in M0 XE: Time [0 (T = 1396 K): x (T = 1338 K)] 55 heating period (T = 1335 K), is shown in Figure 3. The appearance potential observed for Yb+, (7.7 i 1.9) V, is not significantly 140 higher than that reported, (5.9 i 0.10) and (6.25 i 0.01)141 V, 0 for Yb(g). The incongruent vaporization of YbF below 1477 K 2.01 yields primarily Yb(g), and the pressure of the Yb(g) decreases dramatically as the ytterbium composition of the residue decreases from Yb/F = 0.50, 1.3., changes with respect to time. These results, together with the contraction of the cubic lattice (2:. Section 5.2. and Table 7) observed during the initial vaporization of YbF2.01, substantiate the incongruent vaporization behavior of this phase. The incongruent vaporization reaction is illustrated in equation (5-1), where 0.01 S x f 0.19. YbF2(S) = (2/2+X) YbF2+x(S) + (Kl2+x) Yb(g) (5-1) At temperatures greater than 1477 K ion currents for YbF+ and YbF2+ were observed. Figures 4 and 5 illustrate the behavior of the + . . . . . Yb intenSity and the intenSity fractions, [IMX +/ of Yb+, I(total)]’ YbF+ and YbF2+'y§. time. Initially the Yb+ intensity decreased with time while the YbF+ and YbF2+ intensities increased. After 25-30 h had elapsed the intensities became reproducible with both time and temperature. After 33.8 h and 31 2 mass loss, the residue was removed from the mass spectrometer and analyzed. The composition, YbF2.39, and the X-ray diffraction pattern of the residue indicated the pres- ence of only the pseudo-hexagonal phase. These results also support the conclusion of an initial incongruent vaporization reaction char- acteristic of solid solution or nonstoichiometry in the composition region YbF2+x (0.00 flx < 0.40). The reproducible behavior of the ion intensities of the sample with both time and temperature after 56 15 r— 10 r- ION INTENSITY (arbitrary units) 1 1 10 20 30 IONIZATION ENERGY (volts) Figure 3. Ionization Efficiency Curve of Yb+ from YbF 0.40) Confined in Mo (T = 1335 K) 2 L I 40 . < < ”((000_x 57 20)- (arbitrary unit 5) ION INTENSITY 20 30 40 TIME (hours) Figure 4. Intensity of Yb+ from YbF2+x in Mo ‘13 Time (T = 1653 K) (0.00 E x E 0.40) Confined 58 l I L I I 0.6 L D D L o 9 ° 1 A I ‘8 o 3 0.4 r- : .‘bo +Ac: X X E XA. o x X H ' ~ X _ x ' 1:1 0 X 0 D D D 0.2 0 III I 0 CI 0 0 O b I 1 l 1 I 1 1 q 20 30 40 TIME (hours) . + Figure 5. Fractional Ion Intensities of Yb+(D), YbF+(X) and YbFZCO) from YbFZ-I-x (0.00 i x _<_ 0.40) Confined in Mo vs. Time (T = 1653 K) 59 a 31 2 mass loss by vaporization reconfirms the congruent vaporiza- tion behavior proposed for the pseudo-hexagonal phase, YbF2.40. Ionization efficiency curves, Figures 6 and 7, were obtained from the sample discussed in the preceding paragraph for Yb+, YbF+ and YbFz+ before 16 h of heating had elapsed (1.2., in the non- reproducible region) and after 42 h, which was in the region of re— producible behavior. The complex shapes of the ionization efficiency curves are similar to those observed by Zmbov and Margravea4 in their study of reduced lanthanide fluorides. A probable explanation for the shape of the ionization efficiency curves is the presence of two or more molecular precursors. If two species produce the same ion by fragmentation reactions which involve significantly different energies, inflection points can be observed in the ionization efficiency curve for that ion (pf. Section 3.4.). Appearance potentials for a second fragmentation reaction were taken to be the voltages of estimated inflection pointslo8 (pf. Section 3.4.). These second appearance potentials have an arbitrarily chosen uncertainty of i 5 V. The first and second appearance potentials observed during the vaporization of compositions in the region YbF2+X (0.00 f;x f_0.40) are reported in Table 9. Examination of the effusate from YbF3 by mass spectrometry yielded smooth ionization efficiency curves (Figure 8) which are again similar to those reported by Zmbov and Margravef‘4 These smooth curves indicated that YbF3(g) was the only ytterbium containing precursor detectable. The similarity of the fragmentation pattern observed from YbF3 (see Table 10) to those reported for other lan- 43,44 thanide trifluorides for which stable reduced fluorides are 6O ,. I p— D a L D 3 10 'c: U :1 i? B CO H U A...) 0H .0 I ‘66 v r E: a H (D E E. .7- 8 5 r- , H X X X I. I i- I luv :4 J I l 10 20 30 40 IONI ZATION ENERGY (volt s) Figure 6. Ionization Efficiency Curves for Yb+(D), YbF+(X) and YbF:(O) from YbF2+x (0.00 g x < 0.40) Confined in M0 (T = 1667 K) ’ 61 15 L 10 ION INTENSITY’(arbitrary units) 10 10 10 20 30 4O IONIZATION ENERGY (volts) Figure 7. Ionization Efficiency Curves for Yb+(El), YbF+(X) and YbF:(<>) from vol-“2.40 Confined in M0 (T = 1735 K) (displaced abscissa: 0 to 60 V for YbFE, -5 to 55 V for YbF+, -10 to 50 v for Yb+) 62 Table 9. Appearance Potentials of the Ions Detected in the Ytterbium Fluoride System Condensed T Ion Relative lst A.P. 2nd A.P. Composition (K) Intensity (volts) (volts) + YbF2 1335 Yb 100 7.7 i 1.9 ------ + YbF2+x 1667 Yb + 100 8.8 i 2.5 ------ " " YbF 66 8.5 t 1.7 ------ " " YbF2+ 35 11.4 r 2.2 20 a: 5 + + + YbF2.40 1735 Yb + 26 10.0 _ 5.0 23 _ 5 n n + ...... YbF 56 10.8 _ 2.5 H H . + . + Yb:2 100 10 6 _ 2 4 15 - 5 YbF3 1673 Yb 14 25.3 i 1.5 ------ + n n . + . ______ YbF 8 l9 1 _ l 7 n u . + . ...... YbF2 100 14 4 _ 1 1 10.00 g x < 0.40 2Ionization energy of 45 i 5 volts 63 15L A U) J.) --- S: :3 3101- (U H J.) or-l .0 3.- (U V >-‘ E-' H L (D Z E H Z S. 5.. l 1 l 10 20 30 40 IONIZATION ENERGY (volt s) Figure 8. Ionization Efficiency Curves for Yb+(D), YbF+(X) and + YbF2(<>) from YbF3 Confined in M0 (T = 1673 K) 64 Table 10. Fragmentation Patterns for Selected Lanthanide Halides Halide Fragmentation Pattern1 Ionization Ln+ LnF+ LnF2+ Energy LuF3 3 8 100 75 V LaF3 ll 20 100 70 CeF3 l3 19 100 70 YbF3 14 8 100 45 EuF2 33 100 24 30 EuCl2 46 100 12 50 YbCl2 32 100 33 30 1References 43, 44, 56, 142 l '0 a. 13 65 not expected is further support that the effusate consists principally of YbF3(g). During the mass spectrometric investigation of the effusate from YbF3, ion current intensities and their relative ratios were reproducible with both time and temperature. The effusate was mon- itored until 57 mass percent of the sample had been vaporized. The appearance potentials and the fragmentation patterns of the ions observed are listed in Table 9. Comparison of the second appearance potentials (Sf. Table 9) for the ions observed over YbF with those of the ions from the 2.40 effusate over YbF3 reveals a striking similarity. From this similarity one can conclude that YbF3(g) is one of the molecular precursors present in the YbF effusate. The presence of YbF2(g) over 2.40 YbF2 40 is indicated by the first appearance potential observed for + YbF , (10.6 i 2.4) V (2:. Table 9), which is below the appearance potential for YbFz+ in the YbF3 effusate, (14.4 i 1.1) V. The observed fragmentation pattern (Table 9) for the ions in the YbF effusate 2.40 is different from the patterns reported for lanthanide dihalides (Table 10). This difference supports the presence of both YbF2(g) and YbF3(g) in the YbF effusate. No evidence is present in the 2.40 ionization efficiency curves (Figure 7) for a third molecular pre- cursor. Blue g£_gl,143 report the presence of CaF(g) over CaF2(s), but the ratio CaF(g)/CaF2(g) at 1500 K is 10.7 and makes the contri- bution of CaF(g) to the sublimation thermodynamics of CaF2(s) insigni- ficant.45 Because of the reported similarities in the thermodynamic values of the alkaline earth and europium dihalides (2:. Section 2.3.) and because of their similar ionic radii, CaF2(g) was chosen as a model for YbF2(g). From this model no significant amount of 66 YbF(g) would be expected in the effusate from YbF From the 2.40. assumption that no species other than YbF2(g) and YbF3(g) are present in significant amounts, the congruent vaporization of YbF2 40 can be represented by equation (5-2). The uncertainties in the coefficients YbF2 40(s,£) = (0.60) YbF2(g) + (0.40) YbF3(g) (5-2) for YbF2(g) and YbF3(g) in (5-2) were derived from the uncertainty in the composition of YbF Ct 0.04) and are both i 0.04. 2.40 5.4. Distillation Results The complete distillation of YbF3 was carried out to determine the coefficients for reaction (5-3). The presence of YbF3(g) was YbF3.OO(S’£) = a YbF (8,2) + b_YbF3(g) + g F(g) (5-3) 2.40 indicated by the mass spectrometric results (23:. Section 5.3.). Analysis of the residues from mass loss experiments indicated the presence of two condensed phases, YbF3.00 and YbF2.40. From the equilibrium constant for reaction (5-4)144 at the pressures (N 10-5 % F2(g) = F(g) (5-4) atm) and temperatures (z 1500 K) investigated, the pressures of 11 F2(g) can be derived (z 10- atm) and shown to be insignificant. In the distillation experiment YbF3 confined in a Mo cell was evaporated completely and the effusate condensed on the lid of the distillation assembly (Figure 1). Since it was not experimentally possible to stop the distillation at the exact moment before the congruent sublimation of YbF commenced, the composition of the 2.40 condensed effusate represents the combined effusates of YbF3 and YbF2 40. In addition the composition of the condensed effusate is a lower limit since reevaporation of the condensed YbF may have 3.00 occurred during the experiment. The composition of the condensed 67 related to YbF effusate (YbF and YbF3(g) by equation 2.97(4)) ‘3 2.40(4) (5-5). The coefficients a_and p_are found to be 0.05(6) and 0.95(7), Yb = §_YbF +-p_YbF3(g) (5—5) F2.97 2.40 respectively. From these numbers the coefficient for F(g) in equation (5-3) is determined to be (0.03 i 0.36). Substitution of these coefficients into (5-3) yields Yb (5,2) = (0.05) YbF (3,2) + (0.95) YbF3(g) + (0.03) F(g) (5-6) F3.00 2.40 for the congruent vaporization of YbF3 00. The distillation of SmF3 was carried out in a molybdenum assembly, but not enough distillate was collected for quantitative analysis. However, the X-ray powder diffraction photograph indicated the pres- ence of the pseudo-hexagonal phase and SmF was assumed to undergo 3 an incongruent vaporization reaction similar to the one observed for YbF3 [1020, (5-6)]. 5.5. Knudsen Effusion Results 5.5.1. The Congruent Vaporization of YbF 2.40 The congruency of reaction (5-2) in combination with the mass spectrometric results requires the mole fraction of YbF2(g) and YbF3(g) to be 0.60 and 0.40, respectively. Use of this relationship allows the partial pressures of YbF2(g) and YbF3(g) to be calculated from the X-ray fluorescence analysis of the effusate collected on platinum targets. In accordance with previous investigationsS7’96 all the effusate which contained a lanthanide metal and impinged on the target was assumed to have condensed. The natural logarithm of the equilibrium constant for reaction (5-2) for 90 pressure- temperature data points from experiments 1 through 10 (Table 11, 68 Table 11. Experimental Conditions for Vaporization Runs in the Ytterbium Fluoride System Exp. 2 Yb1 (F/Yb)2 Set-upa Cell Orifice Area5 T Range 1 81.9 2.01 + 0 Mo 7.90 x 10.3 cm2 1293-1592 K 2 78.4 2.51 " Mo 1.14 1547-1696 3 78.9 2.44 " Mo 7.59 1520-1673 4 ---- 2.43 + O C(gr) 5.01 1504-1609 5-7 ---- 2.43 Mo 1.12 1566-1742 8-10 ---- 2.43 " Mo 7.28 1452-1640 11-13 75.2 3.00 + 0 Mo 8.33 1342-1620 14:15 " " " Mo 1.11 1511-1794 16 " " " C(gr) 1.10 1521-1667 1Average error for all analyses before vaporization = i 0.3 2 2Composition error = i 0.04 3Estimated value 4M = metal vacuum line; 0 = W-Mo oven: G = glass vacuum line 5Estimated error = i 0.10 x 10- cm2 69 Appendices 2 and 5) and the five corresponding unweighted linear least-squares equation from Table 12 are presented in Figure 9. The first four data points from experiment 1 (fl), also presented in Figure 9, represent pressures for Yb(g) recorded in the composi- tion region YbF2+x (0.00 SLX < 0.40). A change in cell material from molybdenum to graphite had little effect on the equilibrium vapor pressures as evidenced by the results of experiment 4 presented in Figure 9. Also, the change in composition from YbF2.28 (experi- ment 1) to YbF (experiment 2) alters the partial pressures in- 2.49 significantly. Use of the film thickness monitor during experiment 1 reconfirmed the initial incongruent vaporization behavior of YbF2.00. The rate of effusate deposition (vapor pressure) at a constant temperature decreased initially with time (Figure 10),\but eventually became reproducible with both time and temperature (Figure 9 and Appendix 2). From the results of experiments 5 through 10 (performed without the W-Mo oven) the following thermodynamic values are calculated for reaction (5-2) at the median temperature with the errors indicative of the standard deviations of the linear fit: AH9597 = (96.9 i 1.1) kcal mol.1 and 05° i 0.67) cal mol-lK-l. 1597 = (36's 3 Thermodynamic functions for YbF were derived at each temper- 2.40 ature by combination of those calculated from the enthalpy increments reported for YbF 18 (melting point = 1435 K) with the thermodynamic 3 values estimated as described below for YbF3 and YbF2 in the ratio 0.40:0.60, respectively (Appendix 3). From the published heat capa- 25,145,146 cities of CaF2(s), Ca(s) and Yb(s), the heat capacity, 1 1 C3, of YbF2(s) at 298 K was estimated as (17.30 i 0.25) cal mol— K- 70 Table 12. Results of Linear Least-Squares Analyses of Vaporization Reactions in the Ytterbium Fluoride System Exp. Slope Intercept Range m2 40(s, z): 0.60 YbF2(g) + 0.40 YbF2(g) 2n K yg. 104/T 1 — 4.53 r 0.19 17.0 + l. 2 1466-1592 - + _ 2 3.81 _ 0.33 12.7 i 2. .0 1572 1728 3 - 4.195 t 0.087 14.88 i 0. .55 1520-1673 - - o + o o + - 5 10 4 874 - 0 054 18 53 _ 0. .34 1452 1742 YbF3.oo(s,£) = 0.05 YbF2.40(s,£) + 0.95 YbF3(g) + 0.03 F(g) 2n p(YbF3(g)/atm) v_s_. 104/T " - o + o o o " ll 15 4 682 _ 0 021 . 19 29 i 0 14 1342 1794 " o + o o o - 16 4 400 _ 0 088 17 37 i O 53 1548 1703 71 1 1 l “1 ‘10 '- .4 L h 1 E 4.) to \ 3° o fi -12 1- - '-c:’ o C o; E 9 O A O "" q ‘1 LAN '|’ 0 Mg 0.’ V '3 C.‘ 92 ~14 - . a L ' .— 1 l J 1 6.0 7.0 (104/T) x 1 Figure 9. Natural Logarithm of the Equilibrium Constant for the Congruent Vaporization of YbFz.40 [Exp. 1(0), 2(4), 3(E», 4(I), 5(0), 6(X), 7(5), 8(0), 9(V) and 10(7)] and the Pressure of Yb(g) from YbF2+x (0.00 f_x < 0.40) [Exp. 1(a)] vs. Reciprocal Temperature 72 1.8 L 1.6 r 1.4 L RATE OF DEPOSITION (nm/min) 102 '- 1 J l l _l 360 400 440 TIME (min) Figure 10. Rate of Deposition of Yb(g) from YbF Confined in M0 yg, Time (T = 1475 K) ”K (0.01 g x < 0.40) 73 (pi. Section 3.6.6.). The heat capacity of YbF2(s) at its melting point, 1680 K,147 was taken as (21.75 i 0.25) cal mol-1K.1 123 (Sf. Section 3.6.6.). A linear variation of c; with temperature was assumed and equation (5-7) was derived. An enthalpy of fusion of (7.5 i 0.5) c;(YbF2,s) = [(16.4 r 0.5) + (3.19 x 10'3)T] cal mol’lK'1 (5-7) (298-1680 K) kcal mol.1 for YbF2(s) and a heat capacity, CB, value of (23.9 i 0.7) cal mol-lK-l, assumed constant over the entire liquid range for YbF2(£), were used by analogy with the values reported for CaF2(s,£).145 The standard entropies, (YbF2,s) and 3° (YbF3,s), were 298 i 0.50) cal mol-1K-1, respective- 0 S298 estimated as (22.5 i 0.50) and (26.5 6 0 125 . 126 - . 1y, from the schemes of Westrum and Latimer. The F contribu- . o . . 0 tion to 3298(YbF3,s) was derived from the experimental $298 value for CeF3(s)31 and the estimated contribution for Ce+3.127 From these values S° (Yb 298 -1 -1 Cal "101 K 0 0,5) was calculated to be (24.1 i 0.50) F2.4 2 Thermodynamic functions for YbF2(g) and YbF3(g) were calculated from measured and estimated molecular constants. A non-linear geo- metry with a F-Yb-F angle of (140 i 10)°6S and a Yb-F distance of 0.210(5) nm, which was estimated to be the same distance as that reported for CaF2(g),66 were used for YbF2(g). A non-planar geometry with a F-Yb-F angle of (117 i 10)°61 and a Yb-F distance of 0.203(5) nm, which was estimated by the method of Wesley and DeKock,6o were used for YbF3(g). Wave numbers, v1 = (476 i 10), v = (114.5 1 5.0) 2 and v3 = (462 i 10) cm-l,65 were used with a ground state statistical weight of one for YbF2(g). For YbF3(g) wave numbers, 01 = (581 i 10), 92(E) = (100 r 5), 03(2) = (565 r 10) and 04 = (144 r 5) elm-1,61 74 were used with a ground state statistical weight of eight. The un- certainty in the entropy and free energy functions which results from uncertainties in the molecular constants and the statistical 1 weight is i l. cal mol_ K-l. Calculated thermodynamic functions 3 are presented in Appendix 3. The pressure-temperature data of ex- periments 5 through 10 were reduced in accordance with the coefficients of reaction (5-2) and are described in equation (5-8) with appro- E'(cal mol'IK’l) = [(110. r 1.0) x 103]/T - (50.8 r 0.64) (5-8) 7 5 priate standard deviations by the unweighted linear least-squares fit of 2' XE! l/T. Combination of the experimental pressures with the free energy functions (third-law procedure) yielded for reaction - o = (5 2) A8298 (109.83 When uncertainties in the thermodynamic functions are included, i 0.36) kcal mol-1. the second-law derived values for (5-2) become AH398 = (110.7 i 2.3) kcal mol"1 and A5398 = (50.8 i 2.1) cal mol-1K-1; the third-law derived enthalpy with its uncertainty isAH‘é98 = (109.8 i 2.4) kcal mol-1. O O _ ' From 8298(YbF2,g), 8298(YbF3,g) and the second law derived -1 -1 298 (YbF2.l‘O’S) = (2308 i 303) Cal “101 K o O 298 From the derived thermodynamic functions (Appendix 3) and the second-law derived values a boiling point of (2795 i 5) K was cal- + . 3 _ 2 3) i 2.1) cal mol-lK-l, respectively. From culated with an enthalpy and entropy of vaporization of (81. kcal-nol‘lx'1 and (29.1 the third-law derived value for AH398 the boiling point was deter- mined to be (2820 i 5) K with an associated enthalpy of vaporization of (80.1 i 2.4) kcal mol-1. 75 5.5.2. The Incongruent Vaporization of YbF3 The natural logarithm of the equilibrium partial pressure of YbF3(g) for 60 pressure-temperature data points from experiments 11 through 16 (Table 11 and Appendices 2 and 5) and the two cor- responding unweighted linear least-squares equations from Table 12 (Mo and graphite cells) are presented in Figure 11. The change of cell material from molybdenum to graphite did not have a significant effect upon the equilibrium partial pressures of YbF3(g). The stoich- iometry of reaction (5-6) requires that the partial pressures of YbF3(g) and F(g) in the Knudsen cell be related according to (5-9), in which Ln equals Yb. From this equation and the pressure-tempera- pF/[(MF)%(O.O3)] = anF3/[(MLHF3)%(0.95)] <5—9) ture data from experiments 11 through 15 (Tables 11 and 12), the natural logarithm of the equilibrium constant for (5-6) is repre- sented in (5-10). From (5-10) the following thermodynamic values in K = - [(45.8 r 0.20) x 103]/T + (18.7 r 0.13) (5-10) 8 6 were calculated for (5-6) at the median temperature‘ AHi568 = r 0.26) cal moi'lK'l. (91.1 i 0.41) kcal mol.1 and AS° = (37.2 1568 8 The reported uncertainties are the standard deviations of the linear 9 least-squares equation for zn K XE) l/T. Reduction of the pressure- temperature data of experiments 11 through 15 was carried out in accordance with the coefficients of reaction (5-6) by means of the 2' method and the derived thermodynamic functions for YbF and YbF 2 (see Appendix 3) and data in the JANAF tableslaa for F(g). The 3 results are described with appropriate standard deviations by the unweighted linear least-squares equation (5-11). From a combination 2'(ca1 moi‘lx‘l) = [(111.0 r 0.44) x 103]/T - (56.1 r 0.29) (5-11) 5 7 76 T 1 T h- -3 p. )— -10 t. m E U CU \ 39 t. on LI.- g Lo? 5 42}- P -14 P J m fii 6.0 7.0 (104/T) K"1 Figure 11. Natural Logarithm of the Equilibrium Partial Pressure of YbF3(g) from YbF3(s,£) [Exp. 11(0). 1200, 13(0), 14m), 15(0) and 16(7)] vs. Reciprocal Temperature ‘ 77 of the calculated equilibrium constant with the derived free energy -1 functions for (5-6), a value for'AH398 = (106.9 i 0.42) kcal mol 6 was calculated. Inclusion of uncertainties in the thermodynamic functions yielded for (5-6) the following values: second-law method, AH398 = (111.1 i o -l -1 1.3) kcal mol.1 and AS = (56.2 i 1.3) cal mol K ; third-law 298 method, AH298 = (107.0 i 3.5) kcal mol_1. From 8398(YbF3,g), 3298(YbF2.40’S)’ 8398(F,g) and the second- law derivedAS‘é98 for (5-6), 8398(YbF3,s) = (23.9 i 3.3) cal mol-lK-l. 5.5.3. The Congruent Vaporization of YbF2 and YbF3 5.5.3.1. 1223 The difference between enthalpies of formation of YbF3 and YbF2.40 [difference calculated as 0.60 x [AHg(YbF3,s) - AH%(YbF2,s)]} at 298 K, the enthalpy of formation for F(g) and the second-law derived enthalpy for (5-6) were combined to yield for (5-12) AH398 = (113.3 i YbF3(s) = YbF3(g) (5-12) 1.8) kcal mol-1. Similar treatments with the second-law derived entropy and the third-law derived enthalpy yielded for (5-12) 1 -l - -l o = , + , ° = . + . A8298 (58 1 _ 1 4) cal mol K and AH298 (109 0 _ 4 1) kcal mol , respectively. Combination of 3398(YbF3-g) and the second-law derived A8398 -1 -1 - ' o = for (5 12) yielded S298(YbF3,s) (23.8 i 3.4) cal mol K . From the second-law derived values, the extrapolated boiling point was determined to be (2490 i 5) K with an enthalpy and entropy lK-l, of vaporization of (82. i 1.8) kcal mol.1 and (33. i 1.4) cal mol- 7 2 respectively. From the third-law derived value of'AH398, the 78 extrapolated boiling point was calculated to be (2580 i 5) K with -1 an associated enthalpy of vaporization of (77.6 i 4.1) kcal mol . 5.5.3.2. YbF2 The second-law derived enthalpies for (5-2), (5-12) and (5-13) Yb (5) = (0.60) YbF2(s) + (0.40) YbF3(s) (5-13) F2.40 EAH398 for (5-13) estimated as (0 i 2) kcal mol—1, Efif Section 5.5.1.] were used to calculate the enthalpy for (5-14), AH398 = YbF2(s) = YbF2(g) (5-14) (109. i 8.4) kcal mol-1. Similar use of the second-law derived i 6.1) cal mol-1K-1, 0 . _ o = entropies yielded for (5 14) A8298 (46.0 while use of the third-law derived enthalpies resulted in AH398 = (111 r 10) kcal mol"1 for (5-14). o o o _ ' 0 Combination of S298(YbF2,s) and the second law derived AS298 -1 -1 for (5-14) yielded S° (YbF2,s) = (23. i 8.1) cal mol K . 298 5 From the second-law derived value for AH398 for (5-14) and the derived thermodynamic functions (Appendix 3), the boiling point for YbF2 was calculated to be (3045 i 5) K with an associated en- thalpy and entropy of vaporization of (79. t 8.4) kcal mol"1 and 6 (26. i 6.1) cal mol-lK-l, respectively. From the third-law derived 1 value for (5-14), the boiling point was calculated to be (3015 i 5) K with an associated enthalpy of vaporization of (82 i 10) kcal mol—1. 5.5.4. The Congruent quorization of SmF 2.40 The vaporization of SmF was examined by use of the thin 2.40 film monitor and the target collection techniques. During the in- itial stages of vaporization the effusate over SmF behaved in 2.00 a manner identical to that observed for the composition region 79 YbF2+x, 0.00 5_x < 0.40. The rate of deposition (vapor pressure) decreased with time (Figure 12), but eventually became reproducible with both time and temperature (Figures 13 and Appendix 2). Analysis of the residues (Table 8) indicated that the pseudo-hexagonal phase of composition SmF vaporized congruently. The vaporization 2.40(4) reaction was considered to be identical to that observed for YbF2.4O’ reaction (5-2), and is SmF2040(s,£) = (0.60) SmF2(g) + (0.40) SmF3Cg) (5-15) The natural logarithm of the equilibrium constant for (5-15) for 52 pressure-temperature data points from three experiments (Appendices 2 and 5) and the corresponding unweighted linear least-squares equa- tion (5-16) with appropriate standard deviations are presented in in K(5-15) = - [(45.6 r 1.1) x 103]/T + (18.73 r 0.71) (5-16) (1369-1791 K) Figure 13. The first five data points from experiment 1 (Q), also presented in Figure 13, represent Sm(g) pressures measured over the composition region SmF fx (0.00 §Lx < 0.40) during the incongruent 2 vaporization period. During experiment number three a temperature gradient (31 i 7)° was observed between the top and bottom cavities of the Knudsen cell. The temperatures of the top cavity were used and yielded results in agreement with those of the two previous experiments. Use of the results of these three experiments which were per- formed in the metal vacuum system with a W-Mo oven yielded for reaction (5-15) at the median temperature the following thermodynamic values with the errors indicative of the standard deviations of the 80 DEPOSITION RATE (hm/min) J j l J l I 155 195 235 TIME (min) Figure 12. Rate of Deposition for Sm(g) from SmF2+x (0.00 flx < 0.40) Confined in M0 XE} Time (T = 1232 K) 81 I I I l I I ' H I I I ll '8h- - .‘lr1 ' D f'"1 5 (U *- -|11 -1 \ A £9 . a _'m E. F' "U x. 8 B 3 '- ‘,° ‘1 V 81 ii ti; ’30 ‘Q -% 3‘: a t § \ ‘\ -l4- 1 l J l J l l 6.0 8.0 (104/T) K"1 Figure 13. Natural Logarithm of the Equilibrium Constant for the Congruent Vaporization of SmF2.ao [Exp. 1(00, 2(X) and 303)] and the Pressure of Sm(g) from SmF2+x (0.00 _<_ x < 0.40) [Exp. 1(0)] gs; Reciprocal Temperature 82 =(37. + = '1 o (90.5 i 2.2) kcal mol and AS 2 _ linear fit: AH1580 1580 1.4) cal mol ”1K 1. Thermodynamic functions for SmF2 40 were derived at each tempera- ture by combination of those calculated from the entahlpy increments reported for SmF 18 (melting point = 1573 K) with the thermodynamic 3 values estimated as described below for SmF3 and SmF2 in the ratio of 0.40:0.60, respectively (Appendix 3). From the published heat capacities of BaF2(s), Ba(s), and Sm(s),25’145’146 the heat capacity, -1-1 C3, of SmF2(s) at 298 K was estimated as (14.6 +0. 2 S) cal mol K 3 (pi. Section 3.6.6.). The heat capacity of SmF2(s) at its melting point, 1690 K,147 was taken as (21.75_ 0. 2 S) cal mol ”1K 1.123 By assuming a linear variation of c; with temperature, equation (5-17) C3 ucwswwcoo wnu mo coHuaEdmmw may no om>wuwo m msowuma>wo Upmucmum UwumHQOmmm nuwa mosam> om>wumv amalchwnem mcowumw>mu cumu26pm owumwoomww an“: mmSHm> ow>wwmo smalucoomma AFN H 9.5 Ammé H m6.83 Ammé H #63 nomé H $.83 mp5 AFN H 0.63 $30 H «.933 A65 H $.23 Awaé H 0383 mmaEm AFN H 0:63 Aomd H H383 ASS H 66.33 Ara H N.83 mmam AFN H 933 Am; H H383 A630 H $.33 noio H $.23 mmafi AFN H 923 my; H 6333 $2. H £53 A666 H 0323 man» A v—H HOE HGUV A HOE HNUXV A Vm HOE HNUV A HOE Hmoxv T - N T H T .. H T csano 363$me momma momma €me 6 o mac-oomwm unosuwcou new ucmshwcoocH pom omumasono & mom um moo-Honda AHHHvoowcmsucmA wouomamm mo mowEm:%UOEpm£H coflumeHnsm on» cowsumm acmwumaeoo .qH manmh 97 manwawm>m coca .mcowumw>wc upwocmum owumHUOmmm Qua: monam> Um>wumv smauocooom mosaw> oo>wumo zmauopwzh m N mq.qq.o¢.mm mmoawummmma Am.~ H m.mmv Am.moH3 Ao.H H H.663 Am.mmv man» AP... H 6.5 3.8: 3.0 H .23 3.8: $5. Am.m H o.sm3 Am.NoHV AN H omv Aa.moav mesa .. Am.6oav Am.o H 0.6m3 As.o H H.6OHV memo = Ao.soHv As.o H m.mmv As.o H m.NOH3 mama Am.~ H c.6mv Am.~oav AN H mew Am.mm3 mawo : Aa.6oHV Am.o H n.6mv as.o H w.~oav mama Am.~ H 6.mm3 Am.aoHv Aa.o H H.663 Am.mmv mama any“. 2.x“. N. -. 3-3.. mwowwosam AHHvaowcmzuch uwuomamm mo cowumawansm unmahwzoo mcu pom meHm> owewchooeuocs .mH mHan 98 Table 16. Comparison of Pressures Observed by Various Investigators for Gaseous Lanthanide Fluorides at Median Temperatures Molecule - 1n p T D $1111731 11.904 1434 K 6.763 x 10'6 atm SmFB: 11.324 1423 1.208 x 10:: TmF32 14.697 1344 4.124 x 10-7 TmF31 14.577 1344 4.670 x 10-6 YbF32 15.114 1361 2.728 x 10-6 YbF3 13.750 1361 1.069 x 10 1Present study 2Reference 44 method used in this dissertation to estimate the standard entropies, 5398’ of the solids (Sf. Section 5.5.1.) involved the known contri- butions of the cations to the entropies of the various oxides and the measured entropy of CeF3(s). For the gaseous trifluoride molecules the largest source of uncertainty is the electronic contribution to the entropy. Slight variations in the molecular constants change the absolute entropy only slightly. The excellent agreement between second- and third-law derived values for the hypothetical congruent sublimation of SmF3(s), and the congruent sublimation of TmF3(s) supports the use of the electronic energy levels of the corresponding lanthanide ions to calculate the gaseous entropies. The difference between the second- and third-law derived values for the hypothetical congruent sublimation of YbF3(s) is either the result of the estimated values for the entropies or an error in experimental measurements. 99 The thermodynamic functions for the difluorides are subject to errors in both the enthalpic functions and the absolute entropies. No measurements of the thermodynamic functions for any of the lanthanide(II) fluorides have been carried out. Close correspondence has been observed between the thermodynamics of vaporization of the europium halides and monochalcogenides and those of the heavier alkaline earths (Ca, Sr, Ba).5 Use of the thermodynamic functions for an alkaline earth compound is a reasonable means of estimating the thermodynamic functions of the solids. The agreement between the second- and third-law derived values from the congruent sublimations (3) (Table 17) of the intermediate fluorides, SmF (s) and YbF 2.40 2.40 at 298 K indicates the internal consistency of the thermodynamic approximations and is support for their accuracy. The slight dis- agreement in the values for SmF (8) may be due to the uncertainty 2.40 in the measurements caused by the temperature gradient in high temperature vaporization experiment three. The thermodynamic values derived for the congruent sublimation of SmF2(s) and YbF2(s) are compared in Table 18 with values reported for the alkaline earths and europium(II) fluorides. The observed differences in the second- and third-law derived values for Ssz and YbF2 may be ascribed to the uncertainties introduced by thermodynamic calculations with estimated thermal functions. The observed temperature gradient might play a role in the values for Ssz, but all of the values are within the quoted uncertainties which arise from the estimates. The values in Table 18 support the predicted5 correspondence of the sublimation thermodynamics of the lanthanide(II) fluorides to those of the alkaline earth fluorides. 100 meoHumH>mo ouwocmum vmumHUOmmm sud: mmaam> oo>wwoo swauuuwaHN wcowumw>wc uumucmum owumaoommm saws mwSHw> vm>wumo zmanccoomm H Hm.N H a.wsv Ho.H H H.HoH3 Hm.H H H.633 HH.~ H ~.ooH3 as Haem Hm.~ H H.Hmv Hom.o H mm.HOHV H36.o H mm.omv Ho.H H H.0HH3 OH map» A Ix 1HoE Hmov A caoe Hmoxv A 1M afloe Hmov A IHOE Hmoxv H H mam N H mam H H H mom H H mam oHHom Aummv omQ 0:6 omd . omd vamacH Hq.o3 + vamacH Ho.ov u Havoc NacH :oHHommm 6:0 6H mcHuuooo< o8 Nan» new as Naem mwowuosam mumwooeumucH on» mo cowumEHHnam ucwspwcoo mnu How meHm> OHEmchnoEuwnH .AH magma mowucwmuumoc: omumwoommm nu“: mwaam> uw>wwoo sweluuwna 101 meHCHNUHmUCD Uwumfioommm CUM»? MQQHN> UflerHmU 3NHIUCOU¢WM HOH can ms .HH .m mmoamummmmH Hm.~ H o.HH3 HQH H HHH3 HH.3 H c.683 As.» H o.HOH3 a» Hm.N H m.mq3 HH.m H H.30H3 Hw.3 H 6.83 Hm.m H H.683 em Ho.H H H.Hs3 Hm.ma3 Ho..o H Ha.ms3 HHm.o H 66.00H3 9H 11111 1111111 Aw.mqV Aomv mm ----- ------- HH.3H3 HooH3 Hm Hm.m H H.Hs3 Ho.HOH3 HH.m83 Hm.NOH3 mo Hm.H H H.Hs3 Hmm.HOH3 HHH.o H om.ms3 HH~.o H 8H.HOH3 .6 AHIM IHOE Hwov mAHIHoE Hmoxv NAHIx lace Hmov NAHIHOE Hmoxv Humw3wmmm< momma mammq mammq HHmuwz mmowuosam AHHvamumz vouomamm mo :oHumEHHnsm ucmzpmcoo man now moHEmcmooEuonh .mH canoe 102 Brewer's estimates24 of the boiling point,.AH3 and A5: are reported in Table 19 along with the values derived in this work. The experimental and estimated values agree reasonably well for 2, YbF3 and TmF3. This difference indicates that the values estimated for the heavier lan- Ssz and SmF3, but differ markedly for YbF thanides are in error. 6.3. Pressure-Composition Diagrams and Stability Relationships, Figures 16 to 19 are qualitative pressure-composition diagrams of the lanthanide fluoride systems (Eu, Sm, Yb and Tm). The vaporization behavior of the phases in the Eu-F system (Figure 16) has been extrapolated from those observed in the Sm- and Yb-F systems and the reported behavior of EuF2(s,£). The vapor pressures of EuF3(g) are those reported by Zmbov and Margrave.44 The decomposition of EuF3(s) has been depicted because of the behavior observed for YbF3(s) and SmF3(s). The enthalpies at 298 K for reaction (6-1) calculated LnF3(s) = LnF2(s) + F(g) (6-1) from Brewer's estimates23 and the JANAF Tables144 are (134 i 14), (110 i 14) and (115 i 14) kcal mol.1 for Ln = Sm, Eu and Yb, respective- ly. These enthalpies indicate that the decomposition of EuF3(s) is more energetically favored than that for either YbF3(s) or SmF3(s). Thus, EuF3 is likely to vaporize in a manner analogous to the vaporization mode of SmF and YbF3 (of, Section 5.5.2. and 5.5.5.). 3 This vaporization mode is reflected in their pressure-composition diagrams (Figures 16 to 18). Figure 16 illustrates the reported congruent sublimation of EuF2(s) and the postulated incongruent vaporization of all other Eu-F compounds. Figures 17 and 18 depict the behavior found for YbF2(s) and SmF2(s). The vaporization behavior 103 Table 19. Thermodynamic Values for the Congruent Vaporization of Selected Metal Fluorides at Their Boiling Points 0 O Fluoride Tb AHv _1 ASV_1 _1 (K) (kcal mol ) (cal moi K ) Smrz1 (2715 :5) (79.1 i 9.3) (29.2 i 6.8) SmF 2 (2555 i 5) (87. i 9. ) (34. i 3. ) 23 5 1 2 6 SmF2 (2700) (78) (29) SmF31 (2420 i 5) (65.5 i 2.5) (27.1 i 1.9) 2 SmF3 (2420 i 5) (65.5 i 3.2) (27. i 1.3) SmF33 (2600) (62) (24) Yble (3045 i 5) (79.6 i 8. ) (26. i 6. ) 2 4 1 1 YbF (3015 i 5) (8 i 1 ) (27. i 3. ) 23 2 0 2 3 YbFZ (2650) (75) (28) YbF31 (2490 i 5) (82.7 i 1.8) (33.2 i 1.4) pr32 (2580 i 5) (77. i 4. ) (30. i 1. ) 3 6 1 1 6 YbF3 (2500) (60) (24) 1 + TmF32 (2580 i 5) (72.0 i 1.5) (27.9 _ 1.3 + + TmF33 (2500) (60) (24) l . . . . . Second-law derived values with estimated uncertainties 2Third-law derived values with estimated uncertainties 3 O Brewer's estimates; reference 23 104 j I l f -6 P a H o D. g.“ EuF + EuF 2 2.40 3 + 3: .1 9°" N Lu :1 h. 1n 5 h: -atg a a m 3 J a. (V + - '>° ‘3 a.” + m 3 a 71 n: a. .3 a J E m 33 EuF2.40 + Vapor 3 a“; EUF2.25 8‘ 5.". ‘3 + v ‘5 _ apor F\ Equ + Vapor -12 r- - Vapor -14 L- - I L I I I I 2.0 2.4 2.8 F/Eu Figure 16. System (T = 1500 K) Qualitative Pressure-Composition Diagram for the Eu-F 105 ”T l l f -6 P 35 r “5" H by. 5‘; 8- 5 in -8 +- > “3 smF2.40 + smFa + n: 9 ‘8 a.” 5‘1 g. (\<% :> ‘8 ‘3. + A . . m 5 \ .5" 6.” g 3.. 6 6 m '10 h F2.35\ 7* E +Vap0r \ D. (E 8111172.3S + SmF2.40 + Vapor Q3 smF2.40 » F2.40+ Vapor -12 r' Vapor -14 +- I I I I L I 2.0 2.4 2.8 ‘ F/Sm Figure 17. Qualitative Pressure-Composition Diagram for the Sm-F System (T = 1500 K) 106 1 I T I -6 _ u -8 )- "" To "1 u m” YbF + YbF 8‘ of. g 2.40 3 > "1 J 4. (9+ (V a. u. a) 5‘3 3. '53 EH N LI... 3 A YbF2.40 + Vapor '14 1' Vapor '7 1 I L 3 1 L I 2.0 2.4 2.8 F/Yb Figure 18. Qualitative Pressure-Composition Diagram for the Yb-F System (T = 1500 K) 107 \ 1 l 7 l l -6 _ \ 4, a?“ TmF2 4 + TmF3 5 \\ t o O. V w > -8 L +‘H m a. E \ [—1 TmF3 + Vapor A E A.) 2 \ T‘s-10L J.) o L.) o. \\\\\ V c N Vapor -12 _ -14 b 31 I I 11 111 I 2.0 2.4 2.8 F/Tm Figure 19. Qualitative Pressure-Composition Diagram for the Tm-F System (T = 1500 K) 108 of TmF3(£), illustrated in Figure 19, is congruent. The intermed- iate fluoride undergoes an incongruent vaporization reaction to a metal rich vapor and the solid trifluoride. A definite trend in the stability of the divalent state with respect to the trivalent state is illustrated by Figures 16 to 19. The stable, congruently vaporizing compound changes from LnF2(s) through LnF (s) to LnF3(s) 2.40 as the lanthanide element is varied from europium to samarium and ytterbium and finally thulium. Examination of the enthalpies at 298 K for reaction (6—2) helps to clarify the observed trend. 3 LnF2(s) = 2 LnF3(s) + Ln(g) (6-2) Reaction (6-2) defines the relative stabilities of the di- and tri- valent lanthanide fluorides, and the enthalpy for (6-2) is determined by the enthalpies of formation of the di- and trifluorides and the lanthanide metal gas. The chemistry of Eu and to a lesser extent Yb is influenced by the stability of the divalent state. 148,149 Gschneidner has explained this stability in terms of the ground states of the lanthanide metal and its vapor. If a thermodynamic (Born-Haber) cycle for the enthalpy of formation,.AH%, of a compound, LnFm, is depicted as follows: .AH° (Ln) sub ‘ Ln(g) + l-n- FZCg) 3., 2 1 12m 1 mm) +§(0;.2) ans) Hg F2(g) LnFm(s) 4H LnF (a) then AHf IP + 2(DF2) + m EA + W AHSUb(LnF ) +AH b(Ln). (6 3) The ionization potentials for the divalent lanthanides (IP+2) follow 109 a smooth trend increasing from La to Gd (16.61 - 18.26 V) and again A similar trend opposite in sign would be expected for W° due to the decreasing size of the ions (lanthanide contraction). The enthalpies for reaction (6-4) Ln(g) + F2(g) = LnF2(g) (6-4) would be expected to vary only slightly across the lanthanide series, and the enthalpies of sublimation, Aflgub(LnF2), that have been measured have been found to be similar (sf. Chapter 5 and Section 6.2.). A large difference has been found151 for the enthalpies of sublimation for the metals,.AH%(Ln,g). The variations observed have been explained by the electronic ground state of the metal and its gas.149’151’154 The least positive AH%(Ln,g) values are found for Yb, Eu, Sm and Tm, in that order. These elements would have more negative enthalpies of formation for their difluorides, AH¥(LnF2,g), because of their small AH%(Ln,g). A.more complicated trend is found in the ionization energies for reaction (6-5). The Ln+2 = Ln+3 + or (6-5) energies of reaction (6-5) show the expected increases from La to Sm with a large increase at Eu and a decrease at Lu. This erratic behavior results in a more positive enthalpy of formation, especially 3 3 + . . for Eu 3 and Yb+ , and somewhat more pOSitive for Sm+ and +3 148,149,152 Tm Another similar explanation of the relative stabil- . . . . . 5 ities of the di— and trivalent lanthanides has been reported.1 3 The aqueous reduction potentials indicate the trivalent Sm, Yb and Eu aqueous ions have increasingly more positive enthalpies of forma- tion, in that order, as determined by reduction of the trivalent to the divalent ions. The enthalpy of formation of EuF3(s) and 110 Eu(g) are more positive than those of YbF3(s) and Yb(g).23’148’149’151 Also, the enthalpy of formation of EuF2(s) is more negative than that of YbF2(s).23 From these relationships the enthalpy for reaction (6-2) is more positive for Eu than for Yb. For Sm, AH¥(SmF2,s) w AH‘;(YbF2,s), AH‘t’.(Sm,g) > AH%(Yb,g) and AH‘t3.(SmF3,s) < AH‘%(YbF3,s); thus, AH° 298 for (6-2) would be expected to be of a magnitude similar to that observed for Yb as was found in this investigation. For Tm, AH%(TmF2,s) N AH%(SmF2,s), AH%(Tm,g) > AH%(Sm,g) and AH%(TmF3,s) % AH%(SmF3,s), No straightfoward prediction can be made about the vaporization of TmF2(s) from the above considerations. The residue from an attempted preparation of TmF2(s) did undergo an incongruent vaporization to give a Tm-enriched vapor and a reside enriched with TmF3(s). None of the other lanthanide(III) fluorides has been re- duced by a tantalum bomb preparation similar to the one used in this investigation (of, Section 4.2.3.)11 and they are expected to vaporize congruently since in these systems no reduced phase is thermodynamically stable. Although the observed vaporization behavior of the lanthanide fluorides can be rationalized, this behavior could not have been predicted without an exact knowledge of the free energies of all the compounds involved. The dissimilarity observed for the Tm-F system when compared with the Sm- and Yb-F systems can be used cau- tiously to predict the behavior of the Tm-Cl system. The dichlorides, SmClz, EuCl2 and YbClz, are known to sublime congruentlyl‘g’so’S7 while their trichlorides decompose to yield C12(g) and the dichlor- ides.51 The relatively less stable divalent character of Tm might cause TmC12(s) to decompose to an intermediate chloride. If TmC12(s) 111 does undergo congruent sublimation one of the remaining, more tri- valent lanthanide(II) chlorides might exhibit the behavior observed for the Sm- and Yb-F systems. The same tentative predictions can be made concerning the Ln-Br systems. In the Eu-Br system, EuBr2(s) is known to sublime congruentlysa and EuBr3(s) decomposes to give EuBr2(s) and Br2(g).52 None of the other Ln-Br systems has been investigated thermodynamically. However, YbBr2(s) and SmBr2(s) will undoubtedly sublime congruently, but TmBr2(s) might decompose. 6.4. Conclusidns and Suggestions for FUture Investigations This dissertaion has defined the complex and unexpected vapori- zation reactions for the Sm-, Tm- and Yb-F systems. Thermodynamic values have been reported for the observed reactions and values have been derived for the hypothetical congruent sublimation reactions of SmF2(s), YbF2(s), SmF3(s) and YbF3(s). During the investigation for this dissertation, several fluor- ides of unknown structures were encountered. The determination of the room temperature and high temperature single crystal structures of these phases presents a challenging and possibly rewarding in- vestigation due to their very complex superstructure and thermodynamic stability. Calorimetric measurements of the enthalpies of formation and heat capacities of the reduced fluorides [SmF2(s) and YbF2(s) or SmF (s) and YbF 2 40 (3)] would allow for a more accurate 2.40 treatment of the thermodynamic data. The complex reactions observed in the Sm- and Yb-F systems are possibly characteristic of the reactions of other reduced lanthanide halides which exhibit nonstoichiometric regions. Very few of the reduced lanthanide halides have been investigated by thermodynamic 112 methods. This dissertation can serve as a starting point for any- one who cares to brave the unknown vaporization reactions of other lanthanide halides. 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Stull, ed.), Dow Chemical Co., Midland, Mi., 1965. C. E. Wicks and F. E. Block "Thermodynamic Properties of 65 Elements-Their Oxides, Halides, Carbides and Nitrides", Bureau of Mines Bulletin 605, U. S. Government Printing Office, Wash- ington, D. C., 1963. R. Hultgren, R. L. Orr, P. D. Anderson and K. K. Kelley, "Selected Values of the Thermodynamic Properties of Metals and Alloys", John Wiley and Sons, Inc., New York, N. Y., 1963. A. S. Dworkin and M. A. Bredig, J. Phys. Chem., 75, 2340 (1971). K. A. Gschneidner, Jr., J. Less-Common Metals,‘lz, 13 (1969). K. A. Gschneidner, Jr., "Analysis and Applications of Rare Earth Materials", (0. B. Michelsen, ed.) P88. 1, 9, Foto-Trykh, Oslo, Norway, 1973. G. R. Hertel, J. Chem. Phys., 48, 2053 (1968). C. E. Habermann and A. H. Daane, J. Chem. Phys.,‘gl, 2818 (1964). J. Sugar and J. Reader, J. Chem. Phys., 32, 2083 (1973). D. A. Johnson, J. Chem. Soc. (A), 1969, 1528. Do A. JOhnSOU, ibid., 1969, 15250 J. D. Corbett, Rev. Chim. Miner., 12, 239 (1973). APPENDICES APPENDIX 1 X-RAY POWDER DIFFRACTION DATA FOR THE REDUCED LANTHANIDE FLUORIDES Appendix 1.1. X-Ray Powder Diffraction Data for Cubic1 YbF 2.01 I d-spacing h k 2 I d-spacing h k £ 10 0.3237 nm 1 1 1 5 0.1400 nm 4 0 0 7 0.2807 2 0 0 6 0.1285 3 3 1 8 0.1980 2 2 0 5 0.1252 4 2 0 8 0.1688 3 l 1 6 0.1143 4 2 2 6 0.1617 2 2 2 l a = 0.5600(1) nm Appendix 1.2. X-Ray Powder Diffraction Data for Cubic1 YbF2 19 I d-spacing h k z I d-spacing h k z 10 0.3225 nm ' l 1 1 5 0.1396 nm 4 0 0 7 0.2797 2 0 0 6 0.1281 3 3 1 8 0.1973 2 2 0 5 0.1249 4 2 0 8 0.1683 3 1 l 6 0.1141 4 2 2 6 0.1612 2 2 2 1a = 0.5585(1) nm 121 Appendix 1.3. 122 X-Ray Powder Diffraction Data for Pseudo-Tetragonall’2 YbF 2.29 I d-spacing h k 2 I d-spacing h k 2 2 0.4958 nm 3 0.2072 nm 2 0.4701 3 0.2042 10 0.3196 1 0 1 3 0.1989 2 0.3124 8 0.1968 1 1 2 2 0.3103 2 0.1852 2 0.3030 2 0.1724 6 0.2787 0 0 2 2 0.1709 7 0.2772 1 1 0 7 0.1682 1 0 3 2 0.2356 8 0.1675 2 1 1 3 0.2313 6 0.1607 2 0 2 2 0.2230 3 0.1566 3 0.2111 4 0.1397 0 0 4 1a = 0.3925(2); c = 0.5587(2) nm 2Superstructure reflections are not indexed 123 Appendix 1.4. X-Ray Powder Diffraction Data for Pseudo-Hexagonall’2 YbF2.41 I d-spacing h k 2 I d-spacing 2 0.4503 nm 2 0.1791 nm 2 0.3361 1 1 5 0.1693 1 0 10 2 0.3298 8 0.1679 1 1 6 7 0.3262 0 6 5 0.1675 2 0 2 10 0.3215 1 2 3 0.1626 3 0.3123 5 0.1610 0 0 12 2 0.3006 4 0.1607 2 0 4 2 0.2960 2 0.1575 8 0.2790 1 4 2 0.1498 3 0.2415 2 0.1474 2 0.2236 5 0.1393 2 0 8 2 0.2223 3 0.1288 1 0 14 2 0.2208 6 0.1278 2 0 10 2 0.2195 4 0.1272 2 1 2 2 0.2158 0 9 3 0.1252 3 0.2077 5 0.1246 1 1 12 2 0.2043 3 0.1241 2 l 4 3 0.2019 2 0.1148 7 0.1984 1 8 6 0.1139 1 0 16 3 0.1909 4 0.1136 1 2 8 2 0.1881 1 a = 0.3926(4); c = 1.940(2) nm 2Superstructure reflections are not indexed 124 Appendix 1.5. X-Ray Powder Diffraction Data for Cubic1 Ssz 00 I d-spacing h k E I d-spacing h k 2 10 0.3398 nm 1 1 1 4 0.1467 nm 4 0 0 6 0.2940 2 0 0 4 0.1347 3 3 1 8 0.2077 2 2 0 4 0.1313 4 2 0 7 0.1771 3 1 1 4 0.1199 4 2 2 5 0.1693 2 2 2 1 a = 0.5872(1) nm Appendix 1.6. X—Ray Powder Diffraction Data for 1 Pseudo-Hexagonal SmF2.44 I d-spacing h k z I d-spacing h k 6 0.3372 nm 0 0 6 6 0.1745 nm 2 0 10 0.3344 0 1 2 3 0.1684 0 0 12 9 0.2900 1 0 4 4 0.1669 2 0 4 7 0.2056 0 1 8 3 0.1449 2 0 8 7 0.2043 1 1 0 3 0.1335 0 1 14 4 0.1766 1 0 10 3 0.1326 2 1 2 1 a = 0.4086(1); c = 2.0189(7) nm Appendix 1.7. 125 X-Ray Powder Diffraction Data for a Reduced Thulium Fluoride1 I d-spacing h k z I d-spacing h k 2 0.3747 nm (0 1 1)2 4 0.1920 nm (1 3 1)2 3 0.3641 (1 0 1)2 3 0.1890 (3 0 1)2 3 0.3428 (0 2 0)2 3 0.1837 (2 3 0)2 10 0.3241 1 0 2 3 0.1818 (3 1 1)2 4 0.3211 (1 1 1)2 3 0.1940 (2 1 2)2 4 0.3157 (1 1 1)3 2 0.1704 (0 4 0)2 4 0.2856 (2 1 0)2 8 0.1684 2 0 2 8 0.2804 0 0 6 4 0.1652 (3 2 1)2 4 0.2757 (2 0 0)3 3 0.1613 2 0 4 3 0.2692 (- - -)4 2 0.1541 (1 4 1)2 4 0.2485 (1 2 1)2 3 0.1397 2 0 8 3 0.2214 (0 0 2)2 4 0.1283 2 1 2 2 0.2155 0 0 9 2 0.1264 (- - —)4 2 0.2072 (— - -)4 4 0.1250 2 4 3 0.2047 (2 2 1)2 4 0.1141 1 o 16 8 0.1977 1 0 8 1Pseudo-hexagonal: a = 0.3953(1); c = 1.937(1) nm 2Reflections for TmF 3Reflections for Tm O F 3 4 3 6’ reference 139 4 . . Superstructure reflections are not indexed , references 4, 17 and 18 APPENDIX 2 KNUDSEN EFFUSION DATA IN CHRONOLOGICAL ORDER Appendix 2.1. Data for Yb(g) from YbF (0.00 5.x < 0.40) Confined 2+x in M0 T 'an 1293 K 12.753 1323 12.128 1352 11.779 1304 13.000 Appendix 2.2. Data for the Rate of Deposition of Yb(g) XE} Time (T 1457 K) Rate Time 1.89 nm/min 354 min 1.46 373 1.31 393 1.23 421 1.09 447 126 Appendix 2.3. Data from YbF 2.40 127 Effusion Experiments Exp T - 2n K 2 4H398(3rd 13W) (K) (cal mol'lK'l) (kcal mol-1) 1 1466 13.987 23.20 108.91 a = 7.90 x 1523 12.736 20.39 108.92 10_3 cm2 1575 11.736 18.13 109.04 1548 12.385 19.56 109.43 Mo cell 1592 11.572 17.71 109.54 2 1580 11.461 17.32 108.76 1666 10.186 14.29 109.67 a = 1.14 x 1728 9.544 12.61 110.81 10-3 Cm2 1701 9.431 12.57 109.03 1668 10.456 14.82 110.62 MO C811 1633 10.599 15.30 109.09 1601 11.023 16.33 108.62 1572 11.544 17.53 108.52 1640 10.349 14.76 108.70 1685 9.666 13.14 108.99 3 1618 11.120 16.67 109.31 1531 12.471 19.82 108.23 a = 7.59 x 1626 10.898 16.19 109.09 10-3 Cm2 1571 11.912 18.50 108.97 1601 12.682 20.30 108.21 Mo C811 1673 10.157 14.48 109.35 1556 12.073 18.90 108.57 1587 11.575 17.74 108.93 1653 10.451 15.17 109.17 4 1532 13.088 21.04 110.55 a = 5.01 X 1585 11.963 18.52 110.37 10-3 cmz 1504 13.631 22.28 110.35 1608 11.576 17.63 110.56 graphite ce11 1609 11.445 17.36 110.20 5 1569 12.250 19.18 108.97 1606 11.695 17.88 109.47 a = 1.12 x 1660 10.776 15.58 109.66 10-3 cmz 1688 10.281 14.64 109.57 1710 9.911 13.76 109.51 1720 9.888 13.65 109.95 MO C911 1687 10.459 15.00 110.11 1641 11.129 16.57 109.73 1617 11.542 17.52 109.64 1583 12.035 18.68 109.18 Appendix 2.3. (cont'd.) 128 Exp T - fin K 2' .AH398(3rd Law) (K) (cal mo1'1K’1) (kcal mol-1) 6 1566 12.452 19.57 109.41 1608 11.769 18.02 109.83 a = 1.12 X 1676 10.694 15.53 110.29 10-3 Cm2 1696 10.241 14.51 109.89 1740 9.669 13.09 110.26 Mo cell 1724 9.882 13.62 110.14 1669 10.789 15.76 110.22 1655 10.976 16.20 110.02 1633 11.367 17.09 110.01 1606 11.697 17.88 109.48 7 1652 10.687 15.64 108.89 1669 10.497 15.19 109.23 a = 1.12 X 1728 9.722 13.27 109.82 10-3 cm2 1742 9.587 12.91 110.09 1677 10.605 15.35 110.05 M0 cell 1648 11.252 16.78 110.52 1585 12.107 18.81 109.50 1616 11.631 17.70 109.88 1646 11.117 16.52 109.06 8 1599 12.013 18.55 110.07 1549 12.843 20.46 109.62 a = 7.28 x 1509 13.746 22.48 109.80 10-3 Cm2 1517 13.651 22.24 110.06 1545 13.033 20.86 109.95 Mo cell 1499 14.046 23.13 110.06 1487 14.366 23.83 110.23 1469 14.723 24.65 110.07 1531 13.573 22.01 110.68 1566 12.664 20.02 110.08 9 1566 12.464 19.62 109.46 a = 7.28 x 1594 11.931 18.41 109.48 10-3 cm, 1614 11.601 17.65 109.63 1640 11.125 16.57 109.64 Mo cell 1577 12.248 19.13 109.46 129 Appendix 2.3. (cont'd.) Exp T - 2n K 2 AH398(3rd law) -1 -1 -1 (K) (cal mol K ) (kcal mol ) 10 1564 12.579 19.86 109.70 1530 13.160 21.60 109.97 a = 7.28 x 1464 14.892 25.01 110.21 10-3 cm2 1517 13.437 21.82 109.41 1496 14.072 23.20 109.93 Mo cell 1538 13.222 21.28 110.05 1579 12.349 19.32 109.91 1488 14.257 23.61 109.97 1452 15.155 25.60 110.21 1575 12.518 19.68 110.19 Appendix 2.4. Data from YbF 3 130 Effusion Experiments Exp T - 2n p - En K 2 AH398(3rd law) (K) (cal mol-lK-l) (kcal mol-1) 11 1487 12.168 12.067 18.56 107.18 1539 11.057 10.977 15.46 106.87 a = 8.33 x 1620 9.586 9.536 12.36 106.73 10- cm2 1604 9.932 9.874 13.17 106.97 1573 10.443 10.375 14.43 106.88 Mo 0e11 1546 10.922 10.845 15.60 106.86 1519 11.496 11.407 16.82 106.84 1480 12.280 12.176 18.84 107.09 1539 11.085 11.004 15.98 106.95 1568 10.561 10.491 14.70 106.97 12 1435 13.357 13.230 21.37 107.46 1451 13.007 12.888 20.53 107.45 a — 8.33 x 1480 12.319 12.214 18.92 107.21 10-3 cm2 1509 11.732 11.639 17.51 107.18 1569 10.639 10.567 14.85 107.26 Mo cell 1529 11.372 11.286 16.63 107.25 1495 12.060 11.960 18.28 107.33 1461 12.799 12.684 20.03 107.46 1429 13.491 13.362 21.67 107.44 1406 13.977 13.840 22.76 107.25 13 1419 13.676 13.543 22.09 107.29 1369 15.125 14.963 25.24 107.82 a = 8.33 x 1362 15.185 15.022 25.45 107.55 10-3 Cm2 1350 15.420 15.253 25.95 107.28 1342 15.650 15.478 26.45 107.32 Mo cell 1416 13.743 13.609 22.24 107.28 1380 14.574 14.424 24.10 107.11 1405 14.049 13.909 22.91 107.38 1359 15.208 15.044 25.47 107.35 1387 14.472 14.323 23.85 107.31 14 1511 11.615 11.524 17.26 106.95 1616 9.678 9.625 12.58 106.81 a = 1.11 x 1621 9.569 9.519 12.32 106.73 10-3 cm2 1662 8.929 8.891 10.74 106.80 1701 8.391 8.364 9.39 107.00 Mo cell 1726 7.956 7.938 8.35 106.78 1763 7.423 7.416 7.04 106.76 1713 8.214 8.191 8.95 107.01 1683 8.649 8.617 10.03 106.95 1632 9.413 9.365 11.93 106.80 Appendix 2.4. (cont'd.) 131 Exp T - 2n p - £n K 2 AH398(3rd law) (K) (cal mo1’1K'1) (kcal mol 1) 15 1543 10.844 10.768 15.47 106.45 1647 8.998 8.960 11.00 106.26 a = 1.11 x 1707 8.082 8.062 8.74 106.28 10-3 cm2 1743 7.532 7.522 7.40 106.17 1786 6.869 6.873 5.79 105.93 Mo cell 1794 6.787 6.793 5.57 106.01 1738 7.649 7.638 7.66 106.33 1699 8.279 8.254 9.19 106.53 1668 8.721 8.688 10.29 106.43 1610 9.699 9.646 12.67 106.56 16 1584 10.408 1 1640 9.372 a = 1.10 x 1694 8.682 10-3 cm2 1704 8.406 1676 8.945 . 1620 9.796 grapglte 1548 11.088 C9 1 1611 9.925 1699 8.514 1660 9.135 1 . . . . . To retain con51stency and reproduc1b111ty the pressure-temperature data from the graphite cell were only compared to the pressure- temperature data from the Mo cells and not used to derive thermody— namic values 132 Appendix 2.5. Data for Sm(g) from SmF2+x (0.00 E_x < 0.40) Confined in M0 T - 2n p 1113 K 11.161 1219 11.188 1325 11.290 1397 10.983 1451 11.086 Appendix 2.6. Data for the Rate of Deposition of Sm(g) XE} Time (T = 1232 K) Rate Time 8.62 nm/min 138 min 7.71 150 6.22 161 6.02 172 4.53 187 3.97 205 3.70 214 3.37 222 3.25 229 3.10 235 2.85 245 2.67 255 2.63 271 Appendix 2.7. Data from SmF 2.40 133 Effusion Experiments Exp T - 2n K 2' AH398(3rd law) (K) (cal mol-lK-l) (kcal mol 1) 1 1508 11.074 19.46 103.08 a = 4.92 x 1511 11.080 19.47 103.30 10- cm 1498 11.305 19.95 103.15 1556 10.473 18.15 104.33 Mo cell 1488 11.682 20.72 103.58 1543 10.769 18.77 104.44 2 1461 12.850 23.11 105.24 1526 11.591 20.44 105.86 a = 4.69 x 1592 10.397 17.86 106.28 10-3 cmZ 1511 11.732 20.76 105.25 1455 12.795 23.02 104.66 Mo cell 1523 11.443 20.16 105.21 1424 13.409 24.31 104.24 1474 12.268 21.92 104.40 1533 11.227 19.70 105.17 1369 14.858 27.32 104.38 1418 13.479 24.46 104.07 1458 12.634 22.69 104.40 1484 12.077 21.52 104.54 1524 11.365 20.00 105.04 1558 10.677 18.55 105.09 1522 11.399 20.07 105.01 1476 12.150 21.68 104.20 1423 13.251 24.00 103.72 1410 13.706 24.94 104.12 1441 12.918 23.39 104.08 1479 12.166 21.71 104.46 1518 11.459 20.20 104.91 1539 11.043 19.32 105.01 1462 12.467 22.35 104.21 3 1630 8.487 13.89 102.36 1557 9.684 16.58 101.98 a = 1.42 x 1507 10.642 18.61 101.78 10-3 cm2 1662 8.334 13.44 103.61 1716 7.571 11.64 103.92 Mo cell 1570 9.672 16.52 102.74 1506 10.763 18.85 102.08 1596 9.452 15.96 103.56 1675 8.390 13.50 104.51 1556 10.390 17.98 104.09 1601 9.628 16.29 104.37 1635 9.097 15.08 104.65 134 Appendix 2.7. (cont'd.) Exp T - Zn K 2 AH398(3rd law) (K) (661 mol-lK-l) (kcal mol-1) 1682 8.393 13.47 104.94 1724 7.809 12.07 105.12 1758 7.358 10.98 105.26 1791 6.800 9.87 105.26 1789 6.884 9.85 105.15 1766 7.230 10.66 105.30 1731 7.822 12.05 105.55 1705 8.274 13.10 105.75 1659 9.025 14.83 105.76 1608 9.785 16.57 105.31 Appendix 2.8. Data from SmF 135 Effusion Experiments 3 Exp T - 2n p - 2n K 2' AH398(3rd law) (K) (cal mol-lK-l) (kcal mol 1) 1 1694 7.299 7.293 7.75 102.05 1746 6.556 6.564 5.87 101.86 a = 1.11 x 1560 9.608 9.555 13.40 102.78 10-3 cm2 1638 8.227 8.202 10.05 102.43 1684 7.563 7.551 8.35 102.46 Mo cell 1712 7.118 7.115 7.25 102.24 1606 8.841 8.804 11.54 102.81 1650 8.106 8.084 9.71 102.59 1674 7.696 7.682 8.70 102.41 2 1389 13.108 12.986 20.94 101.99 1429 11.959 11.859 18.54 101.47 a = 8.18 x 1461 11.230 11.145 16.99 101.51 10-3 cm2 1495 10.484 10.413 15.39 101.49 1452 11.441 11.352 17.43 101.54 1417 12.290 12.184 19.23 101.64 1404 12.816 12.699 20.31 102.18 1449 11.601 11.509 17.76 101.79 1380 13.306 13.180 21.37 101.88 1353 13.964 13.824 22.75 101.83 1423 12.302 12.196 19.24 102.01 1466 11.258 11.172 17.02 101.86 1397 12.882 12.764 20.47 101.94 1359 13.911 13.772 22.63 102.05 1412 12.572 12.460 19.80 102.07 1453 11.542 11.451 17.63 101.89 1488 10.778 10.702 16.00 101.86 1439 11.826 11.729 19.12 103.06 1485 10.838 10.761 16.12 101.90 3 1419 11.874 11.776 18.12 100.20 1497 10.256 10.190 14.94 100.92 a = 1.16 x 1468 10.950 10.870 16.41 101.11 10-3 Cm2 1518 9.881 9.823 14.12 101.09 1417 12.067 11.965 18.80 101.02 1485 10.535 10.464 15.53 101.02 1553 9.228 9.183 12.70 101.19 1571 9.009 8.968 12.19 101.57 1613 8.272 8.246 10.37 101.38 1659 7.604 7.592 8.66 101.40 1701 6.954 6.954 7.02 101.20 1742 6.277 6.291 5.36 100.75 1721 6.619 6.627 6.20 100.98 136 Appendix 2.8. (cont'd.) Exp T - 2n p - En K 2' AH398(3rd law) (K) (cal mol-1K-1) (kca1 mol-1) 1693 7.097 7.095 7.37 101.34 1649 7.777 7.761 9.08 101.49 1602 8.484 8.454 10.88 101.51 1564 9.121 9.078 12.44 101.54 1525 9.838 9.781 14.00 101.41 1592 8.714 8.679 11.42 101.71 1638 8.015 7.994 9.64 101.75 1639 8.001 7.980 9.60 101.75 Appendix 2.9. Data from TmF 137 Effusion Experiments 3 Exp T - 2n p 2' AH398(3rd law) (K) (cal mol-lK-l) (kcal mol 1) 1 1444 12.346 19.43 107.28 1418 12.955 20.85 107.43 a = 7.06 x 1474 11.841 18.12 107.61 10-3 cm2 1521 10.989 15.97 107.75 1557 10.291 14.24 107.62 Mo cell 1586 9.828 13.05 107.77 1534 10.697 15.26 107.60 1479 11.721 17.84 107.53 1488 11.546 17.40 107.53 1458 12.151 18.90 107.56 1398 13.425 21.93 107.42 1349 14.540 24.50 107.13 1376 14.168 23.56 107.99 1441 12.532 19.83 107.66 1506 11.304 16.74 107.87 1540 10.620 15.05 107.71 1523 11.005 15.98 107.95 1446 12.412 19.54 107.63 1419 13.032 20.97 107.71 1424 12.864 20.62 107.58 1466 12.054 18.63 107.74 1388 13.688 22.52 107.45 1426 12.859 20.61 107.64 1348 14.686 24.80 107.45 2 1474 11.440 17.32 106.44 1537 10.527 14.90 107.25 a = 1.18 x 1586 9.705 12.80 107.38 10-3 cm2 1538 10.548 14.93 107.38 1584 9.774 12.96 107.49 Mo ce11 1634 8.982 10.93 107.54 1699 7.966 8.35 107.42 1732 7.459 7.06 107.30 1809 6.342 4.21 106.90 1765 6.996 5.86 107.25 1733 7.476 7.08 107.40 1708 7.860 8.06 107.50 1674 8.388 9.40 107.62 1638 8.959 10.85 107.68 1599 9.595 12.47 107.79 1647 8.835 10.52 107.76 1675 8.362 9.34 107.58 1697 7.981 8.39 107.42 138 Appendix 2.9. (cont'd.) .. 0 Exp T 2n p E AH298(3rd law) (K) (cal mol-lK-l) (kcal mol-1) 1751 7.214 6.41 107.35 1787 6.649 5.00 107.00 1747 7.203 6.43 107.11 1718 7.672 7.60 107.35 DERIVED THERMODYNAMIC FUNCTIONS FOR SELECTED LANTHANIDE FLUORIDES APPENDIX 3 Appendix 3.1. Derived Thermodynamic Functions for YbF3(g)1 O O O- O _ O- O T Cp ST HT H298 (GT H298)/T (K) (cal mol-lK-l) (cal mo1'1K’1) (cal mol-1) (cal moi'lK'l) 298 17.04 81.83 (2) 81.83 500 18.64 91.09 3631 83.83 1000 19.53 104.38 13242 91.14 1200 19.63 107.95 17159 93.65 1400 19.70 110.98 21093 95.92 1600 19.74 113.61 25037 97.97 1800 19.77 115.94 28987 99.84 2000 19.79 118.02 32942 101.55 1 . . . . For assumptions made in derivation see Section 5.5.2. 2 0 H29 - H° = 4035 cal mol-1 139 140 . . . . 1 Appendix 3.2. Derived Thermodynamic Functions for YbF3(s,£) 2 T Cp ST HT H298 (GT H298),T (K) (cal mol-lK-l) (cal mol-lK-l) (cal mol-1) (cal mol-lK-l) 298 500 1000 1200 1400 1600 1800 2000 23.44 24.18 26.51 27.47 28.57 29.09 29.09 29.09 26.56 38.84 56.30 61.22 70.26 79.08 82.51 85.57 0 4799 17463 22861 34404 47312 53130 58948 26.56 29.24 38.84 42.17 45.68 49.51 52.99 56.10 1Derived using the enthalpy increments from Reference 13 2For estimation of absolute entropy see Section 5.5.2. 141 . . 1 Appendix 3.3. Derived Thermodynamic Functions for YbF2(g) T C; Si “5 ’ H3.98 ’(Gi ' H298)/T (K) (cal mo1'1K'1) (cal mol-1K-1) (cal mol-1) (cal moi 1K 1) 298 12.52 69.47 (2) 69.47 500 13.34 76.18 2627 70.93 1000 13.76 85.60 9435 76.17 1200 13.80 88.11 12191 77.95 1400 13.83 90.24 14955 79.56 1600 13.85 92.09 17724 81.02 1800 13.86 93.72 20495 82.34 2000 13.87 95.19 23268 83.55 1For assumptions made in derivation see Section 5.5.1. 20 H298 -H° = 3125 cal moi"1 Appendix 3.4. Derived Thermodynamic Functions for YbF2(s,£)1 O O O_ O _ O- O T Cp ST HT H298 (GT H298)/T (K) (cal mol-lK—l) (cal mol-lK-l) (cal mo1-1) (cal mol 1K 1) 298 17.34 22.50 0 22.50 500 17.98 31.62 3565 24.49 1000 19.58 44.57 12956 31.62 1200 20.22 48.20 16936 34.09 1400 20.86 51.36 21043 36.33 1600 21.50 54.19 25279 38.39 1800 23.90 61.36 37376 40.59 2000 23.90 63.88 42156 42.80 1 . . . . . For assumptions made in derivation see Section 5-5-1- 142 . 1 Appendix 3.5. Derived Thermodynamic Functions for SmF3(g) 0. - O- O T C; 5% HT ”298 (GT H298)/T (K) (cal mol-lK—l) (ca1 moi’lK'l) (cal mol 1) (cal moi 1K 1) 298 17.99 81.13 (2) 81.13 500 20.13 91.02 3878 83.26 1000 21.61 105.57 14420 91.15 1200 21.75 109.53 18759 93.90 1400 21.78 112.88 23113 96.37 1600 21.73 115.79 27465 98.62 1800 21.63 118.34 31801 100.68 2000 21.52 120.62 36116 102.56 1For assumptions made in derivation see Section 5.5.5. 2H o - 298 H0 = 4202 cal mo1’1 Appendix 3.6. Derived Thermodynamic Functions for SmF3(s,£)1 O O 0.. .. O- O T Cp ST HT H298 (GT H298)/T (K) (cal moi'lK'l) (cal mol-lK-l) (cal mol-1) (cal moi'lK'l) 2 298 25.68 27.09 0 27.09 500 25.68 40.37 5163 30.04 1000 27.18 59.59 19156 40.43 1200 30.12 64.75 24822 44.06 1400 35.98 69.81 31401 47.38 1600 35.60 82.93 51656 50.65 1800 35.60 87.13 58776 54.47 2000 35.60 90.88 65896 57.93 1Derived using the enthalpy increments from Reference 18 For estimation of absolute entropy see Section.5-5-5. 143 . 1 Appendix 3.7. Derived Thermodynamic Functions for SmF2(g) O 0 °_ 0 T Cp ST HT H298 1K'l) (cal moi’lK'l) (cal mol-1) (cal mol-lK-l) _ - O (G? H298)/T (K) (cal mol- 298 15.07 72.59 (2) 72.59 500 15.83 80.60 3134 74.33 1000 16.27 91.76 11195 80.57 1200 16.24 94.72 14447 82.69 1400 16.12 97.22 17684 84.59 1600 15.96 99.36 20893 86.30 1800 15.78 101.23 24068 87.86 2000 15.60 102.89 27205 89.28 1 . . . . . For assumptions made in derivation see Section 5.5.4. 2 298 0 H° -H° = 3558 cal mol-1 Appendix 3.8. Derived Thermodynamic Functions for SmF2(s,£)1 O 0 0-0 -O_O T Cp ST HT H298 (GT H298)/T (K) (cal moi'lK'l) (cal mol-lK-l) (cal mol-1) (cal moi’lK'l) 298 500 1000 1200 1400 1600 1800 2000 14.63 15.91 19.09 20.37 21.64 22.91 23.90 23.90 27.10 34.97 46.97 50.57 53.80 56.77 63.99 66.51 0 3082 11834 15780 19980 24436 36653 41433 27.10 28.80 35.14 37.41 39.53 41.50 43.63 45.79 For assumptions made in derivation see Section 5.5.4. 144 Appendix 3.9. Derived Thermodynamic Functions for TmF3(g)1 T C; S; ”5 ' H3.98 ”(6% ‘ H398)/T (K) (cal m01-1K-1) (cal mol-1K-1) (cal mol-1) (cal mol 1K 1) 298 17.05 82.51 (2) 82.51 500 18.65 91.78 3633 84.51 1000 19.57 105.08 13251 91.83 1200 19.72 108.66 17180 94.34 1400 19.87 111.71 21139 96.61 1600 20.02 114.37 25128 98.67 1800 20.18 116.74 29148 100.55 2000 20.34 118.88 33200 102.28 For assumptions made in derivation see Section 5.5.7. 2 O _ 0 H298 H Appendix 3.10. Derived Thermodynamic Functions for TmF3(s,£)1 = 4024 cal mol- 1 O O O- O _ O- O T Cp ST HT H298 (GT H298)/T (K) (cal mol-lK-l) (cal mol-lK-l) (cal mol-1) (cal mol-lK-l) 298 22.47 27.622 0 27.62 500 24.40 39.79 4771 30.25 1000 26.25 57.34 17482 39.86 1200 26.81 62.17 22788 43.19 1400 23.39 71.60 35159 46.49 1600 33.54 80.68 48460 50.09 1800 33.54 84.63 55168 53.98 2000 33.54 88.16 61876 57.22 1Derived using the enthalpy increments from Reference 18 2For estimation of absolute entropy see Section 5.5.7. APPENDIX 4 MASS SPECTROMETRY DATA Appendix 4.1. Ion Intensity of Yb+ from YbF +x(s) Confined in M0 ys, Time 2 (T = 1338 K) (T = 1396 K) 1+(174)1'2 Time 1+(174) Time 68 10 min 193 109 min 58 72 85 169 16 197 63 201 13 221 56 239 1Ionization energy = 45 i 5 V 2An ion intensity of 100 = 2/3 x 10"12 amp . + 3Measured from time of appearance of Yb peak from YbF2 0 145 Appendix 4.2. Ionization Efficiency Curve Data for Yb+ from YbF Confined in M0 (T = 1335 K) 146 I(Yb+)1’2’3 Volts I(Yb+) Volts I(Yb+) Volts 238 40.35 5 9.46 194 17.67 235 34.87 9 10.15 161 16.28 234 30.75 64 11.40 127 13.81 235 25.45 114 12.78 96 12.37 219 20.43 145 13.25 52 11.34 205 17.36 152 14.15 34 10.71 139 14.93 203 20.27 21 10.41 105 12.42 180 18.67 187 20.02 38 10.76 1I = sum of ion currents for masses 170, 171, 172, 173, 174 and 176 210D current of 100 = 2/3 x 10 3Time = 30 to 90 min after time of appearance of Yb+ peak from YbF -12 amp 2.0 147 + . . + + Appendix 4.3. Intensity of Yb and IntenSity Fractions of Yb , YbF and YbF + 2 2+x ys. Time (T = 1653 K) (0.0 S_x f_0.4) Confined in Mo Yb+ Yb+ YbF+ YbFz+ . 4 + 1 2 + 3 + + Time 1 (174) ' IF (174) IF (193) IF (212) 178 0.763 0.183 0.053 636 min 118 0.645 0.258 0.097 770 68 0.625 0.244 0.131 808 38 0.535 0.307 0.158 921 30 0.532 0.298 0.170 1044 23 0.461 0.359 0.180 1109 35 0.455 0.295 0.250 1222 28 0.377 0.347 0.275 1354 30 0.316 0.294 0.389 1432 18 0.291 0.328 0.381 1452 15 0.299 0.320 0.380 1512 11 0.307 0.356 0.337 1647 10 0.244 0.337 0.420 1787 9 0.255 0.289 0.456 1959 12 0.228 0.317 0.455 2129 12 0.174 0.315 0.511 2169 18 0.238 0.317 0.446 2200 9 0.222 0.292 0.486 2300 14 0.202 0.341 0.457 2343 11 0.187 0.319 0.494 2550 9 0.220 0.275 0.505 2680 100 = 2/3 x 10'12 1 2 3 + Ionizing energy = 45 i 5 V amp “Measured from time of appearance of Yb+ peak from YbF I (174)/tota1 Yb-containing ion current 2.0 148 + + + Appendix 4.4. Ionization Efficiency Curve Data for Yb , YbF and YbF2 from YbF2+x (0.0 5.x < 0.4) Confined in M0 (T = 1667 K) Yb+ YbF+ YbF2+ I+(174)1’2 Volts 1+(l93) Volts 1+(212) Volts 106 29.59 44 29.72 29.2 42.95 96 24.95 35 25.92 23.9 30.95 91 22.00 38 22.64 16.8 25.92 103 19.94 39 20.68 13.3 23.62 79 17.70 23 19.00 12.4 20.96 68 15.70 19 17.22 8.7 19.28 57 13.53 13 15.10 8.0 17.55 48 12.42 12.5 13.12 7.6 15.41 35 11.23 10 12.05 2.9 13.26 8.7 9.85 8.7 11.08 5.9 14.53 3.5 9.29 2.7 10.17 8.9 16.35 9 10.31 12 13.57 I 9.7 18.21 18 10.88 15 15.50 10.6 18.28 31 11.65 20 16.05 14.2 20.69 55 12.61 24 18.55 13.3 22.64 57 14.60 41 28.92 24.8 29.17 84 18.29 44 45.00 31.9 43.72 135 43.45 1100 = 1/3 x 10'12 amp 2 . Time = 800 to 975 min after time of appearance of Yb+ peak Appendix 4.5. Ionization Efficiency Curve Data for Yb+, YbF+ and YbF2+ from YbF2.40 Confined in M0 (T = 1735 K) Yb+ YbF+ YbF2+ + 1 2 + + V°1ts I (174) ’ I (193) I (212) 29.71 43.25 77.86 43.45 22.00 33.00 60.00 37.70 22.00 33.00 51.00 34.67 23.00 30.50 49.00 32.39 20.20 33.00 52.60 29.94 14.79 27.43 39.93 26.63 9.00 22.00 29.00 23.32 7.50 19.50 29.80 21.01 9.50 20.00 26.50 18.78 5.67 11.00 12.53 16.23 9.00 9.67 7.25 15.32 6.00 6.67 5.67 14.38 3.17 5.67 3.67 13.33 5.38 4.88 3.00 12.24 1.75 0.50 0.50 11.33 1100 = 1/3 x 10'12 amp 2Time = 2527 to 2687 min after time of appearance of Yb+ peak from YbF2 00 + Appendix 4.6. Ionization Efficiency Curve Data for Yb , 150 YbF+ and YbF + from YbF3 O(2) Confined in M0 (T = 1673 K) 2 I(Yb+)1’2 Volts 1(pr+)3 Volts Kym-2+)4 Volts 55.7 44.62 26.40 44.15 329.5 45.70 50.3 39.32 26.50 37.74 282.0 37.56 40.0 37.01 26.60 30.63 228.0 30.15 37.3 35.56 19.70 28.95 162.1 25.96 34.8 34.10 16.50 27.37 95.3 21.45 27.3 32.73 15.00 25.70 79.0 19.55 27.3 32.73 8.70 23.93 42.2 17.51 22.0 31.54 5.40 21.95 17.3 15.45 15.5 29.53 9.35 20.45 21.4 15.71 10.2 28.68 1.01 19.67 34.3 17.00 4.00 18.90 54.5 18.62 3.61 21.10 98.0 20.32 5.98 22.72 107.7 22.14 11.30 24.67 129.7 23.64 13.80 26.80 154.7 25.50 17.20 28.23 192.3 29.52 20.80 29.75 277.3 36.57 23.30 34.33 117.0 22.96 25.60 44.07 89.3 21.43 3.20 18.22 60.7 19.66 47.3 18.03 27.2 16.45 11.7 15.32 10.0 14.40 —¥ 1 2I = I I ll 3 2, H 100 = 1/3 x 10' 12 amp ion currents for masses 172 + 174 + 176 ion currents for masses 191 + 193 + 195 ion currents for masses 210 + 212 + 214 7WJLHI.(fl- ‘ 1. APPENDIX 5 UNTREATED DATA FROM KNUDSEN EFFUSION EXPERIMENTS IN CHRONOLOGICAL ORDER Appendix 5.1. Target Collection Data for Yb(g) from YbF2+x (0.00:: x < 0.40) Confined in M0 Counts/30 sec T(obs) TT1 Exposure Before After Time Exposure Exposure 168912 16617; 24794 1273 K -7 K 45.00 min 13864 26441 1302 -7 16.00 13959 22082 1330 -7 10.00 13615 20671 1284 -7 47.00 138742 295942 16654 159203 24449 a = 7.90 x 10’3 cm2, c = 10.21 cm, a = 0.826 cm [see equations (3-5) and (3-6)]; I)(Wien's Law) = -1.646 x 10-5 111 = T(IPTS - 1948) - T(obs) 2Standard Blank Yb(1) 3Standard Yb(1) 151 f __ A!“ 152 Appendix 5.2. Target Collection Data for YbF Effusion Experiments 2.40 Counts/30 sec T(obs) TT1 Exposure Before After Time Exposure Exposure Experiment 1 2 2 16654 159203 24449 1437 K ~6 K 110.00 min 13963 29818 1501 ~15 31.00 14156 28394 1550 ~15 12.00 13993 28772 1525 ~15 20.00 13837 26753 1565 ~14 10.00 141972 286262 16640 157663 _3 2 24464 a = 7.90 x 10 cm , C = 10.21 cm, R = 0.826 cm [see equations (3-5) and (3-6]; 0 (Wien's Law) = ~1.646 x 10’ Experiment 2 2 2 15081 173983 26149 1554 ~14 87.00 13255 37396 1636 ~14 28.00 16033 43377 1696 ~16 5.00 16245 26923 1670 ~15 10.00 13769 34719 1637 ~14 15.00 163022 289012 15100 170723 26346 1603 ~13 33.00 13753 35182 1574 ~14 50.00 13020 34315 1547 ~15 80.00 13611 34147 1610 ~13 34.00 13609 41108 1654 ~14 14.00 127652 350612 15087 170823 _3 2 26157 a = 1.14 x 10 cm , C = 10.25 cm, R = 0.826 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = -1.646 x 10-5 Experiment 3 2 2 16510 175733 26312 1589 ~13 13.00 13762 43448 1508 ~15 70.00 13585 55812 1597 ~13 11.00 12888 44116 1546 ~15 30.00 13086 44540 1574 ~14 17.00 135522 454142 16393 174403 26229 153 Appendix 5.2. (cont'd.) 1 Counts/30 sec T(obs) TT Exposure Before After Time Exposure Exposure 1498 K ~15 K 75.00 min 13482 50100 1642 ~14 4.00 14341 37838 1532 ~15 44.00 13816 52563 1561 ~14 23.00 13496 49443 1622 ~13 7.00 140122 442132 16740 174843 _3 2 26055 a = 7.57 x 10 , c = 10.37 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = -1.646 x 10-5 Experiment 4 2 2 15580 164613 24926 1483 8 45.31 15817 23261 1534 7 27.01 15595 28392 1455 9 85.21 15581 23767 1558 5 17.00 15792 27725 1559 5 15.24 155512 277492 15587 164643 _3 2 25199 a = 5.01 x 10 cm , c = 9.89 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = -1.800 x 10- 5 154 Appendix 5.2. (cont'd.) Counts/60 sec T(obs) TT Exposure Before After Time Exposure Exposure Experiment 5 4 4 9157 87705 13202 1550 K ~15 K 120.00 min 8054 12395 1584 ~13 60.00 8576 12172 1634 ~12 25.00 7875 11584 1662 ~13 15.00 7988 11544 1685 ~15 12.00 79244 12067“ 9283 84745 13376 1694 ~15 10.26 8032 12092 1661 ~13 15.00 8277 11535 1616 ~12 35.00 8576 12502 1594 ~13 55.00 8287 12352 1564 ~15 95.00 78464 121424 8805 88385 13237 a = 1.12 x 10-3 cm2, C = 10.50 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = -1.391 x 10 5 Experiment 6 4 4 8654 8745 , 13225 1547 -15 130.00 8129 12826 1586 -13 65.00 7735 12326 1650 -13 20.00 8258 12337 1671 -14 13.00 8043 12190 1713 ~14 5.00 81424 109754 8659 87935 13233 1698 -15 10.00 8473 12886 1643 -12 22.00 8442 12372 1629 -12 28.00 8224 12327 1608 ~12 45.00 7845 12277 1584 ~13 65.00 78524 124374 8894 87705 13202 ~ 2 a = 1.12 x 10 3 cm , C = 10.50 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = -1.391 x 10-5 155 Appendix 5.2. (cont'd.) Counts/60 sec T(obs) TT1 Exposure Before After Time Exposure Exposure Experiment 7 4 4 8045 80605 12316 1626 K ~11 K 35.00 min 7858 14305 1643 ~12 25.00 7470 12912 1674 ~14 15.00 7362 12109 1702 ~15 10.00 7384 11927 1715 ~14 7.00 75214 111164 8407 82605 11572 1651 ~13 22.00 7559 11735 1622 ~11 37.00 7869 11544 1565 ~15 110.00 7750 12376 1593 ~12 65.00 7324 11814 1620 ~11 35.00 76684 116544 8475 83075 _3 2 12400 a = 1.12 x 10 cm , c = 10.51 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.391 x 10..5 Experiment 8 4 4 8894 86355 12889 1578 ~14 5.00 8292 9621 1531 ~14 34.50 8080 12648 1489 ~11 70.00 8257 12022 1498 ~12 65.00 8299 12137 1527 ~14 40.00 83934 127684 8932 86765 12941 1479 ~11 100.00 8495 12602 1467 ~10 121.00 8372 12014 1449 ~10 220.11 8175 12955 1512 ~13 65.00 7899 12300 1547 ~15 33.10 80544 136534 8865 86745 13201 a = 7.28 x 10.3 cm2, C = 10.61 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.391 x 10-5 156 Appendix 5.2. (cont'd.) Counts/60 sec T(obs) TT Exposure Before After Time Exposure Exposure Experiment 9 4 4 8992 81195 12660 1547 K ~15 K 30.00 min 8106 13045 1573 ~14 16.00 8515 12868 1591 ~13 12.00 8241 12826 1615 ~12 8.00 7909 12887 1558 ~15 26.00 84204 138164 9028 82945 _3 2 12660 a = 7.28 x 10 cm , C = 10.61 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.391 x 10—5 Experiment 10 4 4 8256 80185 12334 1545 ~14 31.00 7548 12966 1511 ~13 60.00 7380 12257 1444 ~10 279.40 7686 12742 1498 ~12 70.00 7369 12319 1476 ~11 122.00 76874 127144 8289 82995 12386 1519 ~14 50.00 7755 12442 1560 ~15 22.00 7814 12719 1468 ~10 151.00 7612 12792 1433 -10 360.00 7382 12511 1556 ~15 22.00 74374 116824 8232 83195 12329 a = 7.28 x 10.3 cm2, C = 10.61 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.391 x 10-5 TT = T(IPTS ~ 1948) ~ T(obs) Standard Blank Yb(1) Standard Yb(1) Standard Blank Yb(Z) Standard Yb(Z) MDWNH 157 Appendix 5.3. Target Collection Data for YbF Effusion Experiments 3.00 Counts/30 sec T(obs) TT1 Exposure Before After Time Exposure Exposure Experiment 11 2 2 14102 141593 22786 1434 K 15 K 46.00 min 11617 25183 1484 14 14.00 11256 23476 1561 13 4.01 12023 26764 1546 13 6.00 12157 27722 1516 14 11.00 124332 295942 13980 137193 22283 1490 14 14.00 12835 26551 1463 15 30.00 12578 29436 1427 15 50.00 12150 25251 1483 14 14.00 11217 23202 1511 14 11.00 111402 269892 13987 142023 22573 a = 8.33 x 10.3 cm2, C = 12.32 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.800 x 10-5 Experiment 12 a = 8.33 x 10' and (3-6)]; D (Wien's Law) = -1.800 x 10- 144212 15512; 24038 1382 16 101.00 13215 23732 1398 16 70.00 13558 23876 1427 15 43.00 13905 26241 1455 15 26.00 13783 27007 1512 14 6.00 138922 230632 14409 150673 24067 1473 15 15.00 14320 25345 1441 15 25.00 14266 23723 1408 16 61.00 14155 25165 1377 16 90.00 13805 22225 1355 16 150.00 135352 196172 14477 154193 24105 3 2 cm , c = 12.30 cm, R = 0.833 cm [see equations (3-5) 158 Appendix 5.3. (cont'd.) Counts/30 sec T(obs) TT1 Exposure Before After Time Exposure Exposure Experiment 13 2 2 14477 149873 23545 1367 K 16 K 120.00 min 13731 22390 1319 17 260.00 14050 18708 1313 17 260.00 12720 17075 1301 17 260.00 12893 16390 1293 17 400.00 132632 174612 14806 150733 23643 1365 16 60.00 13923 18003 1331 16 240.00 13635 20665 1354 16 125.00 13593 19739 1309 17 301.00 13382 18126 1338 16 120.00 141432 180642 14862 149623 23665 a = 8.33 x 10"3 cm2, C = 12.30 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.800 x 10-5 Experiment 14 140332 14716; 23271 1456 15 140.00 12616 22788 1557 13 30.00 10778 25105 1562 13 30.00 10924 26883 1601 13 15.00 10620 25651 1636 14 10.00 109052 278802 13865 144753 23390 1660 14 5.30 11881 26119 1695 14 3.00 12621 26252 1648 14 6.00 11943 24461 1620 13 11.00 10717 25342 1572 13 26.00 118102 280702 13458 146723 23087 a = 1.11 x 10'.3 cm2, C = 12.37 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.800 x 10'-5 159 3 2 Appendix 5.3. (con'td.) 1 Counts/30 sec T(obs) TT Exposure Before After Time Exposure Exposure Experiment 15 2 2 14394 108913 18692 1487 K 14 K 110.00 min 12351 23735 1587 13 16.00 11409 21435 1642 14 7.00 12458 23185 1676 14 5.00 12380 26161 1716 14 2.50 125502 255622 14434 109383 18610 1723 15 2.50 12808 27038 1671 14 5.00 12502 24341 1634 14 8.00 12348 22184 1607 13 16.00 11363 25199 1551 13 36.00 113352 228822 14273 110393 18553 a = 1.11 x 10' cm , c = 12.26 cm, R = 0.833 cm [see equations (3-5) and (3-5)]; D (Wien's Law) = ~1.800 x 10.-5 160 Appendix 5.3. (cont'd.) Counts/30 sec T(obs) TT1 Exposure Before After Time Exposure Exposure Experiment 16 2 2 15767 158823 24750 1555 K ~15 60.00 min 14981 29181 1606 ~13 24.32 14755 30668 1658 ~14 10.00 14333 27169 1667 ’14 8.46 13470 28216 1641 ~14 10.00 147132 246332 15949 160083 24844 1588 ~14 20.00 14673 23373 1521 ~15 75.00 15383 24609 1580 ~14 30.00 14311 25852 1663 ~14 15.00 13818 26353 1625 ~13 12.00 153922 337862 15638 160283 24852 a = 1.10 x 10.3 cm2, C = 12.30 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.800 x 10-5 1T1 = T(IPTS - 1948) - T(obs) 2Standard Blank Yb(1) 3Standard Yb(1) 161 Appendix 5.4. Target Collection Data for Sm(g) from SmF2+x (0.00jS x < 0.40) Confined in M0 Counts/30 sec T(obs) TT1 Exposure Before After Time Exposure Exposure 41472 4128; 15874 1094 K ' -1 K 27.00 min 4077 14951 1201 -6 26.00 4170 13921 1304 -7 28.00 4175 13289 1372 -7 21.00 4113 13180 1426 ~6 33.00 40872 166922 4045 41153 15882 3 2 a = 4.92 x 10' cm , c = 10.00 cm, R = 0.795 cm [see equations (3-5) and (3-6)]; 0 (Wien's Law) = ~1.646 x 10' TT = T(IPTS - 1948) - T(obs) 2Standard Blank Sm(1) 3Standard Sm(1) 162 Appendix 5.5. Target Collection Data for SmF Effusion Experiment 1 2.40 1 Counts/30 sec T(obs) TT Exposure Before After Time Exposure Exposure 40452 4115; 15882 1474 K -3 K 20.00 min 4155 18717 1477 ~3 61.85 4199 48805 . 1475 ~13 20.00 4276 15840 1532 ~15 8.00 4269 14673 1465 ~13 37.00 4109 18796 1520 ~15 12.00 42412 158372 4131 40563 15837 a = 4.92 x 10.3 cm2, C = 10.00 cm, R = 0.795 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = -1.646 x 10-5 111 = T(IPTS - 1948) - T(obs) 2Standard B1ank Sm(1) 3Standard Sm(1) Appendix 5.6. Target Collection and Deposition Data for SmF2 163 Effusion Experiments .40 Counts/30 sec T(obs) TT1 Exposure Before After Deposit2 Time Exposure Exposure Experiment 2 40793 42152 5 15781 14285K -7 K 61.00 min 4224 12221 18.9 mm 1488 ~2 20.00 4207 13416 23.4 1398 ~7 50.00 4178 8205 9.9 1445 ~6 25.00 4010 10438 15.3 1497 ~2 10.00 41243 116253 16.9 4176 42034 15945 1534 ~15 10.00 4212 16569 29.1 1487 ~2 10.00 4081 10298 14.3 1447 ~6 31.00 4167 13148 21.2 1450 ~6 30.00 4157 12905 20.2 1516 ~15 10.00 41763 131073 20.3 4124 41934 _3 2 15733 a = 4.69 x 10 cm , C = 9.02 cm, R = 0.795 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.646 x 10.-5 Appendix 5.6. (cont'd.) Counts/30 sec T(obs) TT1 Exposure Before After Deposit2 Time Exposure Exposure Experiment 3 42313 41712 6 15839 12146' K 25 K 13.00 min 3992 23923 43.8 nm 1546 17 3.00 4130 15486 23.4 1516 16 10.00 4106 13360 20.3 1586 18 4.00 4067 14814 22.9 1551 17 7.00 40363 132493 20.0 4134 42244 15902 1631 18 2.00 4110 13460 20.1 1663 17 2.00 4235 19792 31.4 1695 15 1.00 4271 15377 24.6 1694 15 1.00 4182 15304 25.0 1639 17 3.00 39853 174643 29.9 4147 41904 _3 2 15629 a = 1.42 x 10 cm , c = 10.42 cm, R = 0.795 cm [see equations (3-5) and (3-6)]; 0 (Wien's Law) = 2.630 x 10’ 5 1 \JONU'IL‘LAN TT = T(IPTS ~ 1948) ~ T(obs); TT for experiment 3 = T(IPTS ~ 1948) - T(obs) + 31 K Thickness as determined by quartz crystal Standard Blank Sm(1) Standard Sm(1) a = 4.92 x 10.3 2 C = 8.56 cm Sm(g) cm , C = 10.00 cm 165 Appendix 5.7. Rate Data for SmF2 40 Effusion Experiments T(obs) TT Rate T(obs) TT Rate2 Experiment 23 1433 K ~6 K 0.292 nm/min 1488 K 14 K 0.880 nm/min 1504 ~15 1.01 1428 ~7 0.310 1565 -14 3.256 1488 -2 1.17 -3 2 a = 4.92 x 10 cm , C = 10.00 cm 1398 -7 0.198 1487 -2 1.43 1445 -6 0.610 1447 -6 0.685 1497 -2 1.69 1397 -7 0.232 1346 -7 0.0475 1385 -7 0.148 1393 -7 0.185 1415 -7 0.321 1430 -6 0.425 1450 -6 0.674 1454 -5 0.735 1484 -3 1.35 1489 -2 1.48 1516 -15 2.03 1534 -15 2.91 1434 -6 0.500 a = 4.69 c 10.3 cm2, C = 9.02 cm, R = 0.795 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.646 x 10-5 166 Appendix 5.7. (cont'd.) T(obs) TT1 Rate2 T(obs) TT1 Rate2 . 4 Experiment 3 1546 K 17 K 7.800 nm/min 1624 K 18 K 19.0 nm/min 1479 17 2.41 1491 17 2.43 1430 20 0.940 1429 20 8.33 1575 17 9.00 C = 8.56 cm 1516 16 2.03 1695 15 24.6 1586 18 5.73 1694 15 25.0 1478 17 0.805 1673 16 17.8 1520 16 1.70 1639 17 9.95 1551 17 2.86 1614 18 6.38 1593 18 5.70 1573 17 3.05 1631 18 10.1 1527 16 1.45 1663 17 15.7 3 2 a = 1.42 x 10- cm , C = 10.42 cm, R = 0.795 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~2.630 x 10- 5 1 TT = T(IPTS ~ 1948) ~ T(obs); TT for experiment 3 = T(IPTS ~ 1948) ~ T(obs) + 31 K 2Rate of deposition as determined by quartz crystal 3Pressures calculated by use of (2.4 6 i 0.08) nm/ug Sm “Pressures calculated by use of (2.25 i 0.07) nm/ug Sm 167 Appendix 5.8. Target Collection Data for SmF Effusion Experment 1 3.00 Counts/30 sec T(obs) TT1 Exposure Before After Time Exposure Exposure 35642 3980: 4 43066 1619 K -~ 20.00 min 3537 43066 1663 -14 K 12.00 3589 43731 1714 ~17 5.00 3538 38284 1536 -15 120.00 3529 45172 1608 -13 30.00 36222 441302 3514 41133 43320 1653 ~14 15.00 3464 42285 1680 ~15 10.00 3495 43527 1578 ~14 75.00 3534 58642 1619 -13 20.00 3577 34073 1643 ~14 15.00 35292 376582 3527 40813 _3 2 43283 a = 1.11 x 10 cm , c = 9.99 cm, R = 0.795 cm [see equations (3-5) and (3—6)]; D (Wien's Law) = ~1.646 x 10-5 TT = T(IPTS - 1948) - T(obs) Standard Blank Sm(2) Standard Sm(2) DWNH Temperature varied 60°; target was not used. Appendix 5.9. 168 Target Collection and Deposition Data for SmF Effusion Experiments 3'00 1 Counts/30 sec 2 T(obs) TT Exposure Before After Deposit Time Exposure Exposure Experiment 2 41243 42042 5 6 15553 14335’7 -6 K 21.00 min 3960 15144 29.2 nm 14645’ -5 6.00 3852 11479 18.4 1425 -7 13.00 4102 10857 16.5 14228 -7 17.00 4031 12033 20.0 1417 -7 35.00 39993 146053 27.9 4045 41274 15765 1373 -7 52.00 4091 10533 17.2 1336 ~7 86.00 4158 7997 10.3 1426 -7 15.00 4113 11164 18.6 1413 -7 21.00 4149 11299 19.7 1455 -5 6.00 40043 95743 ---- 4111 42224 2 15617 a = 8.18 x 10.3 cm , C = 10.06 cm, R = 0.795 cm [see equations (3-5) and (3-6)]; 0 (Wien's Law) = ~1.646 x 10’ 5 169 Appendix 5.9. (cont'd.) Counts/30 sec T(obs) TT1 Exposure Before After Deposit2 Time Exposure Exposure Experiment 3 41733 41812 15585 1455 K ~5 K 28.00 min 4213 9085 12.0 nm 1585 ~14 6.00 4221 13899 23.7 1669 ~15 2.00 4107 16302 28.8 1710 ~17 2.00 4082 27259 56.0 1662 ~15 2.00 41833 146413 25.0 4136 41124 15674 1618 ~13 3.00 4166 12189 20.0 1575 ~14 7.00 4034 13324 22.6 1540 ~15 10.00 4094 11469 17.1 1608 ~13 4.00 4174 12704 20.3 1609 ~13 4.00 42643 129793 20.6 4156 40844 15666 a = 1.16 x 10.3 cm2, C = 8.93 cm, R = 0.795 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.646 x 10-5 TT = T(IPTS ~ 1948) ~ T(obs) Thickness as determined by quartz crystal Standard Blank Sm(1) Standard Sm(1) 9.02 cm - 7.28 x 10'3 cm2 ~3 2 - 7.73 x 10 cm Temperature varied 40°; target was not used. 0’ O I II mNGLfibWNi-J 9’ I 170 Appendix 5.10. Rate Data for SmF3 00 Effusion Experiments T(obs) TT Rate2 T(obs) TT Rate Experiment 23 1365 K ~7 K 0.218 nm/min 1433 K -6 K 1.39 nm/min 1403 -7 0.679 -3 2 a = 7.28 x 10 cm , C = 9.02 cm 1464 -5 3.08 a = 7.73 x 10'3 cm2, c = 9.02 cm 1425 ~7 1.27 1392 ~7 0.549 -3 2 a = 8.18 x 10 cm , C = 9.02 cm 1379 ~7 0.353 1373 ~7 0.331 1422 -7 1.17 136 ~7 0.120 1356 ~7 0.218 1387 -7 0.449 1331 ~7 0.114 1426 ~7 1.24 1397 ~7 0.586 1457 ~5 2.63 1437 ~6 1.64 1413 -7 0.938 1455 ~5 2.48 a = 8.18 x 10"3 cm2, c = 10.06 cm, R = 0.795 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.646 x 10.-5 171 Appendix 5.10. (cont'd.) T(obs) TT1 Rate2 T(obs) TT1 Rate2 . 4 Experiment 3 1394 K ~7 K 0.115 nm/min 1710 K ~17 K 28.0 nm/min 1465 -4 0.565 1689 ~16 20.0 1439 -6 0.285 1662 -15 12.5 1484 -3 0.816 1618 ~13 6.42 1392 -7 0.0949 1575 -14 3.21 1455 -5 0.429 1540 ~15 1.72 1529 ~15 1.55 1503 ~15 0.850 1546 ~15 1.92 1565 -14 2.56 1585 -14 3.96 1608 -13 5.08 1628 -14 7.61 1609 -13 5.51 1669 -15 14.4 a = 1.16 x 10‘3 cm2, C = 8.93 cm, R = 0.795 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.646 x 10"5 lTT = T(IPTS - 1948) - T(obs) 2Rate of deposition as determined by quartz crystal 3Pressures for first six data points calculated by use of (2.57 i 0.17) nm/ug Sm; for the remainder, (2.78 i 0.06) nm/ug Sm Pressures calculated by use of (2.4 i 0.04) nm/ug Sm 5 172 Target Collection and Deposition Data for TmF Effusion Experiments Appendix 5.11. 3,00 Counts/30 sec T(obs) TT1 Exposure Before After Deposit2 Time Exposure Exposure Experiment 1 147153 144942 37879 1486 K ~3 K 10.00 min 13083 31101 24.0 mm 1533 ~15 5.00 15391 33817 23.7 1560 ~14 3.00 15691 33347 22.5 1511 ~15 6.00 13638 28499 19.2 1430 ~7 20.00 156413 27496 15.4 14882 14507 38764 1473 -4 11.00 13263 29053 19.4 1517 ~15 6.00 12802 29698 20.6 1488 -2 9.00 13313 30192 21.2 1399 ~7 44.00 13408 27031 16.7 1437 ~6 21.00 126603 268543 17.8 14806 144674 38594 a = 7.06 x 10"3 cm2, C = 9.03 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.646 x 10-5 173 Appendix 5.11. (cont'd.) 1 Counts/30 sec 2 T(obs) TT Exposure Before After Deposit Time Exposure Exposure Experiment 2 148063 146472 38175 1514 K ~15 K 29.00 min 14940 27644 17.5 nm 1558 ~14 20.00 14791 34716 25.2 1700 ~16 2.00 14119 33975 24.4 1733 ~18 2.00 14078 45843 38.7 1676 ~15 3.00 145983 350503 24.7 14840 145944 37446 1643 ~14 5.00 14194 34079 24.5 1617 ~13 7.00 14929 32774 22.1 1719 ~17 2.00 15311 41270 31.0 1754 ~19 1.00 14821 37303 27.0 1686 ~16 2.00 151303 315103 19.8 14754 145844 _3 2 38134 a = 1.18 x 10 cm , C = 8.96 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.646 x 10- 5 DWNH TT = T(IPTS - 1948) - T(obs) Thickness as determined by quartz crystal Standard Blank Tm Standard Tm 174 Appendix 5.12. Rate Data for TmF3 00 Effusion Experiments T(obs) '1"!1 Rate2 T(obs) TT1 Rate2 . 3 Experment 1 1417 K ~7 K 0.634 nm/min 1353 K ~7 K 0.105 nm/min 1393 ~7 0.348 1414 ~7 0.527 1445 ~6 1.04 1473 ~4 1.76 1486 ~3 2.40 1517 ~15 3.45 1533 ~15 4.77 1488 ~2 2.36 1560 ~14 7.50 1419 ~7 0.593 1511 ~15 3.20 1394 ~7 0.322 1449 -6 1.17 1399 -7 0.380 1457 ~5 1.39 1437 ~6 0.843 1430 ~7 0.767 1364 ~7 0.169 1374 ~7 0.219 1400 ~7 0.382 1327 ~7 0.0731 1326 ~7 0.0632 3 2 a = 7.06 x 10- cm , C = 9.03 cm, R = 0.833 cm [see equations (3-5) and (3-6)]; D (Wien's Law) = ~1.646 x 10- 5 r Irr— Appendix 5.12. 175 (cont'd.) T(obs) TT Rate T(obs) TT1 Rate2 . 4 Experiment 2 1451 K -12 K 0.247 nm/min 1676 K -15 8.23 nm/min 1514 ~15 0.603 1643 ~14 4.90 1560 ~14 1.35 1608 ~13 2.80 1515 ~15 0.590 1572 ~14 1.50 1558 ~14 1.26 1617 ~13 3.16 1604 ~13 2.74 1644 ~14 5.03 1667 ~15 7.42 1666 ~15 7.31 1700 ~16 12.2 1719 ~17 15.5 1775 ~19 36.5 1754 ~19 27.0 1733 ~18 19.2 1701 ~16 12.0 1715 ~17 15.7 1686 ~16 9.90 3 a = 1.18 x 10‘ and (3-6)]; D (Wien's Law) = ~1.646 x 10' cm2, C = 8.96 cm, R = 0.833 cm [see equations (3-5) 5 L‘LONv-J TT = T(IPTS ~ 1948) ~T(obs) Rate of deposition as determined by quartz crystal Pressures calculated by use of (3.11 i 0.07) nm/ug Tm Pressures calculated by use of (2.92 i 0.05) nm/ug Tm 176 Appendix 5.13. X-Ray Fluorescence Analysis of Standards Counts/min Sample Counts/ug/min Standard Blank Standard Blank of Standard Yb(1) 3828 i 366 28508 i 290 45574 i 127 25074 i 221 Yb(Z) 1327 i 151 11928 i 148 19376 i 172 10411 i 163 Sm(1) 2066 i 258 8262 i 92 31428 i 144 8482 i 92 Sm(2) 2066 i 258 7128 i 107 85186 i 270 7074 i 46 Tm 5410 i 364 33620 i 438 85568 i 528 34958 i 645 "mmmi“