vaguenniewwsts‘o'I 4 ~ I..'1 . .' ’ y .425; -'o:¢:d?.:a"a VAPORIZATION THERMODYNAMICS 0F YbBr.2 Thesis for the Degree of M. S. MICHIGAN STATE UNIVERSITY MICHAEL DANIEL GEBLER 1976 a g ABSTRACT VAPORIZATION THERMODYNAMICS OF YbBr2 BY Michael Daniel Gebler The vaporization thermodynamics of the reaction YbBr2(£) + YbBr2(g) were described over the 1190-1514 K temperature range by the use of a target collection Knudsen effusion technique. The microgram quantities of effusate which plated onto tar— gets were analysed With X-ray fluorescence.by the use of an external calibration procedure. From a plot of the natural logarithm of partial pres- sures due to YbBr versus reciprocal temperature the second 2 law enthalpy and entropy at the median temperature were 0 _ O _ AHl360 — (66.9 i 3.5) kcal/mole, A81360 — (30.0 i 2.6) eu. Choice of a HgBr2 model system permitted obtained as: thermodynamic parameters of YbBr2(g) to be described thus leading to reduction of median temperature values to a reference temperature (298 K). The estimation of free energy functions by the use of the HgBr model system and an estimated absolute entropy 2 allowed third law analysis of the vapor pressure data. The second and third law values obtained were: 0 - AH298 (2nd law) — (79. i 4.4) kcal/mole, 8 Michael Daniel Gebler = (47. i 3.9) eu; AHO l. O A8298 5 298 3 i 5) kcal/mole. The overall consistency of the data was shown (3rd law) = (72. O 298 the 324 degree range of the experiment. From the reduced by the lack of a trend in third law values of AH over second law values, the enthalpy and entropy and literature values, free energies of formation were calculated as: O O AHf298 f298 -(l70.O i 4.4) kcal/mole. The second law absolute entropy YbBr2(g) = -(90.2 i 0.2) kcal/mole, AH YbBr2(s) = was determined from the entropy of vaporization and entropy of YbBr2 gas (estimated from HgBr values) as: 2 YbBr2(s) = (29. 3.9) eu, which combined with litera- 0 S298 o i ture values of entropy for Yb(s) and Br2(£) allowed calcula- . O _ _ tion of Asf298 YbBr2(s) — (21.7 t o _ _ 0 £298 YbBr2(s) - (163.5 i 4.6) kcal/mole and Asf298 YbBr2(g) = (25.8 t 3.9) eu were determined and subsequently O — _ n AGf298 YbBr2(g) — (97.9 i 1.2) kcal/mole was estimated. By resorting to a PbBr2 model system to obtain thermo- 3.9) eu. Values of AG dynamic functions for YbBr2(£) calculation of AH: = (58.6 i 4.4) kcal/mole was made at the normal boiling point 3 o _ of (2.03 i 0.11) x 10 K. ASv — (28.9 i 2.2) eu was then calculated. VAPORIZATION THERMODYNAMICS OF YbBr2 BY Michael Daniel Gebler A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemistry 1976 DEDICATION To My Parents 1171 ACKNOWLEDGEMENTS I wish to express sincere thanks to Dr. Harry A. Eick for his assistance and understanding during the study. Heartfelt gratitude is also extended to Dr. Heinrich Luke for his many helpful suggestions. The assistance of former members of the High Tempera- ture Group, especially Sandra Bacon and Drs. John Haschke and Alleppey Hariharan, is gratefully acknowledged. Unfortunate lack of close personal contact with them can only be counted as loss but their writings proved immensely rewarding. I wish to thank the Energy Research and Development Administration for the project's financial support. Lastly but foremost the undying moral and financial support of my Mother was beyond measure. To her, as always, will be my lifelong indebtedness. iii II. TABLE OF CONTENTS INTRODUCTION 0 O O O O O O O O O O O O O O THEORETICAL CONSIDERATIONS NECESSARY TO VAPORIZATION STUDIES . . . . . . . . . . . A. Modes of Vaporization and Phase Rule Considerations . . . . . . . . . . . . 1. Modes of Vaporization. . . . . . . 2. Phase Rule . . . . . . . . . . . . Methods of Vapor Pressure Measurement. Vapor Pressure Determinations by the Knudsen Effusion Method; the Use of Target Collection Procedures . . . . . Assumptions of the Knudsen Method. . . Limitations of the Knudsen Effusion Me thOd O O O O O O O O O O O O O O O 0 lo Non-Ideal cells. 0 o o o o o o o o a. Clausing Correction Factor . . b. Correction for Orifice Effects Proper Choice of Collection Geometry . . . . . . . . . . . 2. Vaporization Coefficient . . . . . 3. Striking Coefficient . . . . . . . 4. Interactions with Knudsen Cells. . 5. Non-Ideal Gas. . . . . . . . . . . iv Page 10 10 10 ll 12 13 13 15 TABLE OF III. CONTENTS (Cont.) Analysis of Targets; X-Ray Fluorescence. 1. X-Ray Fluorescence: Basic Temperature Measurement. . . . Thermodynamic Calculations . . l. Second-Law Calculations. . 2. Third Law Calculations . . EXPERIIENTM‘ O O O O O O O O O O O A. B. Preparation of YbBr2 . . . . . Chemical Analysis. . . . . . . I. For Ytterbium. . . . . . . 2. For Bromide. . . . . . . . Method. . X-Ray Powder Diffraction Analysis. . . . Target Collection Apparatus. . Effusion Cells . . . . . . . . Temperature Measurement. . . . Heat Source. . . . . . . . . . Targets. . . . . . . . . . . . Orifice Measurement. . . . . . Miscellaneous Measurements and Procedure for Vaporization . . X-Ray Fluorescence Analysis of Effusate O O O O O O O O O O O l. X-Ray Fluorescence Unit. . Mass of Page 15 16 16 l9 19 21 23 23 24 24 .24 25 25 28 28 29 29 30 30 3O 31 31 TABLE OF CONTENTS (Cont.) IV. 2. Calibration of x-Ray Fluorescence unit 0 I O O O O O O O O O O O O O O O 3. Target Analysis. . . . . . . . . . . . RESULTS AND DATA REDUCTION . . . . . . . . . . A. Elemental Analysis of YbBrz. . . . . . . . B. X-Ray Fluorescence Calibration . . . . . . C. Thermocouple Calibration . . . . . . . . . D. Vaporization Experiments . . . . . . . . . E. Mode of Vaporization . . . . . . . . . . . F. Vapor Pressure Equation -- AH0 and A80 at Mean Temperature of Vaporization Experi- ments. . . . . . . . . . . . . . . . . . . G. Estimation of Thermodynamic Values . . . . H. Second Law Data Reduction to 298 K . . . . I. Value of Absolute Entropy. . . . . . . . . J. EStimation of fef and Afef for YbBr2 . . . K. Data Reduction by the Third Law Procedure. L. Other Thermodynamic Parameters for YbBr2 . 1. From Literature Estimates and Measured Data. . . . . . . . . . . . . 2. From Extrapolation of the Vapor Pres- sure Equation. . . . . . . . . . . . . M. Note on Errors . . . . . . . . . . . . . . DISCUSSION AND SUGGESTIONS . . . . . . . . . . A. Preparation of YbBr2 . . . . . . . . . . . vi Page 32 33 35 35 35 36 37 38 41 42 44 45 45 46 47 47 48 49 50 50 TABLE OF CONTENTS (Cont.) E. x-Ray Fluorescence Procedures. . . . . . Target Collection Knudsen Effusion Tech- nique O O O C O O O O O O O O O O I O O O The Use of Thermodynamic Approximation . 1. Absolute Entropy Approximation . . . 2 O YbBrZ Data 0 O O O O O O O O O O O 0 Suggestions for Future Research. . . . . REFERENCES . . . . . . . . . . . . . . . . . vii Page 50 52 54 54 54 58 61 LIST OF TABLES Page I. Analytical Results . . . . . . . . . . . . . . 35 II. X-Ray Fluorescence Calibration Results . . . . 36 III. Vaporization Experiments . . . . . . . . . . . 38 IV. Data Summary for Vaporization Thermodynamics of Eu(II) and Yb(II) Halides . . . . . . . . . 57 viii Effusion cell-target collection geometry LIST OF FIGURES X-ray fluorescence spectrometer. Symmetric effusion cell. High vacuum Knudsen effusion apparatus . Effusion cell-heating oven arrangement . Pressure of YbBr2(g) in equilibrium with YbBr2(s) . . . . ix Page 17 18 26 27 39 LIST OF APPENDICES Collected Vaporization Data and Third Law Enthalpies for YbBr2 . . . . . . . Enthalpy, Entropy, Free Energy Functions of YbBr2(s,£) . . . . . . . . . . . . . . . . . . Free Energy Function Changes for the Vaporiza- tion of YbBr2(£) . . . . . . . . . . . . . . . Thermodynamic Functions. . . . . . X-Ray Powder Diffraction Patterns. Page 65 67 68 69 70 CHAPTER I INTRODUCTION Experimentally determined valueslfor such thermo- dynamic parameters as enthalpies of fusion, vaporization and formation, as well as for heat capacities are not available for many of the rare earth halides. Indeed, as late as 1964 Novikov and Polychenokl observed the lack of experimental conformation for many values found in tables of estimates such as those by Brewer gt al.2'3 especially for divalent compounds. Since then much interest has centered around the trivalent state. Vapor pressure values and sublimation thermodynamics for most of the lan- 4-10 thanide(III) fluorides have been established. Some vapor pressure values are known for lanthanide trichlo- rides and tribromides.]'1_15 For lanthanide halides in the less common divalent state Polychenok and Novikov16 have reported thermodynamic values for SmClz, EuClz, and YbCl but they assert that the 2 "boiling point" method they used tends to be inherently 17 18 inaccurate. Haschke and Eick and Hariharan have used the Knudsen effusion method to determine the vaporization thermodynamics of EuClz, EuIZ, and EuBr and Hariharan, 2 Fishel, and Eick19 used the same technique to describe the YbCl2 system. It was the intention of the present work to establish experimental values of the enthalpy of vaporization and entropy of vaporization of YbBr2 by the use of procedures similar to those applied by Haschke, Eick, and Hariharan to the analogous EuBr2 system. CHAPTER II THEORETICAL CONSIDERATIONS NECESSARY TO VAPORIZATION STUDIES A. Modes of Vaporization and Phase Rule Considerations 1. Modes of Vaporization When heated to a specific temperature a substance will vaporize in either a congruent or incongruent man- ner. A subStance which vaporizes congruently yields a vapor that has the same chemical composition as that of the condensed phase from which it was obtained; incongru- ent vaporization results when a condensed phase gives rise to a vapor of different composition from that of the con- densed phase. 2. Phase Rule The phase rule: F = C - P + 2 (II-1) establishes many useful relationships for vaporization studies. In II-l the number of degrees of freedom, F, 3 is related to the number of components in a system, C, and the number of phases, P. For a binary system of a condensed (either liquid or solid) phase and a congruently derived vapor, P will equal two in 11-1 above. The number of components, C, will equal one since the vapor and condensed phase are chem- ically equivalent so that the number of degrees of free- dom for the system will be one. Therefore, to obtain a parameter such as vapor pressure it is only necessary to fix one experimental condition such as temperature. B: Methods of Vapor Pressure Measurement A number of methods are available to establish the 20 These fall into two vapor pressure of a system. classifications, the absolute, which include the static and boiling point methods, and the non-absolute which are the effusion and transpiration techniques. The non- absolute procedures rely on the kinetic theory of gases which necessitates the assumption of a molecular weight of the vapors, hence they are not applicable in those systems where vaporization of fragmented or polymeric components invalidates the assumption. However, for less volatile or chemically reactive substances they are the usual methods of choice because they allow the vaporizing system to operate at lower overall temperature than the absolute methods and because they operate at high vacuum. The effusion techniques include an Open, the Langmuir free evaporation, and a closed method, the Knudsen effusion procedure. Both are theoretiCally and in essence the same. The former relies on vaporization from a sur- face of known area and the latter on the amount of effusate which can be lost from an otherwise closed system without significantly shifting the eqUilibrium which is established between the condensed phase and the vapor. Both have advantages and disadvantages, but since the surface area of a vaporizing substance is difficult to determine accurately the latter method, the Knudsen Effusion technique, was chosen for our vapor pressure determinations. C. Vapor Pressure Determinations by the Knudsen Effusion Method; the Use of Target Collection Procedures When certain conditions (see below) are met the kinetic theory of gases allows establishment of vapor pressures according to a method first put forth by 21'22 The Knudsen Effusion technique requires Knudsen. that a small "ideal" (see below) orifice be placed in a sample cell which contains a condensed phase and its vapor in equilibrium such that the amount of effusate which escapes from the orifice does not appreciably shift the equilibrium. The number of molecules striking a unit area of the interior of the cell per unit time, Z, is propor- tional to the number of molecules per unit volume, n, and the average molecular velocity, 5. Precisely: -1 Z = nv/4 molecules cm—zsec (II-2) If an "ideal" orifice, that is, a small, infinitesmally thin, circular orifice is placed in the container so that a small portion of the vapor can escape into a perfeCt void (guaranteed by high vacuum) in such a way as not to affect equilibrium within the cell, then the number of molecules escaping through the orifice of area Ao per sec— ond will be given by: N = AOZ (II-3) Now if a circular target is placed at a distance d above the orifice so that the center of the target is coaxial with the center of the orifice, and if the target has radius r, then the fraction of molecules striking the tar— get can be determined since the effusing vapor follows the cosine distribution law: dN = U_1NO cos edm (II-4) Here No is the total flux at the orifice, e is the angle between the perpendicular and the axis of dw (see Figure 1), the solid angle formed by the effusate which is sub- tended by a target of area dN. Upon substitution in terms of r, d, A0, and Z into the cosine distribution law and integration of the value over the space above the orifice one obtains: 1 N = ZAO(r2/(d2+r2)) molecules sec- (II-5) 3 atm in the and as long as pressure remains below 10- sample cell to meet Knudsen conditions the gas can be assumed ideal so that the ideal gas law can be applied. When 5 = (8RT/flM)1/2 is substituted into 11—2 and the Z so obtained used in 11-5 above, multiplication of 11-5 by the total time effusate is allowed to strike the con- tainer, t, allows the inclusion of the ideal gas law assumption to yield the following equation for equilibrium vapor pressure. 1/2 P = [W/Aot] [ZURT/M] [(d2+r2)/r2] (II-6) If W, the mass in grams of effusate of molecular weight M, is collected in t minutes on a circular target of radius r cm placed d cm above an orifice of AO cm2 area, and R is TARGET RZZI \ COLLIMATOR KNUDSEN CELL Figure l. Effusion cell-target collection geometry. defined in ergs deg.l mole-1, then P is obtained in units of dynes cm-Z, a unit which is easily converted into atmos— pheres. Substitution of appropriate constants into II-6 yields: 1/2 P = [3.76x10‘4 W/Aot] [T/M] '[(d2+r2)/r2] (II-7) atm If a molecular weight of the effusate is known or can be assumed, and if the weight of effusate plated on a target can be determined, then measurement of time in minutes, area of the orifice in cm2, and temperature in degrees Kelvin will yield the vapor pressure of the system when the geometry of the system (hence d and r) is known. D. Assumptions of the Knudsen Method Aside from the fundamental assumption that the orifice is "ideal" the system for Knudsen effusion relies on other assumptions many of which are required by the kinetic theory of gases. These include: 1. Isothermal conditions exist about and within the cell. 2. Molecules are point masses. 3. Isotropy of gas exists in the cell. 4. Molecular velocity distribution is Maxwellian. 5. There are no molecular interactions in the gas 10 6. Orifice walls do not return any molecules to the cell. 7. Molecules do not return to the cell once through the orifice. 8. Loss of effusate occurs by vapor transport only. 9. Equilibrium pressure is maintained within the cell. 1 10. No molecular collisions occur in the orifice. E. Limitations of the Knudsen Effusion Method All of the assumptions stated above would be valid in an ideal system. However, in a real system some of the assumptions can only be approximated and the resulting error must be corrected for by changing equation 11-? so that it includes a number of correction factors. 1. Non-Ideal Cells a. Clausing Correction Factor The basic assumption that the orifice is ideal, which implies infinitesmally thin, is violated immediately in a real system since it is impossible to obtain such an opening in an absolute sense. Therefore, a certain resist- ance to molecular flow occurs, the so-called channeling 23 effect. Clausing demonstrated that the effect is a 11 function of orifice geometry and that one can apply a cor- rection factor (the Clausing Factor), WO' to the usual vapor pressure equations, 11-6, 11-7. He obtained these correction factors in terms of orifice radius and orifice length. Inclusion of WO in 11-? makes the vapor pressure equation: 1/2 P = [3.76x10'4 W/Aot] [T/M] atm [(d2+r2)/r2] [l/Wo] (II-8) b. Correction for Orifice Effects by Proper Choice of Collection Geometry The limits of the cosine distribution law for real knife-edged conical orifices have been examined by Ward.24 He demonstrates through experiment and calculation that when a target geometry is chosen such that only small angles of 6 are subtended there is little or no effect on the cosine distribution law for conical orifices. There- fore, by simply choosing the target geometry such that 9 remains small and by using a conical orifice one need not apply a correction factor. Indeed, if the target is small enough or at great enough distance to receive about 1% or less24 of the effusate the Clausing correction factor can be taken as unity and vapor pressures will be given directly by 11-7. 12 2. Vaporization Coefficient Another of the Knudsen assumptions requires that the vaporizing system be at equilibrium. That is, the vapor- ization coefficient av, defined as the rate of vaporiza- tion compared to the equilibrium rate, is equal to the condensation coefficient ac, defined as the fraction of vapor molecules which recondense. Since the Knudsen effusion procedure allows a certain portion of vapor to escape a steady state loss might arise. The pressure given by 11-7, Pm, as measured will not be equal to the true equilibrium vapor pressure Pe' Motzfeldt25 has derived an expression to relate Pm to Pe assuming that “V = “c and that a resistance similar to a Clausing ori— fice factor develops along the cell wall. In its mathe- matical form the equation is: P =P[1+f(l+—1—-2)] (II-9) e m a Wa Here f = WOAO/A with A0 being the orifice area and A the sample surface area, W0 is the Clausing orifice factor, Wa is a "Clausing factor" of the cell body and a = “V = ac. From equation II-9 it is evident that when Ao/A 5 .01, Pm z Pe provided a, the vaporization coefficient does not differ significantly from unity. Indeed, early work by 26 Rosenblatt has established that finely divided samples 13 (or those with large surface areas) usually have vaporiza- tion coefficients which approach unity. However, it appears that the vaporization coefficient need not strictly approach unity with increasing sample size but is dependent on a number of experimental and system factors which include surface effectsjof the samples. An extensive review of the vaporization coefficient problem was given by Work.27 3. Striking Coefficient If all the effusate striking a target does not adhere to it another source of error arises. One can determine the amount of material which does strike to the target by placing a chilled disc with a hole in its center in front of the target. Any molecules not striking to the target will be reflected back by the cosine law and a fraction of these will adhere to the disc. By measurement of the amount on the target and the amount on the disc a cor~ rection factor can be obtained. 4. Interactions with Knudsen Cells Steps must be taken to insure that the vaporizing compounds do not interact with the cell material. Simple mass difference determinations of an empty cell before 14 vaporization and after 100% vaporization of the cell's content will lend more qualitative insight but the method is limited by the sensitivity of the balance used for mass determination. ’ Usually it is sufficient to rely on X-ray powder diffraction patterns (hereafter called "patterns") of the material remaining in the cell after the vaporization. By comparing the patterns of the residue after vaporization to those of the starting material two determinations can be made. If the patterns before and after vaporization are the same then, reasonably, one can assume no inter- action between the cell and the sample. Further, the vaporization was probably congruent. If they are not the same then chemical analysis (using wet chemical and/or x-ray fluorescence methods) is necessary to establish what materials are present in the residue. If analysis shows that the residue is simply the starting material's ele- ments in different mole fractions then incongruent vapor- ization should be suspected, but if the residual material contains a compound composed in part of the cell's ele- ments then one must try to describe the chemical process taking place to ascertain a correction factor. If a cor- relation cannot be found, then measured values of vapor pressure cannot be related to a specific reaction. 15 5. Non-Ideal Gas Since the kinetic theory of gases is fundamental to the Knudsen effusion theory most of the assumptions men- tioned in Section D are required to insure that its principles are not violated. Many of these assumptions center around pressure build-ups in the cell. If free molecular flow is to be maintained the pressure must not reach the point that molecular interactions occur and a "viscous flow" of molecules results in the molecular flux. Experiments conducted by Meyer28 show that for orifices of areas between 10-4 and 10-5 cm2 the pressure should not 3 exceed 5X10- atm if free molecular flow is to be main- tained. F. Analysis of Targets; X—Ray Fluorescence One must ascertain the amount (mass) of material plated on the targets during the vaporization process before 11-? can be used to compute vapor pressures. Since the amount of plated material is usually maintained in the microgram region to avoid adhesion problems, X-ray fluo- rescence is uniquely suited to the task of mass deter- mination. 16 l. X-Ray Fluorescence: Basic Method When white X-radiation is allowed to shine on a sample it excites inner shell electrons to higher energy levels. Those electrons which return to the ground state emit photons of characteristic wavelength -- the basic fluorescence. The radiation thus given off can be analysed by allowing it to diffract from a suitable crystal and by arranging a detector (such as a scintillation counter) such that it picks up the particular wavelength given off by the element being analysed for. The fluo- rescence X—radiation is analysed according to the Bragg equation: nA = 2dsin e (II-9) where n is the order of diffraction (usually n=l), A is the wavelength of the characteristic radiation, d is the inner planar spacing of the analysing crystal and e is the angle of incidence. Placement of the detector at 26 allows the correct geometry for analysis (see Figure 2). G. Temperature Measurement Figure 3 shows a symmetric effusion cell. When the top cavity is used as a sample container and the entire 17 EOIOOEQ _ W 33.6 8.3332 \ 33.530 %N\ - ---- -%.~-.\ MImEEo-O _ 1291.5 u£~éuc< \— Sm. :xm I [TN- 5% acute-m one. ASH-Mb $852825 3:83.62“. >9. Ix x-ray fluorescence spectrometer. Figure 2. 18 SYMMETRICAL EFFUSION CELL WITH SAMPLE AND OPTICAL CAVITIES cl _/ -— \\\\VJ .I/ i [\\\\\\ \\ K N \\\ ETTA/I F 6/6 8 Figure 3. Symmetric effusion cell. 19 cell maintained in an isothermal environment the bottom cavity should display a temperature identical to that of the top cavity. By placing a thermocouple in the bottom cavity the temperature of the vaporization process can be determined directly. H. Thermodynamic Calculations l. Second-Law Calculations With only one degree of freedom available to a vaporizing system a free energy relationship would be expected between temperature and vapor pressure. That is since: 0 — _ - AGT — RTKnPT (II 10) and o _ o _ o _ AGT — AHT TAST (II 11) we have _ O _ O _ -£nPT — (AHT/RT) AST/R (II 12) 20 where PT is the equilibrium vapor pressure given by II-7 above. From II-12 it can be seen that a plot of ZnPT versus 1/T by least squares regression will yield the relationship of £nP = m/T = b so that enthalpies are T given by the slope of the line: AH = -Rm (II-13) and entropies are given by the y-intercept: AS = Rb (II-14) I—JO The entropy and enthalpy values thus obtained are usually considered those of the mean temperature of the study.29 These values are reduced to a reference temperature according to the following: o _ o 298 _ AH298 — AHT + IT deT (II 15) and o _ o 298 _ A5298 — AST + IT Cp/T dT (II 16) 21 where it is usually necessary to express the heat capac- ities in their analytical forms: C = a + bT (II-17) a + bT + cT-2 0 ll 2. Third Law Calculations The third law treatment utilizes a free energy func- tion, fef, to reduce thermodynamic data to a reference temperature which results in a value of AH398 for each data point. The fef can be defined as: fef = (G; - H398)/T (II—18) or O fef - (H H298)/T ST (II-19) Afef values are calculated from those of fef for each product and reactant by: Afef = E vi fefi - g vj fefj (II-20) 22 where i refers to the products and j refers to the reactants. Once determined, Afef values lead to AH§98 values from: _ o _ o _ Afef — (AGT AH298)/T _ (II 21) or through 0 —— - AH298 — (Afef + R£nPT)T (II 22) when II-lO is substituted into II-21. The advantage of the use of third law treatment is that, although it does not give values of A5398 as the second law does, the treatment results in a value of AH398 for each data point. Analysis of the values thus obtained allows any trend in AH§98 to be displayed. A trend might arise from system- atic error in either pressure or temperature measurement or in the computation of free energy function changes. A large difference in second-law and third law values indi- cates error in measurement of the parameters of vaporiza- tion or indeed, in the basis definition of the vaporiza- tion process itself. CHAPTER III EXPERIMENTAL A. Preparation of YbBr2 YbBr was produced by following the general procedure 2 for rare earth dichloride preparation put forth by DeKock and Radtke.30 The sesquioxide of ytterbium (99.99% Research Chemicals, P.O. Box 14588, Phoenix, Arizona) was dissolved in approximately 150-200 ml of 4.5 N HBr along with NH4Br (Matheson Coleman and Bell) and metallic zinc (Baker). One to three grams of the oxide was used with sufficient quantities of the other reagents to give a ratio of twelve moles to ammonium salt and one and two tenths mole of zinc bromide per mole of rare earth tri- bromide formed in the first step of the reaction. The solution was evaporated to dryness and the dried material transferred to a carbon boat which contained an excess of zinc metal as a reducing agent. After drying under vacuum and low (200°C) temperature, the material was melted in an inert atmosphere to effect reduction. The excess NH4Br was sublimed off and a second attempt was made to remelt the remaining contents of the boat by heating to SOD-600°C 23 24 to insure all of the tribromide was reduced to the dibro- mide. Next the Zn and ZnBr2 were vaporized under high vacuum. The greenish-yellow crude YbBr2 remaining was transferred to an outgassed molydenum crucible and heated by induction in a high vacuum so that it distilled onto a high vacuum so that it distilled onto a quartz condenser (distillation temperature approximately 1145°C). B. Chemical Analysis 1. For Ytterbium A 50-80 mg sample of distilled YbBr2 was placed in a crucible and fired directly to the oxide by heating to 1000°C in a muffle oven (Thermolyne Model F-A1620) for 2-3 hours. 2. For Bromide A 60-80 mg sample of YbBr2 was dissolved in dilute nitric acid solution. A 0.1 N solution of silver nitrate was stirred into precipitate Br- as AgBr. The solution was heated to boiling for l-2 minutes and allowed to settle overnight. A few drops of AgNO3 were added to the solution above the precipitate to insure complete precipitation 25 before the solution was filtered into a sintered glass crucible. The material so collected was dried at 110°C for 1% hours and then weighed as the bromide of silver. C. X-Ray Powder Diffraction Analysis Samples of YbBr2 and the residue left in sample cells after vaporization were prepared for powder X-ray diffraction analysis by sealing small amounts of each sub- stance in plastic bags in a dry box. A Haegg Type Guiner forward focusing camera of 80 mm radius and a Ca Kal 0 radiation source (Au = 1.54051 A, t = 24il°C) powered by l a Picker 80913 generator was used to obtain the powder patterns. D. Target Collection Apparatus Kent31 has described the general setup used during the work. Basicly it is a glass vacuum line (Figure 4) in which the effusion cell is supported above a boron nitride table by tungsten rods. A similar set of rods support a molydenum oven arranged symmetrically about the cell (Figure 5). Directly above the oven-cell arrangement the glass line supports a target magazine fitted with a liquid nitrogen dewar so that the targets can be cooled. The line has apparati which allow target changes while the 26 Figure 4. High vacuum Knudsen effusion apparatus. 27 RCm Figure 5. Effusion cell-heating oven arrangement. 28 system is closed by the use of magnets and iron mechanical parts built into its side. A mercury diffusion pump pro- vides the high vacuum necessary for the experiments. E. Effusion Cells In every vaporization experiment except one the effusion cells were made of molydenum; the basic design of which was given in Figure 3. As stated before, their symmetric nature allows the bottom cavity to be used as a chamber into which the temperature sensing thermocouple is placed while vaporization occurs from an identical top cavity. In one case a carbon insert was used with moly- denum end caps in the usual cell arrangement. F. Temperature Measurement A two foot thermocouple supplied by Omega Engineering was calibrated against the melting point of National Bureau of Standards copper, and the boiling point and ice point of water. The thermocouple was then used in con- junction with a Numetron 914 Numeric Display digital potentiometer (Leeds and Northrup) to read temperatures directly in degrees centigrade. 29 G. Heat Source The oven cell arrangement was heated to and held at constant temperature by a 20-kva Thermonic induction generator coil which was situated as symmetrically as pos- sible about the cell. H. Targets Targets for the vapor study were made of an aluminum backing 2.7 cm in diameter and 0.46 cm thick with a 2.08XO.19 cm circular recession machined in one side. A thin platinum disc was supported in the recession by a stainless steel retaining ring. The platinum discs were cleaned prior to vaporization runs by degreasing with petroleum ether, washing with detergent, scouring with steel wool, and bOiling in dilute nitric acid. The alumi- num backings were treated in a similar manner except they were boiled in distilled water. The retaining clips were scoured with detergent and steel wool. All parts were rinsed in distilled water and dried at 130°C. 30 I. Orifice Measurement The area of the orifices used in the experiments was measured precisely by finding the area of an enlarged photomicrograph (Bausch and Lamb Dynazoom Metallograph fitted with Polaroid attachment) with‘a polar planimeter (Keffel and Esser) and then multiplying by an enlargement factor of 0.ZSXl0-4. The enlargement factor had been found by calibrating the Metallograph's internal scale with a micrometer slide (American Optical Co.). J. Miscellaneous Measurements and Equipment Time was measured to $0.01 minutes by a Lab Con timer. A precision cathetometer with a readibility of 0.005 cm (Gaertner Scientific) was used to measure the cell to target distance. K. Procedure for Vaporization Approximately 0.25 g of YbBr2 was placed in the sample cavity of an outgassed effusion cell in an argon atmosphere glove box. A drOp of dried fluorolube oil was placed over the orifice and the cell quickly transferred to the vacuum line. The cathetometer was used to obtain the height of 31 the top of the cell before the remainder of the glass vacuum system was assembled. After the apparatus had pumped down to <10"4 torr a reading was made of the height of the flat spot on the target magazine. The assembly was heated to ZOO-300°C to insure outgassing before the actual vaporization experiment began. When the vacuum had reached <10.5 torr liquid nitrogen was added to the tar- get magazine's trap and the system heated to vaporization run temperatures. Targets were exposed for periods of time sufficient to plate between two and twelve micro- grams (as ytterbium) on them (times were found by trial and error). L. X-Ray_Fluorescence Analysis of Mass of Effusate l. X-Ray Fluorescence Unit The targets were analysed by a 4-position Norelco Universal Vacuum spectrograph with a broad focus tungsten X-ray tube powered by a Norelco XRG 5000 X-ray generator. The spectrograph was set at a 26 value of 28.88°, the optimum setting for the Lal radiation of Yb for our par- ticular instrument. 32 2. Calibration of X-Ray Fluorescence Unit Since the targets collect between 2 and 12 micrograms of effusate it is necessary to know how many counts per microgram of Yb the detector will "see". To find the value each of six targets was counted blank to determine its background fluorescence at the particular settings used in the experiments. Next each target was plated with 49.6 A of solution delivered by a precision micropipet (Misco). The solutions thus deposited contained between 2.7 and 12.11 miCrograms of Yb made up as a six member series from a stock solution obtained by dissolving a carefully weighed sample of szo3 (99.99% Research Chem- icals) in HCl, boiling the majority of acid Off, and then diluting to 500 ml. The solutions deposited on the target were evaporated to dryness under a high intensity light. Much skill was necessary to perfect the art of plating so that consistent values were obtained target to target, but the remainder of the procedure was trivial. The targets were counted after plating, the Value of the targets' background fluorescence subtracted, a correction of a "standard blank" applied (see Section 3 below) and then the number of counts remaining was divided by the number of micrograms of Yb in the solution that was used to plate the individual targets. The average value of these six 33 targets became the "standard" number of counts per micro- gram Yb used in the analysis of vaporization-plated tar- gets. 3. Target Analysis The method of analysis for vaporization—plated tar- gets is essentially the same as that for the calibration targets given above. That is, it is necessary to find the background fluorescence of the targets before the vaporization run. Once plated the targets are counted again. The difference between the background fluorescence and the plated target's fluorescence should give the fluo- rescence (as indicated by number of counts the detector sees). Due to instrumental and environmental conditions which change from day to day it is necessary to apply a correction factor in the analysis. One obtains the cor- rection factor by counting one particular target blank (unplated) both before the vaporization run (with the other blank targets) and after the experiment is complete when all the other targets are plated.v The difference of its background fluorescence is a direct measure of sys- tematic changes so that the standard blank correction can be defined as the value of (standard blank fluorescence counts before vaporization experiment -- standard blank 34 fluorescence count after vaporization experiment). The so-called "standard blank" correction is then added to the value of the fluorescence of Yb on each individual target to ascertain the correct value of mass of Yb on each tar- get. CHAPTER IV RESULTS AND DATA REDUCTION A. Elemental Analysis of YbBr Table I shows the results of chemical analyses of YbBr2 prepared for the vaporization experiments. Table I. Analytical Results wt % Yb wt % Br Analysis # Theoretical Theoretical l 50.46 51.99 48.74 48.01 2 50.48 48.63 3 51.61 48.90 Average 50.85i0.7O 48.76:0.l These values correspond to the formula YbBr . . 2.08i0011 B. X-Ray Fluorescence Calibration A plot of counts of Lm1 radiation from Yb versus pg of Yb was linear over the range of 2-12 pg ytterbium. 35 Ik' ll.l.l.|‘ I'll I! u I I .II-. III ilulllrlll- [Illa-l .oIII 36 Table II shows the data collected at each concentration and the average number of counts per microgram ytterbium. The average value was Used to obtain mass values used in II-7 which subsequently generated the equilibrium vapor pres- sures listed in Appendix A. Table II. X-Ray Fluorescence Calibration Results pg Yb Counts 1 pg Yb 2.8 1857.1 4.7 1599.8 6.5 2076.2 8.4 2506.9 10.3 2516.7 12.1 1662.8 Average value = 20371405 C. Thermocouple Calibration Numerous attempts were made to calibrate the chromel- alumel thermocouple against the melting points of aluminum, silver, lead, and copper. In the first three cases either the heating rate could not be slowed enough to observe the melting point transition or the metal interacted (alloyed) 37 with the molyendum crucible. With copper a transition was seen in the temperature versus time plot which corresponded well with the melting point reported for the copper sample by the National Bureau of Standards (1083.3°C). Three separate meltings were made with deviations of 0.8, 0.6, and 0.3°C. It is believed that some interaction was beginning between the sample and the Crucible and that the first value of 0.8°C represented the true deviation. Since no other metals were readily available a quick qualitative check calibration was made against the ice point and boiling point of water. The thermocouple showed readings which averaged approximately +1.5° and it was judged that no signifiCant error in temperature measurement would occUr if readings were taken directly with no correction applied for the vaporization experiments (i1.5° presents only a 0.1% error in temperature at 1360°). D. Vaporization Experiments Six independent vaporization experiments were carried out with two different Knudsen cells (different size orifice). All of the experiments were effected in a molyendum cell except number 6 in which the sample was placed in a graphite holder with the usual molyendum end caps. Table III lists the orifice size and temperature range of each vaporization experiment. 38 Table III. Vaporization Experiments Experiment # Area of Orifice (x10“) Temperature Range 1 9.37:0.01 cm2 1207-1296 K 2 9.37:0.01 1190-1279 3 2.94:0.02 ' 1337-1359 4' 3.01:0.01 1300-1478 5 2.78:0.00 1309-1514 6 2.90:0.02 1407-1482 The results of the vaporization experiments are graphically represented in Figure 6. E. Mode of Vaporization Inspection of the X—ray powder diffraction patterns for the sample of starting material and product remaining in the cell after vaporization cataloged in Appendix E shows that YbBr2 was the predominate chemical substance both before and after the experiments. Indeed the pattern showing spurious lines is that of the starting material. These lines seem to have disappeared in the product left after vaporization; indicating that, whatever their cause, the substance has been destroyed by the heating process. By looking at known powder patterns of Yb(BrO3)3 - 9H20, 39 r- r E' "[00 r .. .5 (1°- : - -8.0 T - r " ‘r6.0 6 7 6 I/T(K) x I04 Figure.6. Pressure of YbBr2(g) in equilibrium with YbBr2(s). 40 32 Yb O3, Yb 0 Br, and YbOBr it was evident that the extra 2 3 4 lines in the starting material could not be ascribed to any of these compounds. Comparison of the proceSS which yield the starting material revealed that the only other possible contaminates would be ZnBr2 or YbBr3. Of these the first would be eliminated from a YbBr2 melt very early in the vaporization process because of its appreciable vapor pressure (just such a process of heating under high vacuum was used to supposedly preferentially remove ZnBr2 from the crude YbBr2 in the reaction sequence used to produce YbBr Most probably the contaminate is YbBr3 which 2). "bumped" over during the distillation process used to purify crude YbBr2 in production of the starting material. As a measure of its possible quantative contamination of the starting material one need only look to the elemental analysis of YbBr2 described in IV-A. Here it is shown that the starting material is slightly bromine rich (compare molecular formula YbBr2.08) but a possibility exists for contamination by slight amounts of YbBr3. Indications are the YbBr3 decomposes under heat2 thus giving a possible explanation to the pattern of YbBr2 after the vaporization process has been accomplished. In View of the powder patterns, elemental analysis, and lack of a trend in third law measurements (see IV-K) the mode of vaporization can be ascribed to a congruent process whereby YbBr2(£) vaporizes to YbBr2(g). 41 F. Vapor Pressure Equation -- ABC and AS0 at Mean Temperature of Vaporization Experiments When data of vapor pressure and reciprocal temperature are treated by least squares regression equation (IV-l) results: £n -(3.3 i 0.18) x 104/T + 16.6 t 1.3 PYbBr 7 1 2 (IV-l) in the temperature range 1190 Z T < 1514 K. For compara- tive purposes the vapor pressure equation for the experi- ments with the larger orifice (numbers 1 and 2) is pre- sented as: = -(1.7 i 0.54) x 104/T + 2. + 4.4 (IV-la) 8 _ 1190 < T < 1295 K 0 and the vapor pressure equation obtained by the remainder of the experiments with the smaller orifice is: in _ PYbBr — -(2.2 i 0.1 4 4 9 x 10 )/T + 8. 1 1.3 (IV-1b) 7 1300 < T < 1514 K 2 however, it is equation IV-l which is used in all subse- quent data treatments since, indeed, the third law data treatment (Section IV-K) shows that the values between the 42 two sets of data represented by IV-la and IV-lb are coher- ent with no observable temperature trend. The mean temperature is 1360 K so that through II-13 and II-l4 o o AH1360 and A81360 are calculated as AH§360 = 66.9 i 3.5 kcalémole as° = 33 + 2 en 1360 '0 ‘ '6 G. Estimation of Thermodynamic Values The absence of experimentally determined enthalpies and entropies makes it necessary to resort to estimates of these values for the data reduction process. 0 o o o . . If (HT - H298) and (ST — $298) functions are avail- able for the various phases or can be estimated reasonably then the relationships: 0 o _ T - and o o _ T _ allow substitution into II-15 and II-16 to give: 43 o _ o o _ O _ o _ o AH298 ' AHT +[§ ”1 (HT H298)i g vj (HT H298)j] (Iv-4) and o _ o o _ o _ o _ o AS298 AST +[E “1 (ST 8298) g vj (ST 5298)j] (IV-5) where vi refers to coefficients on products i, and vj refers to reactants j. When necessary entropies can be found in a similar manner by: O A8298 - (IV-6) l PM 6 U) 0 I LJM c (D In vaporization reactions only one reactant exists so that the summation on j is dropped: 0 = 0 _ 0 - 8298. l/vj(Z vi 8298. 68298) (IV 7) j 1 1 Absolute entrOpy can also be calculated in a purely estimative manner by the following relationship due to 34 Latimer33 as reinvestigated by Gronwold and Westrum. It is: O 8298 = g vi S. + E v. M. (IV-8) 44 where 52's are the lattice contributions and Mi's are the magnetic contributions to entropy. Finally thermodynamic values for gases can be esti— mated by choice of a proper model system. Haschke35 reviews the method as applied to rare earth systems, where basically it is established that thermodynamic functions for gases rely mostly on molecular symmetry and not mass 2 is assumed to have th symmetry, and, therefore, values of effects. Following his arguments for EuBrz, YbBr HgBr2(g) are chosen for the model system. Estimated values for gases are those given in the 36 JANAF table, while (B? - H0 298 were found by graphical interpolation of estimates for ) and (S? - 8398) for solids YbBr found in Brewer et a1.2 and Bulletin 605 of the 2 National Bureau of Mines37 (see Appendix B). H. Second Law Data Reduction to 298 K Data from the second law treatment is reduced to from the mean temperature of 1360 K to a reference temperature of 298 K through the use of values compiled in Appendix B and similar values for HgBr2(g) by application of IV-4 and IV-5: = 66.89 + 28.64 - 15.70 = 79. i 4. kcal/mole O AH298 4 45 = 33.01 + 36.9 - 22.36 = 47. H- DJ 0 o A8298 9 en where errors were assumed to be 20% in the values in Appendix B. I. Value of Absolute Entropy The absolute entropy of YbBr2 was found from IV-8 by 33 value for Br- lattice contribution 38 the use of Latimer's (10.9 eu) and Westrum's value for Yb(II) lattice con- tribution (13.1 eu). No magnetic contribution was assumed since Yb(II) has a fully filled 4f shell. The value of absolute entropy thus obtained was, = 13.1 + 2(10.9) = 34.9 en. 00' 0 8298 J. Estimation of fef and Afef for YbBr2 So that the tabulated data computed in Appendix B can be used for data reductions by the third law technique it is necessary to rewrite II-19 as: _ o _ o _ o _ o _ o _ fef — (HT H298)T (ST 5298) 3298 (IV 9) Use of absolute entropy and values of (Hg - H398) and (So - 8398) from Appendix B generates -(GO - T T since it is just equal to fef (see II-18). The use of o H298)/T data 46 II-20, through combination of (G; - H398)/T data of YbBr2(s) in Appendix B and similar data for the vapor assumed equal to that of HgBr2(g)36 allows calculation of estimated Afef for YbBr2 vaporizations (Appendix C). K. Data Reduction by the Third Law Procedure Values of Afef from Appendix C were fitted by least squares regression to a parabola of the form: Afef = aT2 + bT + c (IV-10) to yield; a = -1.2 x 10‘5, b = 3.78 x 10'2, c = -66.12. An excellent fit of data was obtained with the largest devia- tion for any data point being 0.51 eu. Thus obtained, a, b, c along with equation IV-lO when coupled with in PT and temperature values in equation II-22 yield AH398 values according to the third law treatment. The resulting aver- age value, (H398) = 72.3 i 1.5 kcal/mole with no apparent trend with temperature over the 324 degree range of the vaporization. 47 L. Other Thermodynamic Parameters for YbBr2 1. From Literature Estimates and Measured Data Knowledge of AH398,V from the fin PT-inverse tempera- ture plot along with literature values of enthalpies of formation of Yb(g)39 and Br(g)39 combined with the disso- ciation energy of YbBr240 permits calculation of the esti- mated enthalpy of formation of YbBr2(g): AH£398 = 2 Vi AH398. ‘ Z vj AHf398. (Iv‘ll) I 1 j j where, again, vi refers to coefficients of products and vj to those of the reactants: AH398 YbBr2(g) = -90.2 1 0.2 kcal/mole. For the special case of vaporization IV—ll reduced to: o _ 0 _ 0 _ AHf298 - 1/vj(§ vi AHf298i AH298) (IV 12) When i refers to the gas phase and AH398 equals the second law enthalpy of vaporization IV-12 yields 0 —- AHf298 YbBr2(s) — 170.0 f 4.4 kcal/mole. The second law absolute entropy of vaporization was determined from the entropy of vaporization and entropy of gaseous YbBr2 (found for the model HgBr2 gas36) through IV-7. It is, s° 298 YbBr2(s) = 29.0 t 3.9 eu. 48 The value of the absolute entropy combined with the entropies of Yb(s) and Br2(£) (see Appendix D) in O O O AS£298. ‘ S298. ‘ Z vj S298. 1 l J J (Iv-13) where v denotes coefficients on reactants j in formation of compound i, yields A5f398 YbBr2(s) = -21.7 i 3.9 eu. Relationship II-ll allows calculation of AGf398 o o YbBr2(s) from AHf298 YbBr2(s) and Asf298 YbBr2(s) as, o _ _ AGf298 YbBr2(s) - 163.5 f 4.6 kcal/mole. Further o o Asf298 YbBr2(g) can be found from ASf298 YbBr2(s) and the . . O _ entropy of vaporization as. Asf298 YbBr2(g) — 25.8 i 3.9 eu. Combination of the entropy of formation of YbBr2 gas with the estimated enthalpy of formation gives an approxi- o —— mate value of AGf298 YbBr2(g) — (97.9 i 1.2) kcal/mole. 2. From Extrapolation of the Vapor Pressure Equation The normal boiling point of YbBr2(£) was found by extrapolation of IV-l to one atmosphere. It has the value: 3 T = (2.0 i 0.11) x 10 K where error is associated with b 3 enthalpy only. The data of (Hg - H398) for YbBr2(£) were determined in the 1200-3000 K range by choosing a PbBr2 model system. Graphical interpolation yields (H3026 — H398) = 46.85 kcal/mole for the liquid and again by 0 H298) - o resorting to HgBr2 values for gases, (H2026 - 49 25.62 kcal/mole for YbBr2 gas. From IV-4 AH: is calcu- lated as 58.6 i 4.4 kcal/mole and, since A83 = Hg/Tb, i 0: ASv 28.9 2.2 eu. 2 M. Note on Errors The problem of combination of errors in thermodynamic cycles was handled in the preceding sections by a treat- 41 In essence if Xi(1 s i s n) is a ment due to Feller. set of variables with associated standard deviations oi, the deviation in their sum, y, is 0y according to: (IV-14) Since data used in thermochemical cycles are visually independent IV-l4 should be a reasonable estimator of error. CHAPTER V DISCUSSION AND SUGGESTIONS A. Preparation of YbBr2 The method followed for the preparation of YbBr2 outlined in III-A provided an adequate source of starting material although one final step was added to the process as outlined by DeKock and Radtke,30 namely the distilla- tion of the reduced product. It was found that appreci- able quantities of the oxide formed if the system leaked air or if the inert gas used during the high temperature reduction contained any 02 or H20. The oxide formed as a crust upon the dark green melt. By distillation the separation of the reduced [Yb(II)] bromide could be effected from the oxide. B. X-Ray Fluorescence Procedures The X-ray fluorescence technique theoretically pro- vides a rapid and direct microanalytical determination. However, when operated in a non-vacuum mode the actual number of counts the instrument records is dependent on 50 51 air pressure. The blank counting procedure should correct for the problem, that is, it should eliminate those sys- tematic errors due to day to day variability of the instru- ment, but in fact the count rate seemed to vary rapidly -- even during a 20 minute analysis. Surely such changes cannot be ascribed to air pressure but other variables not so easily accounted for come into play. It was found that during a long analysis (of the order of 45 minutes) the number of counts steadily decayed. Although initially the standard blank was counted often during the analysis runs it was decided to count it before and after each tar- get. Still count changes were suspect even during the two minutes needed to analyse each target. In addition the necessity of keeping the counts low (required by remaining in the microgram region) caused any error in counting to be proportionally higher than would the same deviation cause if the counts due to plated material were high. It is my belief that whatever instrumental cause is responsi- ble for the count variation is the weak point of the entire experimental procedure. Mechanical means are at hand to insure that assumptions necessary to the techniques are not violated, but no such mechanism exists to remove the heretofore inexplicable drop in count rate. At best one must count only three or four targets then allow the unit to "rest" for at least one hour before continuing the analysis. Even so, moment to moment changes cannot be 52 accounted for and the most one can hope for is that the variance from the true count not be more than an acceptable percentage. C. Target Collection Knudsen Effusion Technique The highest vapor pressure attained during the vapori— zation experiments was 2.5 x 10'.3 atm. The value is of the order of magnitude of the upper pressure limit beyond which molecular flow cannot be maintained but not above the pres- sure limit given by Mayer.28 ‘(See Section II-E.5.) As expected no discontinuity was displayed for values obtained by varying the area of the orifice, thus creditability is given to the assumption that Knudsen conditions of equi- librium were maintained in the effusion cell. However satisfying the second law and third law data seem, one problem remained throughout the experiments. Upon inspection of the interior of the effusion cells after the vaporization it was noticed that at least some material had blocked the orifice of the cell. Such behavior is ascribed to a temperature gradient across the cell by Haschke,35 a condition thought to be corrected by the placement of the cell assembly in a symmetric oven. Indeed, optical pyrometer measurements indicated that no temperature gradient existed across the oven, top to bottom but of course, no such measurement could be made on the 53 cell itself. Lack of a trend in the enthalpies derived by the third law data treatment suggests that even if a temperature gradient did exist it had little effect upon vapor pressure. An alternative to a temperature gradient could be selective condensation of the vapor on the lid of the cell interior during the cooling process. Direct evidence of such a situation is not at hand but it seems reasonable since a possible mechanism exists whereby the top and bottom of the cell might lose energy more rapidly than the sides of the cell. First, the walls of the cell are at least twice as thick as the lid since the sample container consists of an insert and end caps; the walls are composed of one layer of insert and one of end cap while the lid is formed only from the end cap. If the extra mass of metal in the sides retains its heat longer than the smaller mass of the lid then selective condensation might occur. Sec- ondly the oven which is about the cell has only two Openings, one at the top directly above the orifice of the cell and one coaxially placed at the bottom of the oven. Since the system cools in a high vacuum the only possible way for the cell and oven assembly to release energy is through infrared radiation. The oven essentially stops direct radiation of the cell and a back radiation system might be established -- except at the lid and bottom of the 54 cell where it can lose radiation directly to the external environment. Should either condition lower the temperature of the lid preferentially to the walls then selective con- densation could occur. D. The Use of Thermodynamic Approximation 1. Absolute Entropy Approximation The value obtained by equation IV-8 for the estimated absolute entropy (34.9 eu) falls outside the range of the calculated absolute entropy (29.0 i 3.9 en). The differ- ence could be ascribable to the measured AS at the median temperature if one can assume the HgBr2 model system repre- sents YbBr2(g) accurately since it is a simple combination of these two entropy values in IV-7 which yields the abso- lute entropy. Indeed, it was because of the probability of variation in these two absolute entropy values that A8398, the calculated (IV-8) value was used in estimation of fef's for the third law determinations. 2. YbBr Data 2 Most of the determined values are consistent with available estimated values. The equilibrium vapor pressure is within the limits put forth by Brewer.2 Estimation of 55 the normal boiling point results in a value (2026 K) in good agreement with Brewer's2 estimate. However the value of As: of 28.9 eu is outside the range of Trouton's rule. However, Gschneidner42 points out that liquids boiling much higher than room temperature tend to have higher entropy of vaporization values and recommends a value of 25.5 eu for such substances. Even so, a high value such as 28.9 eu could only come from a value of AH: which is too large. Indeed, a scan of the JANAF36 tables shows a defi- nite trend toward increasing (HT - H398) values with increasing molecular weight for liquid compounds of metal dibromides. The PbBr2 model system was chosen for YbBr2(£) to minimize AHV to bring it as closely in line with the estimated value as possible. Lack of proper model systems in the rare earth series precludes the strict application of an estimative system. The AHO second law value of 79.8 i 4.4 kcal/mole is 298 40 some 8 kcal/mole above the value estimated by Feber (71 kcal/mole); the average third law value of 72.3 i l. kcal/ 5 mole is in much closer agreement. The AHfCZ’98 YbBr2(s) = -170.0 f 4. kcal/mole is also somewhat lower than the 4 estimated value of -l6l kcal/mole40 again probably due to the use of the AHgg8 (second law) value which is higher in magnitude than it should be. The overall magnitude of error in second law values can be shown by examination of IV-l, IV-la, and IV-lb. 56 Here one sees that the error in the definition of a least squares line can greatly affect the slope (and hence the enthalpy) and the intercept (thereby the entropy). Indeed even if the slope is known to within a small error proba- bility the variance in intercept could be appreciable since the slope is of so great a magnitude. As stated before, the accuracy of the system rests on the consistency shown by the third law treatment without which one would be hard pressed to find reason to join data which forms the two equations (IV-la and IV-lb) into an overall vapor pressure equation (IV-l). Ultimately the correctness of any data set can only be ascertained by comparison to the trends established by other researchers when no mechanism exists to ascertain in an absolute fashion the necessary relationships. To address the question of molecular geometry, DeKock and Wesley43 have linked the degree of non-linearity in the rare earth halides to the s-d orbital separation through actual measurement of infrared spectra of some divalent rare earth halides. On passing from the difluoride to the dichloride the bond angle opened for samarium and europium by some 20°, but for some unexplained reason ytterbium remains invarient with increasing molecular weight (greater s-d orbital separation) of the attached halide. Nonethe- less they point out the strong correlation between the 57 alkaline earth halides and those of the rare earths and it was upon that basis that a linear structure was chosen for YbBrZ. Thermodynamic vaporizations have been carried out on both YbClZ17 and YbF2.44 The latter case proved to be incongruent but many of the vaporization parameters were nonetheless described or estimated. Table IV presents values from these references and those found by 18 Hariharan for the analogous Eu(II) compounds. Table IV. Data Summary for Vaporization Thermo- dynamics of Eu(II) and Yb(II) Halides m5 M32 Mmb ”“2 AH298 kcal/mole Eu(II) 100.8:2.5 84.9:l.l 79.8251.5 75.4:1.l AH298 kcal/mole Yb(II) 109.0e8.5 84.7:l.l 79.814.4 A8298 eu.Eu(II) 48.932.5 48.331.8 48.012.0 48.111.9 A5298 eu Yb(II) 46.0:5.6 48.031.1 47.6:3.9 AfihmummEmu) wgam Wyn? fijfl? Bfiflfi AH3,kcal/mole Yb(II) 61.7:l.o 58.614.4 0 . Asv eu Eu(II) 31.7:1.O 25.2240.7 25°1i1°0 26.1:0.7 Asg_eu Yb(II) 26.710.7 28.912.2 58 In view of these data it is evident that the YbBr2 system presents values which are in line with those derived for related systems. Even though the amount of scatter in the data points and the resultant error would indicate that the overall value should be somewhat suspect, the system proved to be well-behaved in that consistent values were obtained which allowed the description of the vaporization parameters of YbBr 2. E. Suggestions for Future Research Examination of Figure 5 shows considerable variance in the individual data points. In addition those with most average variance are at the lower temperatures. These points were taken early in the experiments before partial remedies were found for the counting technique problem with the X-ray fluorescence unit and before it was determined just how long to expose targets to obtain plated quantities in the calibration region. While there are enough points to establish that no trend in measurement exists I felt it invalid to eliminate any of them through statistical means since such a procedure would have negated the overall importance of the initial experiments which were intended to have equal weight given to them as latter experiments. At present it is unknown whether or not the linearity of the data at higher temperatures is due to a variable in the 59 vaporization process or elimination of some random errors due to improvement in the skills of the investigator. Obviously what is needed is additional experiments at the lower temperatures so that more data can be obtained for that region. Also the gap between the lower and higher temperatures could be filled in since it is the region where one would expect a cell with an orifice of inter- mediate area between those used to supply data. Regardless of the amount of data obtained the enthalpies and entropies at a reference temperature will only be as reliable as the system used for reduction to that temperature from the Operating temperature of the experiments. Since the choice of the HgBr2 model system for YbBr2(g) was dependent on the necessity for D00h symmetry should the YbBr2 molecule prove to be non-linear then revaluation of the system with a new model system would be necessary. Finally it should be pointed out that at least one other system exists for estimation of the thermodynamic properties of materials. Through theories developed by statistical thermodynamics, known rotational, vibrational and electronic states of a molecule allow calculation of its heat capacity, (HT - H398) and 5; functions. Although more pleasing in essence, it too is dependent on assumptive techniques when the necessary preliminary data from meas- ured spectra are not known. Hariharan18 has applied the 17,35 method to Haschke's data for EuBr and obtains 2 60 somewhat differing values. His treatment, while more eloquent in nature than extrapolation of estimated thermo- dynamic values, is only as reliable as his estimates from the extrapolation of data for the alkaline earth bromides. Of course should the electronic, vibrational and rotational spectra of YbBr2 become available then the system would yield absolute data reduction from median temperatures to any reference temperature. REFERENCES REFERENCES l) G. Novikov and O. Polyachenok, Usp. Khim., 33, 732 (1964); Russ. Chem. Rev., 33, 342 (1964). 2) L. Brewer, L. A.,Bromely, P. W. Gilles, and N. L. Lofgren, "Chemistry and Metallurgy of Miscellaneous Materials", Paper 6 (L. L. Quill, ed.), McGraw-Hill Publications, New York, NY, 1950. 3) L. Brewer, ibid., Paper 7. 4) R. W. Mar and A. W. Searcy, J. Phys. Chem., 71, 888 (1967). 5) M. Lim and A. W. Searcy, ibid., 10, 1762 (1966). 6) H. B. Skinner and A. W. Searcy, ibid., 72, 3375 (1968). 7) R. A. Kent, K. F. Zmbov, A. S. Kanaan, G. Besenbruch, J. D. McDonald, and J. L. Margrave, J. Inorg. Nucl. Chem., 28, 1419 (1966). 8) K. F. Zmbov and J. L. Margrave, J. Chem. Phys., 45, 3167 (1966). 9) G. Besenbruch, T. V. Charlu, K. F. Zmbov, and J. L. Margrave, J. Less-Common Metals, 12, 375 (1967). 10) K. F. Zmbov and J. L. Margrave, ibid., 12, 494 (1967). 11) E. R. Harrison, J. Applied Chem., 2, 601 (1952). 12) V. Shimazaki and K. Niwa, Z. anorg. allg. Chem., 314, 21 (1962). 13) J. L. Moriarty, J. Chem. Eng. Data, 8, 422 (1963). 14) O. G. Polyachenok and G. I. Novikov, Russ. J. Inorg. Chem., 8, 793 (1963). 15) F. Weigel and G. Trinkl, Z. anorg. allg. Chem., 317, 228 (1970). 61 l6) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 62 O. G. Polyackenok and G. I. Novikov, Russ. J. Inorg. Chem., 8, 1378 (1963). J. M. Haschke and H. A. Eick, J. Phys. Chem., 88, 1806 (1970). A. V. Hariharan, Ph.D. Thesis, Michigan State University, East Lansing, MI, 1972. A. V. Hariharan, N. A. Fishel, and H. A. Eick, High Temp. Science, 8, 405 (1972). P. Clopper, R. Altman, and J. Margrave, "The Character- ization of High Temperature Vapors", J. Margrave editor, John Wiley and Sons, Inc., New York, NY, 1967. M. Knudsen, Ann. Phys., 88, 75 (1909); English Translation by L. Venters, Argonne National Labora- tory (1958). M. Knudsen, ibid., 28 999 (1909); English Translation by K. D. Carlson and E. D. Cater, Argonne National Laboratory (1958). P. Clausing, Physica, 8, 65 (1929). J. W. Ward, R. N. R. Mulford, and R. L. Bivins, J. Chem. Phys., 81, 1718 (1967). K. Motzfeldt, J. Phys. Chem., 88, 139 (1955). G. M. Rosenblatt, J. Phys. Chem., Z8, 1327 (1967). D. E. Work, Ph.D. Thesis, Michigan State University, East Lansing, MI, 1972. H. Mayer, Z. Phys., 88, 373 (1929); English Transla- tion by K. D. Carlson, Argonne National Laboratory (1958). ' W. S. Horton, J. Res. Nat. Bur. Std., 88 A, 533 (1966). C. W. DeKock and D. D. Radtke, J. Inorg. Nucl. Chem., 88, 3687 (1970). R. A. Kent, Ph.D. Thesis, Michigan State University, East Lansing, MI, 1963. TIN-m 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 63 Sets 16 to 18, Powder Diffraction File, Inorganic Volume, No. PdlS-lBiRB (1974), Joint Committee on Powder Diffraction Standards, 1601 Park Lane, Swarthmore, Pennsylvania, 19081. W. M. Latimer, "Oxidation Potentials", 2nd ed., Appendix III, Prentice Hall, Englewood Cliffs, New Jersey, 1952. F. Gronwold and E. F. Westrum, Jr., Inorg. Chem., 8, 36 (1962). . In J. M. Haschke, Ph.D. Thesis, Michigan State University, East Lansing, Michigan, 1969. D. R. Stull and H. Prophet, "JANAF Thermochemical Tables", 2nd ed., U.S. Government Printing Office, Washington, D.C., 1971. C. E. Wicks and F. E. Block, Bulletin 605, "Thermo- dynamic Properties of 65 Elements -— Their Oxides, Halides, Carbides, and Nitrides", U.S. Department of Interior, Bureau of Mines, U.S. Government Printing Office, Washington, D.C.,‘l963. E. F. Westrum, "Advances in Chemistry Series 71. Lanthanide/Actinide Chemistry", R. F. Gould, Ed., American Chemical Society, Washington, D.C., 1967. R. Hultgren, R. L. Orr, P. D. Anderson, and K. K. Kelly, "Supplement of Selected Values of Thermodynamic Properties of Metals and Alloys", private communica- tion, R. Hultgren. R. C. Feber, "Heats of Dissociation of Gaseous Halides", AEC Report LA-3l64, Los Alamos, New Mexico, 1965. W. Feller, "An Introduction to Probability Theory and Its Applications", 2nd ed., John Wiley and Sons, Inc., New York, New York, 1960, pp 215-6. K. A. Gschneidner, Jr., Solid State Phys., 88, 275 (1964). C. W. DeKock and R. D. Wesley, High Temp. Sci., 8, 41 (1972). R. M. Biefeld and H. A. Eick, J. Chem. Phys., 88, 1190 (1974). 45) 64 H. Barnighausen, H. P. Beck, and H. W. Grueninger, Proceedings of the 9th Rare Earth Research Conference, , 74 (1971), National Technical Information Service, .8. Department of Commerce, Springfield, Virginia, 22151. ‘ t'."_~ ‘ * 1'.&.' In‘l‘lll'lllll‘l'llll APPENDICES 65 Appendix A: Collected Vaporization Data and Third Law Enthalpies for YbBr2 Orifice . T (K) pg YbBr2 -£n PT (211:3?) méfigmn AHCZ’98 1295 19.30 9.999 atm 9.37 cm2 45.16 min 73.997 kcal/mle 1208 3.67 11.293 30.24 42.949 1245 5.84 10.812 30.18 73.607 1259 4.52 11.061 30.15 74.921 1278 9.09 10.357 30.22 74.085 1231 5.66 10.852 30.30 73.017 1215 5.24 10.931 30.13 72.423 1190 2.91 I 11.530 30.15 72.616 1219 3.09 11.460 30.21 73.901 1262 3.26 11.418 31.12 75.966 1338 15.93 8.600 2.94 30.13 72.377 1359 22.37 8.256 30.22 72.428 1311 19.55 7.370 3.01 10.455 67.925 1300 8.55 8.576 15.21 70.563 1322 5.84 8.550 10.21 71.504 1346 10.66 7.941 10.22 70.986 1332 7.02 8.359 10.17 71.460 1363 13.24 7.712 10.16 71.140 1384 14.41 7.400 8.16 71.237 1401 8.45 7.464 5.13 72.186 66 Appendix A (Cont.) T(K) ug YbBr2 -£n PT Oriiége Ooiizggion AH398 (x10 ) 1421 11.91 7.123 atm. 3.01 cm? 5.18 min 72.141 kcal/mole 1445 9.84 6.812 3.16 72.348 1477 14.89 6.374 3.12 72.535 1310 10.42 7.891 2.78 10.16 69.238 1364 16.67 7.181 8.15 . 69.746 1382 9.85 7.424 6.18 71.213 1407 9.32 7.284 5.13 71.957 1437 8.04 6.943 3.18 72.359 1462 7.73 6.577 2.14 72.444 1470 8.37 6.486 2.12 72.543 1480 7.52 6.320 1.62 72.513 1494 6.46 6.005 1.02 72.219 1514 5.13 5.894 0.73 72.800 1503 4.34 6.296 0.92 73.498 1407 9.89 7.286 2.90 5.12 71.962 1427 9.25 7.110 4.04 72.378 1481 8.12 6.250 1.53 72.353 67 Appendix B: Enthalpy, Entropy, Free Energy Functions of YbBr2(s,£) T(K) (HT ' H398) (ST ’ 5398) ‘(GT ' H398)/T 1000 20,000 cal/mole 29.00 eu 43.90 en 1100 22,400 31.50 46.04 1200 24,800 34.00 48.23 1300 27,200 36.00 49.98 1400 29,600 37.50 51.26 1500 32,000 39.00 52.57 1600 34,400 40.00 53.4 T—"I"'- 68 Appendix C: Free Energy Function Changes For the Vaporization of YbBr2(£) T(K) -Afef 1000 40.061 en 1100 38.927 1200 37.689 1300 36.839 1400 36.413 1500 35.914 1600 35.855 Appendix D: Thermodynamic Functions . Thermodynamic Phase Function at 298 K Value Reference Yb(g) AH? kcal/gfw 36.35:0.2 39 Br(g) AH? kcal/gfw 26.740 36 Yb(g) A68 kcal/gfw 28.285 39 Br(g) AG? kcal/gfw 19.700 36 Yb(s) 50 en 14.30:0.04 37 Br2(£) 8° eu 36.384 36 YbBr2(g) Do kcal/gfw (180) 40 70 oma v.5 mH.N om ha.m moo H.ma ma.m 0H HN.N om mN.N omm >.HN ov.m om hm.m om He.~ HHN h.mm h¢.~ om me.~ ooa m¢.N HNH m.mm Hm.~ om mv.m om om.m oe nmm.m ow Q.m¢m.m oam m.o mm.m om Hm.~ om Hm.~ oma ¢.HH no.m 0H oo.m om NH.m HHA w.mm mm.m om Hm.m om o~.m Hoa h.em mm.m ow mo.m om mm.m om woa.v xmm3 >Hm> nwm.v oe Q.ON~.¢ oaa wooa m>.v mom mh.¢ om mh.¢ mmDMMHp mh.m wow th.m .. . . . 1...... REA. -EM... .8... .1... .8“... AH... Uomflmm memopmofi “60.33% MWMMMMDAMH mswfiwwm $5..me wwmmafihH magnum/mums”... mcumpumm COHDOUHMMHO Hmp3om hamlx um xflpcmmmd 71 mv . Amm .mmm mmmv momnw mo 858.3 on mac 398mg 9 . Ami, mowv 8303mm.» gogmmm . Nummd 9.8 Name” now 5.85me haulx :392 89G Egg i mma H.m wm.a oa amm.H NNN . ~.o Ho.a OH om.a omm H.H mm.H om nmm.a Hmo m.mH qo.~ mom mo.~ ma mo.~ can m.m HH.~ mom . mo.~ S x 5 aoflmwflmm «SB.» .8. :oflmmflmm mammfiommmun .96 coflmwflmm QMmcmmmmmuo cOfluomHmmm a mmcflommm-c . _> umpm«_aamo ca . . .> muommm fimcmufi 33:35 53:35 N «.oamo umpmasoamu m>HumHmm mcacflmamm puscoum m>flumHmm mamsmm “mam A.ucouv m xflwcmmmd "'itTifitfll’IILtiMiflfirLillmflfflmiflfiflylrflmfi'ES