n. -. .........~‘nnn' THE VAPORIZATION AND THERMODYNAMICS OF THORIUM DICARBIDE Thesis fan! the Degree cf N1. 0. MICHIGAN STATE UNiVERSITY Richarei A Kent 1963 LIB RA R Y , Mnflfasn State University MICHIGAN STATE UNIVERSITY EAST LANSING, MICHIGAN ABSTRACT THE VAPORIZATION AND THERMODYNAMICS OF THORIUM DICARBIDE by Richard A. Kent Quantitative investigations of the vaporization of refractory in- organic compounds are basic to the study of systematic trends in the thermodynamics of vaporization processes and of chemical bonding in gaseous molecules in part because of the comparisons which can be made between their results and those for the corresponding oxides. The characterization of the fundamental properties of thorium dicarbide is of interest both from this basic standpoint, and from its evaluation for possible applications in nuclear technology. Thorium dicarbide of high purity was prepared by the reaction of graphite either with thorium metal or thorium dioxide and the subse- quent homogenization of the crude product by heating at approximately QhOOOK in a graphite crucible in high vacuum. The vaporization of thorium dicarbide over the temperature range 2100 to 2SOO°K was investigated by the Knudsen effusion method. Samples were evaporated from inductively heated graphite or tungsten effusion crucibles and known fractions of the total effusate were collected on fused silica targets which were assayed for thorium by a neutron activa- tion technique. Chemical and X-ray diffraction analyses of both start— ing materials and residues were performed. The rate of effusion of thorium-containing species measured in the target experiments was expressed in terms of an "effective vapor pres- sure" P which, when combined with the molecular weight of 256.06, E) Richard A. Kent gave directly the rate of evaporation of thorium dicarbide. An empiri- cal equation, fitted to the data by the method of least squares, gave log P - ho 73$(i 717) + 8.7u2(: 0.30h). B(atm) = The observed volatility varied by a factor of 10:5 over the LOO degree temperature range and at 2360°K was about 0.025 per cent that of thorium dioxide and about 0.006 per cent that of thorium metal. Combination of the published mass spectrometric data for the vapor— ization of thorium dicarbide and the target data measured in this in— vestigation, yielded the data requisite to a linear treatment of the individual vapor species as a function of reciprocal temperature. By means of the second law of thermodynamics the following values were obtained: For the reaction ThCZ(S) = Th(g) + 2C(graphite) (I) AH:96 = 176.92 : 3.30 kcal/mole, A5298 = 3h.h9 t 0.6h e.u. For the reaction AH:98 = 196.2u : 3.30 kcal/mole, A5396 = h2.81 t 0.72 e.u. values were estimated for the free energy functions of ThCZ(S) and ThC2(g) and these were combined with the published data for graphite and Th(g) to yield the following values calculated from the third law of thermodynamics: Richard A. Rent For the reaction T = Th 2 . hCZ(s) (g) * C(grapmte) (I) AH:98 = 175.82 1 0.68 kcal/mole. For the reaction AHgge = 20h.96 : 1.25 kcal/mole. The enthalpies obtained for the dissociation reaction (I) were combined with the published value for the enthalpy of vaporization of thorium metal and the following values for the standard enthalpy of formation of ThCz(s) were calculated: From the second law, 1H398 = — u0.32 : 3.33 kcal/mole. From the third law, AHggB = — 39.22 t 0.8h kcal/mole. THE VAPORIZATION AND 'I'HERMODYNAMLCS OF THORIUM DICARBIDE By Richard A. Kent A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of IDCTOR OF PHILOSOPHY Department of Chemistry 1963 ACKNOWLEDGMENTS The author wishes to express his sincere thanks and appreciation i; to Dr. Harry A. Eick for his guidance, encouragement, and friendship L throughout the course of these investigations. i Appreciation is also extended to nw' collegue, Robert E. Gebelt, E“ for his many helpful suggestions and interest during the course of this study. A deep sense of gratitude and appreciation is extended to the author's wife, Susan, for her patience and understanding which have made this investigation possible. Financial support from the Atomic Energy Commission is gratefully acknowledged. TABLE OF CONTENTS I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . A. General Incentives for this Research . . . . . . . B. Previous Investigations of the Thorium-Carbon" System . . . . . . . . . . . . . . . . . . . 1. General . . . . . . . . . . . . . . . . 2. Thermodynamic Investigations . . . . . . . C. The Specific Purpose of this Research . . . . . . II. VAPORIZATION STUDIES . . . . . . . . . . . . . . . . . . A. General . . . . . . . . . . . . . . B. Thermodynamic Relationships in vaporization Studies . . . . . . . . . . . . . . . . . . . . 1. Second Law Determination of vapor Pressure. 2. Third Law Determination of vapor Pressure . C. The Knudsen Effusion Method . . . . . . . . . 1. Some Principles of Molecular Bffusion from a Knudsen Crucible . . . . . . . . . . . . 2. Vapor Pressure Equations . . . . . . . . 3. Two Fundamental Requirements in Effusion Studies . . . . . . . . . . . . . . . . . h. Some Practical Requirements in Bffusion Studies . . . . . . . . . . . . . . . . . III 0 WERIWNTAL O 0 O O O O O O O O O O O O O O O O O O O O A. Summary of the Experimental Approach . . . . . . . B. The Preparation of Thorium Dicarbide . . . . . . . 1. Materials . . . . . . . . . . . . . . . . 2. Methods of Preparation and Apparatus . . . C. Analysis of Thorium Dicarbide . . . . . . . . . . 1. X-ray Powder Diffraction Patterns . . . . . 2. Chemical Analyses . . . . . . . . . . . . . D. Effusion Experiments . . . . . . . . . . . . . . . . .Apparatus .i. . . . . . . . . . . . . . . . Measurement of Dimensions . . . . . . . . . Measurement of Temperature . . . . . . . Preparation of Targets . . . . . . . Procedure for V01atility Measurements . . . Analysis of Targets . . . . . . . . . . . . O\U'l£"w NH PAGE ll l2 12 1h 16 16 17 18 2O - W TABLE OF CONTENTS - Cont. PAGE Iv. RESULTSANDDISCUSSION 119 A. Convention Chosen for the Expression of Results of Effusion Experiments . . . . . . . . . . . . A9 B. Individual vaporization Experiments . . . . . . . 50 l. EXperiment A . . . . . . . . . . . . . . . 50 2. EXperiment B . . . . . . . . . . . . . . . 5h 3. Experiment C . . . . . . . . . . . . S? h. Summary of the Determination of " "Effective Pressures" . . . . . . . . . . 63 5. Conditions Related to the Measurement of vapor Pressures . . . . . . . . . . . . 66 C. Treatment of the Data . . . . . . . . . . . . . . 69 1. Calculation of PTh and PThCZ from PE . . . 69 2. Calculation of Free Energy Functions . . . 7S 3. Calculation of the Enthalpies of vapor- ization for Experiments A, B, and C . . . 8h D. Analysis of Errors in the Measured "Effective Pressures" . . . . . . . . . . . . . . . . . . . 86 B. Other Investigations . . . . . . . . . . . . 88 1. The Results of Lonsdale and Graves . . . . 88 2. The Results of Jackson and Co-workers . . . 93 F. Suggestions for Further Research . . . . . . . . . 96 1. The Thorium-Carbon System . . . . . . . . . 96 2. Determination of Thermodynamic FunctionS' for Vapor Species . . . . . . . . . . . . 96' LITERATURE CITED . . . . . . . . . . . . . . . . . . . . . . 98 APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . 101 A. Supplementary Experimental Data . . . . . . . . . 102 B. Tabulation of Physical Constants . . . . . . . . . 110 C. Temperature Measurement for Exposure No. b, Experiment B. . . . . . . . . . . . . . . . . . . 111 iv TABLE II. III. IV. VII. VIII. IX. ?< )CLI. XIII. XIV. XV. XVII. AII. AIII. LIST OF TABLES PAGE Hydrolysis products of thorium monocarbide and thorium dicarbide . . . . . . . . . . . . . 6 Distribution of hydrocarbon hydrolysis products of some inner transition metal dicarbides . . . . . . . . . . 6 Assigned indices for Film A-1068 . . . . . . . . . . 29 Assigned indices for Film A-1077 . . . . . . . . . . . . 31 Corrections for Pyrometer No. 1572579 . . . . . . . . . . 38 Spectrophotometric determination of thorium . . . . . A6 Activity ratios observed and expected for standard discs. b8 Data for Experiment A . . . . . . . . . . . . . . . . 53 Data for Experiment B . . . . . . . . . . . . . . . . . . 58 Data for Experiment C . . . . . . . . . . . . . . . 6h PTh andPThCZ from Experiments A, B, anc C . . . . . . . 72 Free energy functions, cal/deg-mole . . . . . . . . . . . 77 Thermodynamic functions H¥-H398, cal/mole . 78 Values of 8;, cal/deg-mole . . . . . . . . 78 Third law values of the enthalpies of vaporization of ThCZ 85 vapor_pressures calculated from the data of Lonsdale and Graves . . . . . . . . . . . . . . . . . . . . . . . 90 Third law values of the enthalpies of vaporization of ThC2(s) calculated from the data of Lonsdale and Graves. 91 Data for series P-l to P-9 . . . . . . . . . 10h Data for series P-10 to P—l5 . . . . . . . . . . 106 Temperature measurement for exposure no. h, Experiment B. 111 LIST OF FIGURES l. Tentative phase diagram for the thorium-carbon system 2. Schematic diagram of the apparatus used to prepare thorium dicarbide . . . . . 3. Schematic diagram of the apparatus used for effusion experiments . . . . . . . . h. Beer's Law plot for thorium—morin complex . 5. Schematic diagram of crucible support assembly for eXperiment C . . . . . . . o 6. Temperature calibration curve for experiment C 7. The effective vapor pressure of thorium dicarbide as a function of reciprocal temperature . 8. The temperature-dependence of the partial pressure of thorium vapor in equilibrium with solid thorium dicarbide . . . . . . . . . 9. The temperature-dependence of the partial pressure of thorium dicarbide vapor in equilibrium with solid* thorium dicarbide. . . . . . 10. The temperature—dependence of the effective vapor ‘ pressure of thorium dicarbide vi a o I 0 PAGE 26 35 AS 61 65 73 7h 92 ERRATUM After this thesis was accepted, it was found that pyrometer No. 1572579, which was used in this work, no longer conformed to the calibration data obtained from the National Bureau of Standards. The implication of this observation is that the temperatures reported herein vary from seventeen degrees too low at 1900°C, to twenty-five degrees too low at 2200°C. I. INTRODUCTION A. General Incentives for this Research Thermochemical and mass spectrometric investigations in recent years have shown that previously unsuSpected gaseous molecules contain- ing heavy metal atoms are rather common in the vapor phases of refrac- tory compounds in equilibrium with their solid phases. The study of vaporization processes not only provides for the measurement of vapor pressures and the preparation of new substances, but also served to help establish the nature and kinetics of high temperature reactions. Moreover, much of the data required for the testing of the theories of chemical bonding come from high temperature vaporization experiments. Good thermochemical measurements on a large number of refractory systems of heavy metals are necessary both to provide stepping stones to the simplification of the theory of chemical bonding and to enable formulation of empirical treatments for techno- logical purposes. To date, systemization of vaporization behavior and.detection of trends, for example, of dissociation pressures, have been hindered, not only by the considerable absence of pertinent data, but also by the poor reliability of much of the data available. While no single experimental investigation can provide more than a small contribution to these goals, each accurate characterization of a particular molecule is a definite advance in this direction. This study of the vaporization and dissociation of thorium dicarbide was undertaken with these thoughts in mind. 1 2 B. Previous Investigations of the Thorium-Carbon System 1. General The preparation of thorium dicarbide in an electric arc furnace was first reported by Troost (l) and confirmed by Moissan and Etard (2). The existence of the monocarbide was established by Wilhelm, Chiotti, Snow, and Daane (3). Wilhelm and co-workers (3,h) investi- gated the system thorium—carbon and constructed, on the basis of X— ray diffraction and melting point data, a tentative phase diagram in which they assume that a continuous series of solid solutions crystal- lizes from melts between thorium monocarbide and thorium dicarbide. Further, they assume that at some lower temperature these solid solu- tions decompose into a thorium-rich phase and a phase based on thorium monocarbide, on the one hand, and into two phases nearly corresponding to the compositions ThC and ThCZ, respectively, on the other. Accord- ingly, their phase diagram shows two miscibility gaps with critical points at approximately two weight percent carbon and 19750, and be— tween about six and seven weight percent carbon at about 23000. At approximately 12.5 weight percent carbon and 25000 thorium dicarbide forms an eutectic with graphite. It is unlikely that such a constitution exists since a continuous transition from the structure of thorium via that of the monocarbide to that of the dicarbide cannot occur. Hansen (5), using the data of Wil— helm and co-workers, has constructed a more amenable phase-diagram which is shown in Figure 1. This diagram should, of course, be regarded only as a rough approximation and is presented here only to give a con- ception of what the phase relationships could be. Although there is no evidence as yet as to the existence of the carbide Tth3, this phase Weight Percent Carbon 10.0 6.0 3.0 2.0 lj 0.5 15.0 I 11.0 I 2800. A- m 2 memnmmpcoo moopmon . ouspmnoaaoh 7O 20 30 to 50 60 Atomic Percent Carbon Tentative phase diagram for the thorium-carbon system. 10 Figure l. 2200- b may exist in analogy to U203. Wilhelm and Chiotti (h) report the mono- carbide to be cubic (NaCl-type) with the lattice parameter a0 = 5.3bA, corresponding to a density of 10.67 g per cm3. The crystal structure of the dicarbide was first investigated by von Stackelberg (6), who reported a tetragonal structure involving pairs of carbon atoms which he assumed to be acetylene ions. This structure has also been reported for calcium carbide and the rare earth dicarbides. However, by using X-ray and neutron diffraction techniques, Hunt and Rundle (7) established that thorium dicarbide crystallizes as a monoclinic structure, space group C2/t, with a0 = 5.53A, b0 = b.2hfi, Co = 6.56A, B = 10h9, and with four ThCZ molecules per unit cell. As in the structure suggested by von Stackelberg, the monoclinic structure contains groups of carbon pairs. However, the carbon-carbon bond dis- tance is 1.52, a distance close to the accepted single bond value, which would seem to eliminate acetylene ions. The arrangement of the thorium atoms about the C2 groups combines single, double—, and triple bond character and, according to Hunt and Rundle, covalent character for the thorium-carbon bonds is indicated. The electron structure suggested by the authors is closely related to that proposed by Rundle (8) for inter- stitial compounds of the type MX, including thorium monocarbide. Hunt and Rundle assume that both the mono- and dicarbide of thorium have metallic character. Reports in the literature on the hydrolysis of thorium dicarbide are sparse and often contradictory. Moissan and Etard (2) reported the hydrolysis to yield u7.7h % acetylene, 29.37 % methane, 5.76 % ethylene, and 17.12 % hydrogen. Modic (9) reported that the major hydrolysis product was methane. Lebeau and Damiens (10) found the hydrolysis to 5 yield 15 % acetylene, 3.1 % methane, 2.8 % ethylene, 10.7 % ethane, 59.6 % hydrogen, 2.h % higher paraffins, and 6.b % higher olefins. One of the major difficulties inherent in these investigations is obtaining samples of a single phase. The early work on the hydrolysis of thorium dicarbide probably suffers most in this regard. Engle, Goeddel, and Luby (11) who studied the hydrolysis of thor- ium dicarbide in moist air propose the following reaction: ThCz + H20 = ThOZ-XHZO + H2 + aliphatic hydrocarbons. They report the hydrocarbons to consist of methane and ethane gases and C4- and C5 condensed hydrocarbons-~no acetylene was observed. An in- crease in temperature or decrease in sample size increases the reaction rate and thorium dicarbide was observed to hydrolyze about ten times as fast as uranium dicarbide, the reaction going to completion in one to five hours. The authors also observed that the rate was affected by carbon content, carbon deficient samples having lower reaction rates. Kempter and Krikorian (12) have studied the hydrolysis of thorium monocarbide and dicarbide at 25° using a mass spectrograph. The reac- tion products are listed in Table I. Since thorium monocarbide yields mainly methane on hydrolysis, it seems likely that Modic hydrolyzed the monocarbide rather than the dicarbide. Palenik and Warf (13) studied the hydrolysis of lanthanum and cerium dicarbides. For purposes of comparison, the results, along with those of Kempter and Krikorian are listed in Table II. Hydrogen and methane are not included in the totals since Palenik and Warf used liQUid nitrogen to condense the hydrolysis products and did not collect these gases. on runs made at 25° they obtained about five mole percent non condensables. .t . a , v. d ‘1 TI .tl‘llll'llllliil x u . m o o>0bm mcoonmooepzmn .omN pm mmquouuxr mcmudp pooapouq mcobumoonphc Hmpop Mo bemused oHoa cw pommopQXo mambou Mada ---- acm.m 0H.N ON.N euueannuean: Om.N Om.~N Om.~@ om.H© mmcxxad Om.mN om.mH 00.0H Om.HH mocmxaa om.wo Om.m4 om.ON wo.mN mocmxfid No: None Note Nona anuaueam ...mopmnumowp Hmong combwmcmpu mecca maom Mo moodpopn mmmzqoupxfi nonpwoonpzn mo cowpsbmpbmwm .HH ofinmh .ocmuumn macs an eummuudxu mflmpoo Hfidm o.m m.m m.aa e.w m.H m.a m.mm ma.m m.m mm.m N.AN None --- --- --- --- --- N.a mm.m ma.o --- a.ee m.a one smuo 6a a e e e e p w o N N a. N e>on< m o m o m o rho moo em 0 mmo N: o :0 m manhuuam .mpmbpwomp aswuonp new commemoocoa adwnocp mo mvosvoum wwwmqonpzr .H oabdh f: ‘l f /" , ‘I . I ' . ‘ . _ _ / \ ,1 , '. I," I. 1 s.‘ ‘ , 1 .’ ~ \‘ I 4'11: I A I ' I". g 7* I . I. -- c I - I. i A . I ’ .\ .‘ ~ ' _ s g ‘_ - n . . . it ___"' A 7 It is apparent that the prediction of Palenik and Warf concerning thorium and uranium dicarbides, "the two electron oxidation in the hy- drolysis reaction is expected to produce more hydrogen and hydrogenated hydrocarbons than in the case of the rare earth dicarbide", is consistent with the hydrolysis data for thorium and uranium dicarbides. A simple representation of the overall reaction might be something like the fol- ::, lowing: I I Thc2 + 2H20 = Th(0H)Z + CZHZ E mom)2 + 2H20 = Th(0h)4 + H, i_ ‘ Csz + H2 = CnH2n+2 + CnHZn. 2. Thermodynamic Investigations The melting point of thorium monocarbide is reported by Wilhelm and Chiotti (h) as 26250, and that of the dicarbide as 26550. Prescott and Hincke (1h) studied the reaction Th02(s) ThC2(s) + 2c0(g) bc(graphite) in the temperature range 2057 to 2h9h°K by measuring the pressure of the carbon monoxide produced and found the enthalpy of reaction to be AHgge = l9h.8 kcal/mole. From this, they calculated the heat of form- ation of solid thorium dicarbide to be AH‘Z’Q8 = —78.9 kcal/mole. Rath and Becker (15) recalculated this quantity using their determination of the heat of formation of thorium dioxide and found the enthalpy of formation of the dicarbide to be AHgga B -h5.7 kcal/mole. Krikorian (16), using Prescott and Hincke's data and estimated free energy func; tions, obtained an enthalpy of formation AHgga = -33 i 8 kcal/mole. Meslan (17) on the basis of emf measurements on the cell Th(S)/LiCl-K01(eutectic) + 5% ThCl4(l)/ThC2,C . t; ' I ‘1'“. ’ found.the free energy of formation of thorium dicarbide to be -36.h kcal/ mole at 800°. Brewer and co-workers (18) have estimated -h5.6 kcal/mole to be the standard enthalpy of formation of solid thorium dicarbide. Lonsdale and Graves (19) have studied the dissociation of thorium di- carbide over the temperature range 2300 to 2900°K using the Knudsen effusion method. The effusate was collected on cooled graphite targets 1 1 which were assayed for thorium by means of neutron activation analysis. They report that, in the temperature range studied, the vapor pressure of thorium gas over solid thorium dicarbide may be represented by the 5 equation: 1: (atm) = ‘ 37’6007 I’m + 7'39 i 0-39- \ log P They obtained a second law heat of dissociation of 172.0 3 h.6 kcal/ mole from.which they calculated the heat of formation of thorium di- carbide to be AHgga = - h6 i 6 heal/mole. No calculation of the standard enthalpy of formation by the third law technique is reported; their calculations are based on the assump— tion that the gaseous species consist only of thorium gas and polymeric carbon. However, a previous mass spectrometric investigation of the carbon-rich end of the Lanthanum-carbon system by Chupka and co-workers (20) showed that both lanthanum and lanthanum dicarbide are important gaseous species. The ratio of pressures, P(laCZ)/P(La), was found to increase from 0.2 at 2200°K to 0.8 at 2600°K. Jackson, Barton, Krikorian and Newbury (21) have completed a mass Spectrometric investigation of the vaporization process and thermo- dynamics of solid thorium dicarbide. They report that the vapor species 9 consist of both thorium and thorium dicarbide. The presence of gaseous thorium monoxide in the system.was found to be dependent on sample prep- aration techniques. The ratio of gaseous thorium dicarbide to gaseous thorium over solid thorium dicarbide was found to vary from about 1.2 at 2h00°K to about 1.8 at 2600°K. By means of a second law treatment of the data, Jackson and co-workers calculated the following enthalpies: ‘0. ThCZ(S) = ThCZ(g) AH398= 188.1 1 3.1 kcal/mole ThCzts) Th(g) + 2c( graphite) ; AHggs= 160.3 1*: 3.2 kcal/mole. From a least squares calculation, assuming ACP to be zero, they obtain the following expressions for the vapor pressure of each species over solid thorium dicarbide: 39 368 t 163 = — h for ThC2(g), log P(atm) T + 7.20 i 0.65, - 35,025 i 1AA In addition they calculated the enthalpies by a third law method: ThC2(S) = ThC2(g) ; AH398= 212.8 1 1.5 kcal/mole, ThCZ(s) = Th(g) + 2C(graphite) 3 AHggee 18h.7 i 1.5 kcal/mole. Using the reported value (22) of the enthalpy of sublimation of thorium metal, AHgge = 136.6 : 0.5 koal/mole and the enthalpies given above, the authors calculated the following standard enthalpies of formation for thorium dicarbide. II H- Second Law, AHgga -23.7 3.5 kcal/mole, Third Law, 1H398 = -u8.1 : 2.0 kcal/mole. The third law result agrees well with the second law result obtained by Ltnnsdale and Graves and with the value estimated by Brewer. However, the large discrepancy between the second and third law re- sults indicates the probable presence of systematic errors. A possible 10 eXplanation, as given by the authors, may be that the thorium dicarbide phase has a variable solid solubility of carbon as this behavior is not uncommon in carbides. The most common causes for such a discrepancy, however, are errors in temperature measurement. Also, the enthalpies determined by Jackson and co-workers by the third law method are some- what temperature dependent, indicating a systematic error. C. The Specific Purpose of This Research various workers in the past have experimentally determined the '5 I I I L enthalpy of formation of thorium dicarbide. The values obtained range from about - 2O kcal/mole to about -50 kcal/mole. Recently, two at- tempts involving the Knudsen effusion method have been made to deter- mine this quantity—-the mass spectrometric investigation by Jackson and co-workers and the study of Lonsdale and Graves. While the second law results obtained by Lonsdale and Graves are reasonably close to the third law results of Jackson and co-workers, their failure to take into account the species ThCZ( ) and the discrepancy between the second and third law values determingd by Jackson and co-workers seem to justify further investigation of the vaporization and dissociation of thorium dicarbide. This project was undertaken to prepare pure thorium dicarbide; to repeat the investigation by Lonsdale and Graves of the vaporization and dissociation of thorium dicarbide employing the Knudsen effusion method; and, taking into account the findings of Jackson and co-workers regard- ing the gaseous species involved, to compare the measured values of the entropy and enthalpy of vaporization and dissociation and the standard enthalpy of formation determined by this method with the values deter— mined by Jackson and co-workers in their mass spectrometric investigation. the; ’37 . the 0 II. VAPORIZATION STUDIES A_G_ee_r_1 When we investigate the vaporization process of a given substance we can obtain, in addition to the vapor pressure, information concerning the thermodynamic nature of both the condensed phase or phases and of the gaseous species produced. By studying the temperature dependence of the vapor pressure or partial pressures of individual species we can determine the values of the enthalpy and entropy changes accompany- ing the vaporization (or dissociation) process, commonly termed the heat and entropy of vaporization (or dissociation). In addition, we can determine the standard enthalpies of formation of solid compounds and gaseous molecules. The phase rule E = 9-P+2 expresses the relationship between the number of degrees of freedom.§ (the variance) which must be specified in order to completely define a system in a thermodynamic sense, and E and P, respectively the number of components and the number of phases in equilibrium in the system. Consider, for example, a two component system in a closed container in which condensed material is in equilibrium with vapor. There are two ways for the pressure to be temperature dependent. One way is if there are three phases present. Since the vapor constitutes one phase, there must be two condensed phases, solid or liquid or both. The other way is if some additional restriction is imposed on the system, i.e., if the overall composition of the vapor is the same as that of the condensed ll 12 phase. The latter case is defined as a congruent vaporization process. Both situations are said to be invariant because a change in one variable, 3.9., the temperature, to a new fixed value uniquely redefines the total pressure. The congruence of a vaporization process can be demonstrated by examining the residue after successive evaporation experiments. In a congruent process the overall composition of the residue will not change during the evaporation. For three component systems the number of degrees of freedom is 5 ‘.E and the number of additional phases or restrictions must be in- creased hy one to make the pressure a function of temperature only. A study of the vapor pressure or related rate of evaporation of a given substance with time at a given temperature, combined with chemical and X-ray diffraction analyses before and after the evaporation, permits a deduction of the behavior of the condensed phase involved and thus renders meaningful any thermodynamic values obtained from further evap- oration studies with the same substance. B. Thermodynamic Relationships in vaporization Studies 1. Second Law Determination of vapor Pressure Consider the reaction at TOK, = M M(s or 1) (9)- For this reaction 0: 0- °=-RTan. (1) AFT AHT TAST The equilibrium constant for this reaction is expressed in the usual manner as the product of partial pressures raised to appropriate powers; in this case K is PM(g)' If we consider ACP to be a constant for the 13 reaction, T AH? = AH: +‘j: ACP dT = AH: + ACP(T - G) ‘ (2) and as? = AS: + ACP ln(T/e) (3) where O is the reference temperature, usually 298.160K. If we combine equations (1), (2), and (3) we have = o = 0 _ _ ° _ -RT ln ng) AFT 1H0 + ACP(T o) T139 TACP 1n(T/0) (h) ‘ This gives rise to two cases of interest: (a) ASP is approximately zero If we assume that ACP is zero for the reaction, equation (h) re- duces to _ o 0 ' -RT 1n PM(Q) - 1H9 - T150. (5) or . 0 AH: ASO 1°9 P11(9) ‘ ' "_"2.303RT * "2."3"—03R (6) which is the familiar Clausius-Clapeyron equation in which R is the molar gas constant and 2.303 is the natural logarithm of ten. After PM(g) has been measured, we graph log PM(g) against l/T over the temperature range studied; AH: is obtained from the slope and as: from the intercept. The assumption that ACP is zero for the reaction implies that the heat capacities of the gaseous products are equal to those of the con— densed phases, a situation which is virtually never true for non-ideal systems. If heat capacity data are available or can be estimated for both reactants and products, it is possible to obtain values of A113. and lb 0 AST poses, to a suitable reference temperature 9. for each temperature, and to extrapolate them, for tabulation pur— (b) ACD is not zero but is constant —I' If we make the assumption, not that the heat capacities of the gaseous and condensed phases are equal, but that the difference between them, ACP, is constant, we have, from equation (h), AH° ACP(T - e) ACPln(T/0) 15° log P = - e - + —— + e (7) M(g) 2.303RT 2.303RT 2.303 R 27303n‘ which is of the form log PM(9) = -A/T + B lnT + c. (8) 2. Third Law Determination of vapor Pressure Because the slopes of the various experimental plots are sensitive to small errors in temperature measurement it is advisable if possible, to check the values for enthalpy and entropy determined by the second law method against a method based on the third law of thermodynamics. When this third law method is employed, the heats and entropies of va- porization or dissociation so obtained may be more reliable than the second law values because of a decreased sensitivity to errors in the measured temperatures. The third law method makes use of the free energy function, fef, defined by %-° Hi - H° fef = (fi—g) ' (fi—g) “ S; (9) where, as above, 0 is the reference temperature. For convenience in calculations the free energy functions are often tabulated relative to 298.16°K, thus the relation 15 0 0 0 0 F ‘ H298” H ‘ H298 ( T T (TEHf---) - S; (10) is employed with standard heats of formation AHggec Equation (10) can be related to the 0°K free energy function by the relation 0 O O O 0 0 .ET - H298 FT _ HO H298 - H0 (—T——> = (—-—T—--> - (—-—f—-—). (n) For the vaporization reaction M(5 or 1) = M(g) ° 0 0 o o 0 FT ’ H298 ET ‘ H298 AFf AHzge Afef “ ("’T""’)(g) ' ("“7T"")(s or 1) ’ '7?" ' T (12) but, 0 - _ = — ART - RTan RTlnPM(g) (13) so that 0 Afef = — Rln PM(g) - AH298 (1h) T thus 11129., = - TAfef — RT 1n PM(g) (15) or 0 0 o F&.- H298 AH298 = - T A(—-sf—-——- - 2.303 RT log PM(g). (16) Thus, provided that the free energy functions are tabulated, an independent value of the heat of vaporization (or dissociation) may be calculated for each pressure measurement. The free energy function may be evaluated for a given substance if measured heat capacities are available. In the case of a gas, the free energy function may be evaluated from spectrosc0pic data if such are available. 16 Unfortunately, heat capacity and spectr0300pic data are not always available, and the standard tabulations of free energy functions [see for example, references (23) and (2h)] and those found in individual pub- lications for substances at high temperatures often do not contain data applicable to the problem at hand, and we muSt often accept the second law values of enthalpy without third law confirmation. It is possible, however, to estimate free energy functions for a given compound with fair accuracy, if those for related compounds are known. Such semi- empirical estimates are frequently used to provide a third law check of the second law heats and entr0pies. C. The Knudsen Effusion Method 1. Some Pringiples of Molecular Effusion from a Knudsen Crucible Consider a closed inert container which is at a fixed uniform temp~ erature and is located in a vacuum. If this container or crucible con- tains a condensed phase which is in equilibrium with its vapor, the pres- sure inside the crucible will be the equilibrium vapor pressure and, if the vapor behaves ideally, we can show from kinetic theory that the number of each kind of molecule striking a unit area of the crucible wall in unit time is nE/h where n is the density of the gas in molecules per unit volume and E is the average molecular speed. In 1909 Knudsen (25,26) demonstrated that if the wall were thin and contained a small orifice of known area the number of molecules which would effuse through this Opening in unit time would be the same as the number which would strike an equal area of the wall in the same time. Thus, by determing the number of molecules which effuse through this orifice in a given time we can measure the vapor pressure of the substance in the crucible. 17 The number of molecules which are effused by molecular flow per unit time per unit solid angle in a given direction above the plane of the orifice is described, for an ideal "knife—edged" orifice, by the cosine law which may be written as dz = 20¢) dso cos a d... dt. (17) For a derivation of the cosine law and a discussion of its applications the reader is referred to the work of Carlson (27). In equation (17) dz represents the number of molecules leaving the orifice in time t from the element of area dSo in an elementary solid angle do) at the angle 0 t0 the normal to the orifice plane at dSo. The total rate of emission from the entire orifice is Zo = nE/h molecules per cm2 per unit time. Integration of equation (17) shows that in a given time equal numbers of molecules pass through equal areas located anywhere on a large sphere tangent to the orifice thus, if the orifice is ideally thin, it is necessary only that we know the distance to and the angular orientation of a target anywhere above the orifice in order to calculate the fraction of the total effusate that strikes the target. 2. vapor Pressure Equations There are several ways in which we can determine the number of molecules which leave the crucible through the orifice in a given time. The simplest method is to determine the weight lost by the crucible during the vaporization by weighing the crucible before and after the experiment. We can relate the partial pressure P of the vapor species of molecular weight M to the weight W of that species effusing in time t through an orifice of area So by the equation 1, = SIgIgfiifiTf/Z (18) 18 where T is the absolute temperature inside the crucible and R is the molar gas constant. This result corresponds to an expression of the pressure in terms of the rate of effusion, Z moles, of vapor as /2. z 1 P = §;E(2NMRT) (19) In the high temperature investigation of a vemy slightly volatile substance it is often more convenient to condense a known fraction of the actual weight loss of the crucible. If a circular target of radius r is placed at a distance d from the orifice and is coaxial to it, it can be shown (27,28) that the pressure P is related to the weight w gained by the target according to the equation: 1 2 P = sztIZIIT) /Z(q Izdz) (20) 01‘ _ 0.022557 T l/2 2 + d2 p _ T—SOTLW) (T__r_2_), (21) When the units on w , So, t, and T are grams, cmz, seconds and degrees Kelvin, respectively, equation (21) gives the pressure in atmospheres. 3. Two fundamental Requirements in Effusion Studies (a) Free molecular flow The pressure inside the effusion crucible must be low enough that collisions between gaseous molecules are so infrequent that each molecule leaves through the orifice without affecting the trajectories of the others. Knudsen (26) in his experiments on the flow of gases through thin-edged orifices observed that hydrodynamic flow effects caused the mass of gas effusing from a region at a known pressure to be greater than that expected when the pressure was above certain values. The IIIIIII: 19 values corresponded to a ratio of mean—free path (X) to orifice diameter (D), X/D, of about ten and this value has often been quoted in the liter— ature as the upper limit of molecular effusion and thus of the effusion method. Subsequent experimental investigations (29,30,31,32) give mutually inconsistent information on the upper limit. Unfortunately the problem is a complex one and no theoretical treatment has yet been presented which accurately predicts the pressure at which departure from molecu— lar flow should occur for a given species. (b) Orifice shape The second fundamental limitation to the validity of pressure measurements by the effusion method is the shape of the orifice. If the orifice has the form of a tube of finite length, the distribution of molecules effusing through it will no longer be given by the cosine law because reflections from the orifice wall will change the distri— bution of molecules at large angles to the normal. Also, there is a corresponding probablility that a molecule which has struck the wall will, as a result of such a collision, be returned to the cavity, re— sulting in a decrease in the measured vapor pressure. Clausing (33,3h) has investigated the flow of gases through ori- fices of finite length and obtained integral equations whose approximate numerical solutions yield dimensionless correction factors which take iiito account the length of the orifice. When these correction factors, Pic), which range from zero to unity are applied, equation (21) becomes 0.022557w (%)1/2(r2 + d2). wosot r2 (22) 20 Further discussions of this correction factor are found in the work of Carlson (27), Freeman and Searcy (35), and others (36,37,38). h. Some Practical Requirements in Effusion Studies Whereas, the fundamental requirements listed above pertain to all Knudsen effusion experiments, there are many practical requirements which depend on the materials and techniques employed in a particular experiment. Some of these requirements are as follows: (a) A reaction between the crucible material and the vaporizing sample may either lower the apparent vapor pressure of the condensed phase by taking it into solution or into chemical combination, or raise it due to the formation of a new, stable species. Typical examples of the former are the low vapor pressures reported for the alkali hydrox— ides by early workers who used nickel or other metals for crucible materials. More recent studies by Spinar and Margrave (39) have shown that in non-reactive crucibles fashioned from single crystals of mag— nesium oxide, the vapor pressures of the alkali hydroxides are many times higher than previously reported. Examples of the latter are the following. In studies of the vaporization of zirconium dioxide (hO) and thorium dioxide (bl) from tantalum crucibles, the gaseous species tantalum monoxide was found to contribute to the weight loss of the crucible (h2,h3). An attempt should be made to characterize the va— porization process. A change in crucible material may reveal reaction lDetween the sample and the crucible. Chemical and X-ray diffraction estualyses should be performed on all starting materials as well as on $126? residual substances and sublimates. LE)! Cf) 1,), CPU: 1 {LIB ' 21 (b) The residual pressure in the vacuum.system must be low enough to preclude scattering of the effusing vapor or reaction of the sample with residual gases. (0) The effusion crucible and the sample contained therein must be at a known, uniform temperature. Winterbottom and Hirth (hh) have shown that when the top of the crucible is at a higher temperature than the bottom there is a departure from molecular effusion as pre- dicted by the cosine law with a resultant increase in the contribution of surface diffusion to the total flow. Moreover, if the top of the crucible is cooler than the bottom there is the possibility that the vapor will condense at the orifice of the crucible thus reducing the amount of sample which leaves through it. (d) The area of the evaporating surface and its location must be such that the saturation pressure is maintained within the effusion cru— cible. In addition, the orifice shape and size must be such that not only is the saturation pressure maintained within the crucible, but also that the temperature uniformity within the cavity is not disturbed. Carlson (26) carefully analyzes these problems and discusses previous experimental investigations and attempts (h5,h6) to treat theoretically the problem of vapor saturation within the effusion crucible. (e) The fraction of impinging molecules which stick to the target must be known, and the walls of the vacuum system must condense and retain all effusate striking them so that the target receives material CUIly from the orifice. (f) If the vaporization process is to be followed by weighing the £11~L1c31b1e before and after the vaporization, the volatility of the cruc- ,ple itself must be known and taken into account. 1 - _‘1 22 (g) The physical dimensions of the apparatus must be known accur- ately and allowance made for changes effected by temperature. (h) The molecular weights and relative abundances of the vapor Species must be known. The means by which and the degree to which these various experi- mental requirements were met in the present investigation are discussed later in the text. III. EXPERIMENTAL A. Summagy of the Experimental Approach Thorium dicarbide was prepared by the reaction of graphite with either thorium metal or thorium dioxide. The total vapor pressures of gaseous species containing thorium were determined as functions of temperature by the Knudsen effusion method in which the effusing species were collected on cooled quartz targets in a system of known geometry, and the targets were assayed for thorium by neutron activation techniques. From these data, the parital pressures of Th(g) and ThC2(g) in equi- librium with ThC2(s) were calculated. The vapor pressure data thus determined were combined with the data of Jackson and co-workers (21) who identified the vapor species and determined their relative abundances as a function of temperature using a mass spectrometer. Second and third law calculations were made of the enthalpy and entropy changes accompanying the reactions ThC = ThC 2(3) 2(g) and Th0 = fni + 2c . . 2(3) (g) (graphlte) These data were combined with the measured enthalpy of vaporization of elemental thorium (22) and the standard enthalpy of formation of the solid dicarbide was determined. £3. The Preparation of Thorium Dicarbide 1. Materials Reagent grade thorium nitrate tetrahydrate of 99.9 per cent total arity was obtained from the J. T. Baker Chemical Company, Phillipsburg, 23 I I' I; .' . it 1 I lull} 211 New Jersey, and was ignited in platinum crucibles at 10000 to produce thorium dioxide. Thorium metal powder of 99.1 per cent total purity was obtained from K E K laboratories, Inc., Jamaica, New York. Reac- tion crucibles were fashioned from ultra-high purity graphite obtained from the United Carbon Products Company, Inc., Bay City, Michigan. This graphite was used also in the preparation of thorium dicarbide. 2. Methods of Preparation and Apparatus Thorium dicarbide was prepared by the reaction of thorium dioxide and graphite heated together either as a powder or in the form of pel— lets pressed in a die of ”carborized" steel with a pellet bore of 5/16- inch. Average sample size ranged from 0.5 to 2.0 grams, and pressing at 5,000-10,000 p.s.i. resulted in pellets ranging in height from about 1/8 to l/h-inch. The reactant charge, powder or pellet, was loaded directly into a graphite crucible which had been outgassed previously at about 20000. The crucible, fashioned from 3/h-inch graphite rod, was 1 l/8—inches high and was bored with a reaction well 7/16-inch in diameter and 5/8- inch deep. A graphite lid, fashioned to provide a snug fit over the tapered outer wall of the crucible was drilled with a 50 mil diameter centered orifice to allow gases to escape. A black-body hole hO mil in diameter was drilled.l/h-inch deep into the base of the crucible. Three to mil tungsten legs, B/L—inch in length, force-fitted at 120° intervals around the base into l/h-inch deep holes, supported the cru- cible. The crucible was arranged in a vacuum-system shown schematically in Figure 2. The apparatus consisted essentially of a vacuum system 25 Water VYCOr , Outlet\\\\ {/f_-::\<" Condenser I Crucible ‘\:\‘\ 0 Induction e Coil g Quartz Table—Li-w" ° \ Hr \\ 2. Veeco Ionization Gauge ~\\Water Inlet .ox’ To Rough Pump 9“ and.Helium Tank ‘ ‘<] (> 3-Stage Mercury - Diffusion Pump Prism g§::;:%er Re-entrant Trap ’/,/*T" Cooled by Liquid Nitrogen Figure 2. Schematic diagram of the apparatus used to prepare thorium dicarbide. 26 equipped with a Vycor water—cooled condenser, a support for the crucible and an optical window. A large diameter re—entrant trap cooled with liquid nitrogen was located between the 3-stage mercury diffusion pump and the reaction chamber. The residual pressure in the vacuum system was monitored with a Veeco ionization gauge and could be maintained at about 1 x 10‘7 mm Hg with the crucible cold. The crucible stood on a fused silica table which sat on a Vycor support. The support table was provided with a l/h—inch diameter centered hole and the temperature of the black—body hole in the base of the crucible was measured, from below, with a Leeds and Northrup model No. 8622—C optical pyrometer. The crucible was heated with a 20—kva Thermonic 250-h50 kilocycle in- duction furnace. Thorium dicarbide was prepared according to the reaction: Th02(s) + 1.0 ThC2(S) + 200(7). (graphite) g When the samples were heated in vacuum the pressure within the system increased due to outgassing of the reactant graphite. At about l700°K a high pressure surge which indicated the effusion of carbon monoxide gas due to the above mentioned reaction, occurred within the system. This temperature was maintained until the pressure dropped to l x 10_5 mm Hg or less, whereupon it was assumed that the reaction was complete. The temperature was then increased to above 2000°K for varying lengths of time before heating was terminated. After the crucible had cooled, the vacuum system was opened to the atmosphere and the product was re- nuaved from the crucible and stored under a dry helium atmosphere until j t. ivas used for either analysis or an effusion experiment. The reaction product, a brittle, yellow, metallic appearing, sinter- fl mass, was proved to be thorium dicarbide by both chemical and X—ray 7 10y 27 powder diffraction analyses. In each preparation, chemical analysis indicated the presence of trace amounts ofgnaphite in the product. When the reactants were heated in pellet form, the sample remained in- tact throughout the heating process, although the pellet did expand somewhat in size. For the reaction between thorium metal and graphite, the components were mixed in the desired mole proportions and pressed into pellets, using the technique described previously. A new graphite crucible was fashioned, identical to the one described previously, but with larger overall dimensions. The reactants were heated in vacuum to produce thorium dicarbide according to the equation: Thu) + = T1102“). 2C(graphite) Since no carbon monoxide gas is given off in this reaction it was pos- sible to heat to the desired temperature quickly without encountering gaseous discharge. This product was identical to the one prepared by the reaction between graphite and throium dioxide. Brief descriptions of the individual preparations are given in Appendix A. C. Analysis of Thorium Dicarbide 1. X-ray Powder Diffraction Patterns X-ray powder diffraction photographs of the samples were obtained using Cu Kfi radiation (Tau = 1.5h183) and a Debye-Scherrer X-ray powder camera of llh.59 mm diameter. The samples of thorium dicarbide were gground to a fine powder with an agate mortar and pestle in an inert sitlnosphere and loaded into 0.3 mm diameter Pyrex capillaries. With the exception of one sample, P-lh, which was prepared at a low temperature, the X-ray powder diffraction patterns of all samples 28 indicated the presence of only thorium dicarbide, and in some samples, trace amounts of graphite. When the d values of the X—ray photographs* of the samples were checked against the values on ASTM card No. 5h3—DB for thorium dicar— bide it was found that not all of the lines could be identified. 0n investigation of the d values listed on this ASTM card indicated that the values were taken from the data of von Stackelberg (6) for ”tetra- gonal" thorium dicarbide. It was noted earlier that Hunt and Rundle (7) have shown that thorium dicarbide has a monoclinic structure, space group C2/E. Although Hunt and Rundle reported hkl values they did not list the corresponding d values. Kempter and Krikorian (l2) resolved this problem by converting from the complex monoclinic lattice to the more convenient pseudo—orthorhombic lattice. Starting with the Hunt and Rundle monoclinic parameters they found the pseudo-orthorhombic parameters to be a0 = 10.5552, bo = 8.2338, and co = h.201A. Using these parameters and the monoclinic hkl values reported by Hunt and Run- dle, and, making use of the transformation matrix, monoclinic to ortho- rhombic OHI—i l—‘OO OI—‘I—I d values were calculated for each monoclinic hkl value listed by Hunt and Rundle. Because the X—ray diffraction patterns of all samples except P-lh were identical, only one has been listed in Table III. *In the entire text, "X-ray photograph" refers only to X-ray powder diffraction patterns. .mm-maa .oz come zem< .ooseanum no been AmoOV one mm m undo .o .oHCHHoocoz .n .xuN> n > flmcouum u m nezwcoa u E wxmoz u 3 .m mNa.mNN issuer- .; .. . .moa .ano Han amm.a wwm.a .mmn.mma 2 an mon.a aos.a oNN.moo m ma sOm.H mem.a mam 3: on wmw.a mmm.a mam 3>> as mam.a mam.a Hma.moa 3: mm amm.a mam.a on 3>> ma new som.a amm.a maa.mam m NH smm.a wnm.a moa.ama 3: an mam.a mam.a fine 3: Ha amm.a mmm.a Hma 3 mm mmo.m omo.m mom 2 0H mom.H mom.a cmH 3 mm ooH.m mmo.m Ono a a woa.a o~a.~ www.mmm 32 an mam.m mem.m NHH 3 w o, Nam.a mom.a mmo.mam 3> oN mom.m som.m was 3> a .2 mmm.a wmm.a was 3>> ma mmo.m mmo.m men m o wen oam.m Hmm.m HHH m> m woa.mam oaN.m Ram.m Noo.ooN m: a «mo.a oao.a .ooa.aoo m an mm.m on.m wan m m mao.a Nao.a mmm.amn : RH Rom.m mm.m oANoov 3>> m aaa.a NaR.H maa.aam m: ca mm.m om.m can 3> a Amv.oamoo Amy.nooo base maunncoocH coma va.oanoo va.mooo ease naoamcoocH been .m©OH|< EHHM pom moomecw poemwmm< .HHH oHan g. 0 30 Film A—1068 (sample P—12) was used because it had somewhat sharper lines than other films. The X—ray photograph of sample P-lh (film A-lO77) indicated the presence of both thorium dicarbide and a dominant new phase of cubic symmetry. No ASTM card was available for thorium monocarbide, but Wilhelm and Chiotti (h) have reported a cubic (NaCl-type) structure for ThC with a0 = 5.3h2. Using their data, d values were computed for thorium monocarbide and were found to be identical to those of the cubic phase on film A-lO77. Table IV lists the indices assigned to the lines on this X—ray photograph. 2. Chemical Analyses It was stated in the preceding section that the X—ray photographs of the samples indicated the presence of only thorium dicarbide, and in some cases, trace amounts of graphite. If, indeed, these are the only phases present, the problem of analysis becomes a relatively simple one. The procedure used, in brief, was as follows. A weighed portion of the sample was dissolved in dilute hydrochloric acid, and the free graphite was collected by filtration, dried and weighed. The thorium in the filtrate was precipitated with a suitable reagent and ignited to thorium dioxide for weighing. The combined carbon originally present was calculated by difference. At first, varying concentrations d?efiher nitric and hydrochloric acids were used to dissolve the dicarbide samples. However, it was observed that when nitric acid was employed it was impossible to obtain reproducible graphite analyses; in all cases the amount of graphite ob- tained was higher than expected with a corresponding low result for the mi“ I i .' _ , \ // / / /‘ ' i . ‘1‘ _. \\\~..___, ‘ , .“ ~" 11. : . A I?» ‘ as"! _¥.EI‘ .. - " . ' f*' . . ' 3' I . 9. l, ‘l' I I! _ --" . ' t -- 7 - " \ .1 j L g ,- I , ’5' e‘ . .. \_ 31 Table IV. Assigned indices for film A-1077 a Thc2 ThC Line Intensity dobs.(A) hkl dcalc.(A) hkl dcalc.(X) 1 w 3.25 111 3.29 2 s 3.05 111 2.068 3 w 2.93 111 2.9L0 h s 2.65 . 200 2.658 5 w 1.96 31l,11§ 1.96h 6 s 1.88 220 1.879 7 w 1.76 002,g20, 1.763 221 8 w 1.75 113,311 1.7hh 9 vs 1.60 311 1.603 10 MS 1.53 222 1.53b 11 w 1.h7 222,223 1.168 12 MS 1.33 too 1.329 13 s 1.22 331 1.219 in s 1.19 h20 1.189 a. W = weak, M = medium, S = strong, V = very. 32 combined carbon. It has been observed (A?) that nitrates of the rare earths catalyze the oxidizing power of nitric acid with regard to or- ganic compounds. Furthermore, Sasaki, Ichikawa, Imai, and Uruno (h8) reported that while thorium dicarbide was completely soluble in all concentrations of hydrochloric acid, the solubility in nitric acid was dependent on the acid concentration with a minimum solubility occur- P‘ ring at about 6M nitric acid. For these reasons, all analyses subse- quent to the first three were performed using hydrochloric acid to g hydrolyze the samples. ! The first method used to determine thorium involved precipitation V with oxalic acid. The procedure was as follows: After the graphite had been collected by filtration, the filtrate was heated to the boiling point and an excess of a saturated solution of oxalic acid was added The precipitate was digested for 6-10 hours on a steam bath, filtered, while hot, into a tared alundum filter crucible, and ignited at 10000 to thorium dioxide for weighing. While the precipitation with oxalic acid yielded accurate and re— producible results, a great amount of time was involved in the diges- tion of the precipitate. Since thorium was the only cation present, the use of ammonia as the precipitating agent yielded results which were as accurate and which could be obtained in a much shorter time. The following procedure was adopted and used in the analysis of all samples subsequent to sample P-12. (a) To a weighed sample (0.05 to 1.0 g) in a 250 ml beaker add 100 ml 0.5M HCl and heat for 30 minutes on a steam bath to insure the dissolution of all the thorium not present as thorium dioxide. The 33 combined carbon present is hydrolyzed to gaseous and condensed hydro— carbons while the free graphite remains unchanged. (b) Filter the graphite into a tared filter crucible, dry for one hour at 105°, cool and weigh. Ignite the contents of the crucible for one hour at 10000 to drive off the carbon as carbon monoxide, cool the crucible and reweigh. In this manner any thorium dioxide originally present may be determined in addition to the free graphite. (c) Transfer the filtrate from step (b) to a hOO m1 beaker and add aqueous ammonia until a precipitate forms, about pH6. Heat the sample to the boiling point, add more ammonia to insure complete precipitation, filter the thorium hydroxide, while hot, into a tared alundum filter crucible and ignite the precipitate to thorium dioxide by heating at 10000 for one hour. Cool and weigh the crucible, determining the thor- ium as thorium dioxide. (d) From the original sample weight the amount of combined carbon can be calculated by difference. Analyses were run in duplicate whenever possible, and the precision obtained was t 0.5 per cent. On some samples an additional thorium determination was made by direct ignition of a weighed sample to thor— ium dioxide. Again, agreement in results was always i 0.5 per cent. It should be pointed out that due to the rapid hydrolysis of thorium di- carbide in moist air, care must be taken to keep moisture from the sample before the analysis is performed. D. Effusion Experiments 1. Apparatus The apparatus used in the effusion experiments was similar to the 3h one used by Ackermann, Gilles, and Thorn (h9) for measuring the vapor pressure of uranium dioxide and is shown schematically in Figure 3. Es- sentially, the apparatus consisted of a pumping system, an evacuated Vycor condenser, a support for the effusion crucible, an optical window, and a device for presenting targets to the effusate. Below the target magazine were a magnetically operated fused silica shutter for control- ling exposure times and a magnetically operated tungsten push—rod for ejecting exposed targets into the Pyrex receiver. Again, the crucible was heated with a 20—kva Thermonic high-frequency induction furnace. Three effusion crucibles were used in this research. Crucibles ‘f ,———-———.——., A.” far No. 1 and No. 2, used in experiments A and B, were fabricated from graphite rod and with the exception of the orifice diameters were ident- ical to the one described previously for the preparation of thorium dicarbide. Crucible No. 3, used in experiment C, was made of tungsten and was obtained from the Kulite Tungsten Company, Ridgefield, New Jersey. The crucible was l-inch high with an inner bore of 3/h—inch diameter. Since a small amount of nickel (0.1-0.3%) Was used as a binder in the fabrication of the tungsten crucible, the crucible was heated at 23000 in high vacuum to volatilize the nickel. The crucibles used will be discussed later with the individual effusion experiments. 2. Measurement of Dimensions Equation (21) requires the measurement of three linear dimensions for calculation of the vapor pressure. These dimensions are the dia— meter of the orifice of the effusion crucible, the distance from the or— ifice to the target collimator for each experiment, and the diameter of the collimator. 35 Dewar for Liquid Nitrogen Kovar Seal I 31655 Bottom of Dewar Copper Magazine for Targets Stainless Steel Collimator Pyrex Table E—ga-Sofi Iron Slug NI \J) Quartz Shutter r “(X Receiver for o 0 Water Outlet Exposed Targets : ° 0 o l o d o ~——€rucible Englictlon The quantity Al/TT is approximately constant for all temperatures, and the relationship (26) in which T0 was the observed temperature, was used to calculate true temperatures from the apparent temperatures measured during the experi- ments. The pyrometer correction factor obtained from the data in Table V was applied before the value T0 was substituted into equation (26). The determination of A l/T involved the measurement of relatively small temperature differences at about 15000 and extrapolation to higher temperatures. The calibration was made at 1500° because the pyrometer scale can be read most accurately at this temperature. As an example, the temperature determination for target No. h from effusion experi— ment B is shown in Appendix C. LO Comparisons were made for the effusion crucibles between tempera— tures in the cavity, measured from above, and in the black body hole, measured from below. The temperature difference between the top and bottom was found to change approximately linearly with temperature and the use of a graphite radiation shield to warm the crucible lid was found to reduce greatly this difference. For crucible No. 2, the dif— ference between the top and bottom temperatures was 18.6° at 1900°, but with the graphite shield in place, this difference was reduced to about 5°. The temperature measurement of the tungsten crucible used in experiment C will be discussed later in the text. Effusion exper- iments B and C were carried out with one or more graphite shields around the crucible. The hot effusion crucibles remained at temperatures constant to t 1° over periods up to several hours, except during experiments in which heavy deposition of graphite on the condenser walls occurred at high temperatures. Constant temperatures were attained after the de- posits reached what presumably was constant reflectivity, but a down- ward drift of temperature tended to set in later, perhaps because of absorption of power by the now heavy deposits or because of partial shielding of the effusion crucible from the high-frequency field. Even in these cases readjustment of input power permitted maintenance of temperatures constant to within i 3°. In all target exposures temperatures were measured in groups of four readings to permit determination of temperature with a precision of i 1° for each group, so that any real drift with time could be de- tected. The measurements were repeated frequently enough to give several bl such groups during an exposure. The arithmetic average of all temper- atures was taken as the temperature of the exposure. h. Preparation of Targets Effusate from the effusion crucibles was collected by condensation on fused silica targets. Each l-inch diameter by 1/16-inch thick target was cleaned in boiling, concentrated nitric acid, washed in distilled water, and baked one hour at 600°. When cool, each target was mounted in a 3/8-inch thick aluminum ring (cassette) and held there by a phos- phor bronze Spring. The targets so mounted were stacked in the copper magazine soldered to the bottom of the liquid nitrogen container at the top of the condenser (Figure 3). The angular fraction of the total effusate impinging on a target was defined by the stainless steel collima- tor supporting the stack. 5. Procedure for Volatility Measurements The procedure employed during a given series of target exposures was as follows. The sample was loaded into the effusion crucible, the targets stacked in the magazine and the apparatus Shown in Figure 3 was assembled and evacuated. When the joints were well seated, the system was opened to the atmosphere, the collimator shutter assembly was re- moved and the orifice-to-collimator distance was measured. The system was re-evacuated, the magazine Dewar was filled with liquid nitrogen, and heating was begun when the residual pressure dropped to below 10"6 mm Hg. The effusion crucible was heated to the desired temperature and maintained there for at least 30 minutes to attain a steady state., Then the collimator shutter was opened, the time, read from a Precision Sci- entific Company "Time-It" electrical timer with the dial graduated to h2 0.01 minutes, was recorded and the temperaturelwas measured. When the desired exposure time had elapsed, the shutter was closed, the target was ejected into the Pyrex receiver, the next target fell into place, the temperature was adjusted to a new value, and the cycle was repeated. When a given series was concluded, the crucible was allowed to cool in the high vacuum for several hours before the system was opened. The sample was then removed for chemical and X-ray powder diffraction anal- yses. A series of targets was exposed at successively increasing temper- atures over the range of a given experiment, followed by a series at successively decreasing temperatures. This procedure gave unreproduc— ible temperature-dependent trends only in experiment A. The data from the vaporization experiments are tabulated later. 6. Analysis Targets At the conclusion of an effusion experiment the exposed targets were removed from the receiver, taken from the aluminum cassettes and wrapped in aluminum foil. The targets, together with a set of stand- ards, also wrapped in aluminum foil, were placed in an aluminum can and shipped to the Argonne National Laboratory where they were irradi- ated in the CP—5 reactor for 9 hours at a neutron flux of about 1012 n/cmz/Sec. The reaction of interest was: 232 233 _E;__ 233 - 233 5 Th (n,y) Th 23m > Pa figfi> U (1.6x10 y). 310kev. y The irradiated targets were returned to this laboratory and the 310 kev. gamma rays of the Pa233 were detected with a Model N—22l Hamner single— channel scintillation counter. AB The standards for the neutron activation analyses were prepared in the following manner. Fused silica discs of the type used as targets were cleaned in boiling concentrated nitric acid, washed in distilled water, and baked at 600° for one hour. Next, a known amount of a stan- dard solution of thorium nitrate was placed on the discs which were subsequently evaporated to dryness in a desiccator. (a) Analysis of standard solutions The standard solutions were prepared by aliquot dilution of another standard solution, S—I, containing approximately 1600Y of thorium per tflmvzmnmwKH-M? milliliter. Solution S—I was analyzed by the gravimetric method des- cribed previously and found to contain 1598 Y of thorium per milli— liter. A series of solutions was prepared by aliquot from solution S—1 and then were mixed for at least 30 minutes with a magnetic stirrer to insure homogeneity. These solutions were then analyzed by the Spectrophotometric method described by Fletcher and Milkey (50). This method involved the formation of a 1:2 thorium—morin (5,7,2',h'-flavanol) complex. The procedure recommended by these authors was as follows: 1) To a 50 m1 volumetric flask add 1.0 ml of 0.63M HCl or HN03. 2) Add a known amount of a solution containing 60 Y or less of thorium, free from other ions. The pH of the solution should previously be adjusted to 2.0. V 3 Adjust the volume to 20 ml with distilled water. h) Add 2.0 ml morin reagent (0.lg morin per 100 ml ethanol). 5) Mix well. 6 v Adjust the volume to 50 ml with distilled water, stopper, and mix well. 11 7) Let stand a half hour to attain equilibrium. 8) Using water as the reference solution, measure the absorbance at th mu, using a Beckman Model DU spectrophotometer. The authors claimed the sensitivity range to be 0—60 Y thorium per mil- liliter of solution. A Beer's law plot, absorbance vs. concentration was made and is shown in Figure h. A least squares calculation allowed all points to be fitted to a straight line curve until the concentration reached about 90 Y of thorium per millimeter. At thorium concentrations greater than this the data do not follow Beer's law. The absorbance, the con— centration of the samples as determined from the aliquot, and the concen- tration determined by the Spectrophotometric technique are listed in Table VI. (b) Activation analysis of standard discs In order to test the accuracy of the neutron activation technique for the assay of thorium on effusion targets, a preliminary experiment was conducted. The two solutions used in preparing the standard discs were prepared by aliquot from the original standard solution, S—I, and were analyzed spectrophotometrically. The absorbances, corrected for the blank were; solution A, 0.019, solution B, 0.030. The concentrations, calculated from a least squares treatment of the data listed in Table VI, were; solution A, 3.150 y/ml, solution B, h.936 y/ml. Five standard discs were prepared: Disc 1. 19.3 x 10‘3 ml solution A (6.080 x 10'6 g thorium) Disc 2. 22.37 x10-3 ml solution A (7.0h7 x 10‘s 9 thorium) Disc 3. 27.63>(lO-3 ml solution B (13,638x10_a g thorium) 115 .XoHnSoo cmuoanesfieocu now poan Ina m.nuom .4 madman H£\> ncowpmuocoocoo asmnoch 0.wH 0.0H 0.:H 0.NH 0.0a 0.w 0.0 0.: 0.N 0 _ _ _ _ _ _ _ _ _ 00.0 H0.0 \0 Ln 0 O O O N O O @0.0 m0.0 0H.0 HH.0 NH.0 eoueqaosqv b6 Table VI. Spectrophotometric determination of thorium 1.....- this? “mamaiizihzt... 0.019 3.196 3.150 0.036 5.917 5.910 0.039 6.392 6.397 0.0h7 7.392 7.695 0.058 9.588 9.h80 0.077 12.78h 12.56h 0.092 111.792 111.999 0.098 15.980 15.972 0.112 l8.h90 18.2h5 0.118 19.176 19.219 0.197 31.960 32.0hl h? Disc 1. 27.19 x 10‘3 ml solution B (13.121 x io'Bg thorium) Disc 5. Blank. The standard discs were wrapped in aluminum foil, shipped to the Argonne National Laboratory for 9 hours irradiation at a neutron flux of 1012 n/cmZ/sec and returned to this laboratory where the ganmaractivity was followed for three weeks. The activity ratios observed by counting the gamma-activity of the discs, and the standard deviations, together with the expected values are listed in Table VII. gm...__x ”Ia-u The amount of thorium found on discs 1 and 3, based on disc 2 con- taining 7.0h7 x 10_8 g were: Disc 1. 6.0uo x 10‘6 9 Disc 3. 13.551 x 10‘6 g. The differences between these amounts and the amounts expected were 0.26 and 0.6h per cent for discs 1 and 3, respectively. From these results it was concluded that this technique would yield an accurate and sensi— tive determination of the thorium on the effusion targets. Deposits on the discs were thin enough so that absorption effects were negligible. It should be pointed out that the discs had to be removed from the aluminum foil wrapping before they were counted because the aluminum foil was found to have a much higher initial activity than the discs themselves. Table VII. 18 Activity ratios observed and expected for standard discs No. Days Since Activit Ratios Corrected for Background and Blanka Irradiation Disc 2 Disc 1 Disc 3/Disc 1 Disc 3/Disc 2 5 0.890 2.131 2.397 6 1.110 2.016 2.011 7 1.267 2.188 1.726 10 1.101 2.165 1.916 11 1.112 1.880 1.617 12 1.168 2.361 2.022 13 1.162 2.320 1.995 11 1.259 2.398 1.905 17 1.261 2.516 1.990 18 0.928 2.058 2.216 19 1.708 2.269 1.328 21 1.059 1.909 1.801 21 1.162 2.262 1.917 25 1.013 2.030 1.951 Mean Ratios _17162_: 0.186 2.181 t 0.181 1.923 t 0.211 Expected Ratios 1.159 2.213 1.935 a! Disc 1 was dropped and discarded. IV. RESULTS AND DISCUSSION A. Convention Chosen for the Expression of Results of Effusion Experi- ments Use of the Knudsen effusion technique to determine the temperature dependence of the total volatility of a given substance when combined rs. 1‘1 - , with the use of the mass spectrometer can provide data more reliable ; 1 than that obtained from the latter alone as well as results impossible 1 to obtain by the former alone. For example, assume that some binary compound AB evaporates by the two processes b AB = AB (8) (g) and AB = A + B . (S) (g) (g) A precise effusion study in which the total rate of effusion of solid AB is determined as a function of temperature would give at each temper- ature an "effective pressure" PB calculated from equation (21): PE = PAB + FAVMAB/MA' (27) Here PAB and PA represent the partial pressures of AB molecules and A atoms in the effusion crucible. It was pointed out previously that Jackson and co-workers (21) in their mass spectrometric investigation of the vaporization of thorium dicarbide observed that the principal reactions were: ThCZ(s) = ThC2(g) and T = + . . hC2(s) Th 2C1graphxte) b9 50 The convention chosen here was to calculate "effective vapor pres- sures" PE from the gamma—counting data for each experimental measurement by the assumption, for convenience, that the vapor had the average molec- ular weight 256.0603, that of thorium dicarbide. The gamma—activities of the targets were converted to the equivalent weights of thorium di— carbide that would give rise to these activities, and these weights and the above molecular weight were inserted into the effusion equa- tion (21) to obtain values of P It follows from equation (27) that E' the "effective pressure" PE is related to the partial pressures PTh of thorium atoms and PThC of thorium dicarbide molecules by the equation: 2 PE = PTth + PTh‘VMrhcz/ MTh. (28) This choice of convention seemed justified for the following rea- sons: First, because PE is directly related to the rate of evaporation of thorium dicarbide through equation (21); second, P is a function E easily compared with P and P - in plots of the data; third, since Th ThCZ PE amounts to a fair approximation of the total pressure of vapor species in equilibrium with solid thorium dicarbide, a graph of log PE against 104/T is a convenient reference for quick comparison of the total volatilities of thorium dicarbide and other refractory compounds The determination of PTh and P from P will be discussed later. 2 ThC E B. Individual vaporization Experiments 1. Experiment A The thorium dicarbide used in this experiment was in the form of a 0.817 g pellet which had been annealed by heating it in a graphite crucible in vacuum at 22l6°K for 90 minutes. The pellet was placed in 51 a graphite effusion crucible which was arranged in the vacuum system. The system was heated for 2 hours at 1915°K to aid in attaining a low initial residual pressure, 1.9 x 10.6 mm Hg. A total of eleven targets were exposed with individual exposures ranging from 60 to 200 minutes. The first five targets were exposed at successively higher temperatures and the next five at successively lower temperatures. Target No. 11 was "exposed" at 2123°K for 60 minutes with the shutter closed to determine the efficiency of the shutter in shield- ing targets. Target No. 5 jammed in the collimator and it was necessary to open the vacuum system and eject it manually. It was not thought necessary to remeasure the orifice-to—collimator distance as only the shutter assembly had been moved. The system was re-evacuated to l x 10'.6 mm Hg and the remainder of the targets were exposed. A chemical analysis was not performed before the experiment. An- alysis of the residue after the vaporization showed the stoichiometry to be ThC1.989. The X-ray photograph of the residue (film A-1039) in- dicated the sample to be ThCz. A series of standard solutions of thorium nitrate was prepared and analyzed spectrophotometrically and standards for the neutron activation analysis were prepared as described in section D-6, Chapter III. The amount of thorium on these discs was as follows: Disc 1. 13.837 x 10—8 9 Disc 2. 18.225 x 10—5 9 Disc 3. 26.971 x 10‘8 9 Disc 1. 31.208 x 10‘6 9 Discs 5 and 6. Blanks. A.- 3 “- 3.“.QL [I‘m ‘ “'ET" i J ""1 52 The standard discs together with the targets were wrapped in aluminum foil and sent to the Argonne National Laboratory for neutron activation. After the irradiation, the amount of thorium on the standard discs, based on disc 1 containing 13.837 x 10_5 g, was found to be: Disc 2. 18.258 1 0.006 x 10-5 9 Disc 3. 26.969 t 0.101 x 10-3 9 Disc 1. 31.205 1 0.070 x 10'9 g. Target No. 11 which had been "exposed" with the shutter closed was found to have no gamma—activity above background, indicating that the shutter did indeed protect the targets from the effusate. When the values of log PE were graphed against 104/T for the ten effusion targets the first three points were found to lie above the curve. This was believed due to the initial formation and vaporization of the gaseous species Th0. Darnell, McCollum, and Milne (22) in their investi- gation of the vaporization of thorium metal observed the occurrence of initial high pressures due to the formation of this species which has a higher vapor pressure than thorium metal. They reported that as heat- ing continued the pressure dropped because there was no longer suffic- ient oxygen in the system to form this species. Jackson and co-workers (21) also reported that they observed an initial occurrence of gaseous Th0 and that this species disappeared with prolonged heating. The data for targets No. 1 through No. 10 are presented in Table VIII, in which "effective pressures" PE were calculated in accord with the previously outlined convention. A least squares equation of log PE as a function of reciprocal temperature permitted the calculation of the following values for the heat and entropy of vaporization, from the slope 53 Table VIII. Data for experiment A Exposure Temperature Exposure Time Th Collected PB No. (0K) (mm) x 105(9) (atm) A-1 2120 120 5.210 8.580 x 10'9 1 1-5 2505 120 17.900 2.983 x 1o"6 A-6 2175 120 13.136 2.185 x 10'8 = 1-7 2357 120 1.931 3.126 x 10‘9 A-8 2291 120 0.397 6.327 x 10‘10 H A-9 2195 121 0.133 2.051 x 10‘1o A-lO 2123 188 0.032 3,111 x 10‘11 Al/T : 0.1123 x 10'4 Orifice diameter : 1.01775 i 0.0218 mm at room temperature 1.05111 mm at exposure temperature Orifice-to-collimator distance : 11.582 cm Collimator diameter : 1.90751 i 0.0019 cm ' IIIII 51 and intercept, respectively: AH 188.85 kcal/mole, and AS 11.06 e.u. 2. Experiment B This experiment was designed primarily to determine whether the composition of the condensate was time dependent by studying the vola- tility as a function of time at a constant temperature. For this ex- periment, two 1.5 g pellets were pressed from the same mixture of graphite and powdered thorium and heated together to produce thorium dicarbide. These pellets were annealed together at 2173°K for 2 hours. One pellet was analyzed before the vaporization experiment and the stoichiometry was found to be ThC2.oe- According to the data of Kemp- ter and Krikorian (12) such a stoichiometry is unlikely. The amount of combined carbon present was calculated by difference and probably the excess weight which led to the high value for the combined carbon was due to oxygen. If the sample contained only 0.1? weight per cent oxygen, present in solid solution, the overall formula would be ThC109800.03. This sample was found to contain 11.2 weight per cent excess free carbon. The second pellet was used for the effusion experiment. After the system had been assembled and the dimensions measured, the sample was heated at 2100°K for 2 hours in an attempt to reduce the residual oxygen activity. Seven targets were exposed; the first four at 2333°K for times ranging from 290 to 600 minutes. The remaining targets were exposed at higher temperatures. For the first four eXposures a graphite radiation .n-nr—q—r‘ ‘1. ‘ 1 L I '3‘ 1' III!- 1‘ kw a ‘3; _— SS shield was placed around the crucible. After these targets had been ex- posed, the system.was opened to the atmosphere, a second graphite radia- tion shield was placed over the first, the system was again evacuated, and the orifice-to-collimator distance was remeasured. At the exposure temperature for target No. 7 (25850K) gaseous discharge occurred within the system, probably due to the volatilization of carbon monoxide gas from the crucible itself. When the system.was opened the orifice of the crucible was found to have become clogged with graphite, indicating a fairly large temperature gradient across the crucible, even with two radiation shields in place. There was a very heavy deposit of graphite on the walls of the condenser. Some of this graphite may have come from the sample since analysis of the residue after the vaporization showed the stoichiometry to be ThC1.90 with the excess graphite reduced to 0.86 weight per cent. It is more likely, however, that the deposit came from the crucible which apparently had not been outgassed at a high enough temperature. The change in the stoichiometry of the sample to ThC1,9° was probably due to the removal of oxygen from the system and the formation of a more pure dicarbide. X-ray photographs of both the starting material and the residue (films A-1078 and A-1079, respectively) were identified as being char- acteristic of the phase ThCZ. A series of standards for the activation analysis was prepared as described for experiment A. The amount of thorium on these discs was as follows: Disc 1. 10.183 x 10'8 9 Disc 2. 10.183 x 10"8 9 Disc 3. 73.703 x 10’8 g 56 Disc 1. 77.550 x 10'” 9 Discs 5 and 6. Blanks. As before, these standard discs were wrapped in aluminum foil and ir- radiated together with the effusion targets for this experiment. Stand- ard disc 3 was broken and discarded. The amount of thorium on standard discs 2 and 1, based on disc 1 containing 10.183 x 10-39 was found to be: kc. Disc 2. 10.136 1 0.21 x 10'8 g E Disc 1. 77.666 1 0.16 x 10‘8 g. E When the values of log PB were graphed against 1/T it was observed E: that three of the exposures at 2333°K resulted in virtually the same % measured "effective pressures" while the value for the fourth exposure was somewhat lower. A least squares calculation of log PE as a function of reciprocal temperature indicated the heat and entropy of vaporization to be: AH = 176.20 kcal/mole, AS = 35.62 e.u. These values were lower than those calculated for experiment A. It was pointed out above that the orifice was found to be clogged with graphite after exposure No. 7. It is probable that this clogging of the orifice was a gradual process, and if so, failure to take into account the re— duced orifice area in equation (21) would indeed lead to low calculated pressures, and hence, a lowering of the values of the slope and inter— cept of the curve. With this thought in mind it was decided that the composition of the condensate probably did not change with time at a given temperature. 57 The data for this experiment are presented in Table IX. When these data are compared with those for experiment A it is apparent that the initial heating at 2100°K had eliminated or at least reduced the problem of formation and vaporization of the species Th0(g). However, the heavy deposition of graphite on the walls of the condenser and the gaseous discharge which occurred at 2585°K indicated the need for a different crucible material if the temperature range was to be extended beyond 2500011. 3. Experiment C For this experiment it was decided to use a tungsten crucible in an attempt to extend the temperature range. The crucible was described previously, in Section D, Chapter III. Although the crucible was pro- vided with a tungsten lid, the lid did not fit snugly and a new one was fashioned from molybdenum. The crucible and lid were outgassed in vacuum at 20000 for 2 hours to volatilize the nickel binder. A heavy deposit of nickel formed on the condenser walls and the orifice in the lid clogged; The crucible was further heated in vacuum, with no lid in place,at 22000 until no more deposit was observed to form on the condenser walls. Another lid was fashioned, this time of tantalum, and the crucible was heated at 20000 for one hour with the tantalum lid in place. Only a slight deposit formed on the walls of the condenser and the orifice appeared to remain unchanged. A graphite cup, with the same inner bore as the pellet press, 5/16-inch, was machined so that it fit snugly into the crucible, and the crucible with tantalum lid and graphite cup in place, was heated in vacuum at 21000 for one hour. Again, no change in the orifice was apparent. \ \h— and I ”I; . ' fill. 1. 11'! . .' ‘ q 1 v1- -«.~ »~ I S “‘~ .. =‘A“.9,su."~ r “1. “"1." I n ' 'II 58 Table IX. Data for experiment B Exposure Temperature Exposure Time Th Collected PE No. . (0K) (min) x 108 (9) (atm) B—l 2333 600 2.107 2.082 x 10‘9 B-2 2331 300 1.205 2.081 x 10'9 B-3 2331 300 1.111 1.971 x 10‘9 B—1 2331 290 0.900 1.610 x 10'9 B-5 2186 180 6.907 2.069 x 10'8 B-6 2516 270 11.522 2.917 x 10’8 Al/T : 0.0901 x 10‘4 Orifice diameter : 0.63525 i 0.0112 mm at room temperature 0.63931 mm at exposure temperature Orifice-toscollimator distance : 11.515 1 0.007 cm for targets 1 to 1 11.533 i 0.011 cm for targets 5 and 6 Collimator diameter : 1.90751 i 0.0019 cm. 59 Because the crucible was not fitted with leg holes in its base it was placed on a stand fashioned from 15 mil sheet tantalum with three 60 mil tantalum legs spot-welded to the base at about 1200 intervals. However, because of the weight of the crucible, this assembly proved to be unstable, the crucible falling off the stand if too large a voltage increase was applied to the coil. A new support assembly was fashioned and is shown schematically in in Figure 5. Both the graphite block and the boron nitride table were provided with l/1—inch holes drilled through the centers to allow measure- ment of the temperature of the crucible base with an optical pyrometer. The graphite block stood on three 60 mil tantalum legs, 1 l/1-inches long, force-fitted at 120° intervals into l/1-inch deep holes drilled into the base. These legs were in turn force-fitted into three ident— ical holes in the top of the boron nitride table. This assembly proved to be stable regardless of the power increases applied to the coil. Because there was no black body hole in the base of the crucible the vacuum system was provided with both top and bottom optical window and prism assemblies and a temperature calibration experiment was con- ducted in which the temperatures measured for the crucible orifice (black body hole) were compared with the apparent base-temperatures. The difference between top and bottom temperatures was found to vany linearly with the temperature and a least squares fit of the data showed the slope and intercept to be 1.00811 and —l.61955°C, respectively. The graph of top temperature against bottom temperature is shown in Figure 6. During the effusion experiment the apparent temperature of the crucible base was measured and corrected to the cavity temperature. 60 ... Tl—C’iAvfi 1' Ta Lid Tungsten Crucible ———————AGraphite Cup Graphite Block Three 60 mil Ta Legs Boron Nitride Table Quartz Support for Crucible Figure 5. Schematic diagram of crucible support assembly for experiment C. 2200 88% 2° Top (true) Temperature 0C PETS 88§8 ‘8 61 TOP: Al/T = 0.0817 x 10‘4 BOTTOM: Al/T = 0.0761 x 10‘4 l I l J l l l l I l 1300 1100 1500 1600 1700 1800 1900 2000 2100 2200 Apparent Bottom Temperature °C Figure 6. Temperature calibration curve for experiment C. 62 Two 2.0 g pellets were pressed from the same mixture of thorium and graphite powders and were heated together to prepare thorium dicarbide. The pellets were annealed at 2275°K for 2 hours. One pellet was analyzed chemically before the vaporization experiment and the stoichiometry was found to be ThC1.993 with 0.87 weight per cent excess free carbon. The second pellet was used for the experiment. 5— After the system had been assembled the crucible was heated at 2100°K for 3 hours to reduce the residual oxygen activity. A graphite radiation shield, which had been used during the temperature calibration experiment, was placed over the crucible lid. Twelve targets were exposed with individual exposure times ranging from 111 to 300 minutes. Targets were exposed at successively higher temperatures until the maximum temperature was attained, and then at successively lower temperatures until the target magazine was empty. Fbur of the targets were used to test for total condensation of the effusate on the targets. The results of these "bounce check" experi- ments are discussed later in the text. Although a deposit of graphite formed on the walls of the condenser, it was not as heavy as those formed when graphite crucibles were used. Analysis of the residue indicated the stoichiometry ThCZ,0° with 0.71 weight per cent.free carbon. X-ray photographs of both the start- ing material and residue (films A-1203 and A-l201, respectively) were identified as being characteristic of thorium dicarbide. A series of standards for the activation analysis was prepared and the amount of thorium on these discs was: Disc 1. 1.327 x 10‘3 g Disc 2. 2.221 x 10‘s 9 63 Disc 3. 2.196 x 10'6 9 Disc 1. Blank. These standards together with the targets were irradiated as before. The amount of thorium on discs 1 and 2, based on disc 3 containing 2.196 x 10'6 g was found to be: Disc 1. 1.332 1 0.067 x 10'6 9 Disc 2. 2.287 1 0.116 x 10‘6 g. The data for this experiment are listed in Table X and a least squares treatment of the values of log PE graphed against reciprocal temperature indicated the heat and entropy of vaporization to be: AH = 188.11 kcal/mole AS = 10.93 e.u. 1. Spmmary of the Determination of Effective Pressures The graph of the values of log PE against 104/T for the three vapor- ization experiments is shown in Figure 7. A least squares treatment of the data leads to an "effective heat of vaporization" of 185.10 t 3.15 kcal/mole, and the log of the "effective pressure" P as a function of E temperature is given by the equation: log PE(atm) = - §9&12%£31l11 x 104 + 8.712(: 0.301). (29) The determination of the values of the partial pressures P and P Th ThCZ in equilibrium with solid thorium dicarbide is discussed later, in Section C. Table X. 61 Data for experiment C Exposurea Temperature Exposure Time Th Collected PB No. (0K) (min) x 108 (9) (atm) c-3 2210 180 0.326 3.652 x 10'10 c-1 2321 180 1.118 1.618 x 10‘9 F“ c-5 2359 180 2.687 3.092 x 10‘9 i 0.6 2151 180 12.391 1.151 x 10‘8 c-7 2198 120 16.206 2.878 x 10‘8 :p_ c-8 2130 120 5 .670 9. 932 x 10“9 51 c_9 2368 120 2.071 3.587 x 10’9 c—12 2257 120 0.303 5.000 x 10‘10 A 1/T : 0.0761 x 10'4 Orifice diameter : 0.93555 t 0.013 mm at room temperature Orifice-to-Collimator distance : 0.93658 mm at exposure temperature Collimator diameter : 1.90751 1 0.0019 cm 10.62375 1 0.0096 cm aExposures l, 2, 10 and 11 were used in testing for total conden- sation of the effusate on targets and the results are described elsewhere. Logarithm of Effective Pressure, Log PE (atm) 65 Temperature OK 2500 2190 230,0 2 20? 5'30 O 1 X -9J3- [1 X \x £1 -10.0"' A Experiment A C) Experiment B x Experiment C b 15 -11.0 I l L l J I I I 1.0 1.1 1.2 1.3 1.1 1.5 1.6 1.7 Reciprocal of Temperature, 104/7 (deg '1) Figure 7. The effective vapor pressure of thorium dicarbide as a function of reciprocal temperature. 66 5. Conditions Related to the Measurement of Vapor Pressures (a) Crucible Materials The materials used for the construction of effusion crucibles must have certain characteristics before good measurements can.be made with them. Among the necessary properties are low volatility, tightness with respect to leaking, and chemical inertness to the sample. Both P- graphite and tungsten can be heated inductively and both retain their E mechanical strength over the temperature range of this study. In all three vaporization experiments, chemical analyses and X-ray photographs of both starting materials and residues indicated no reac- F tion between the crucible and the sample. The only change detected in the sample, whether heated in graphite or tungsten crucibles, was that the percentage of free carbon in the sample was lower in the residue, as would be expected. While a more complete study would be required to prove noninteraction, it was concluded that the effect of chemical interaction between the sample and the crucible, if any, was within the limits of experimental precision. The heating of the thorium dicarbide samples in graphite crucibles quite often resulted in a heavy deposit on the walls of the condenser below the level of the effusion crucible orifices. When this deposit could be identified it was found to be graphite. This deposit severely limited the temperatures which could be attained because with the ac- cumlation of a large deposit, there was a corresponding danger of breaking the condenser. In all experiments a light deposit, presumed to be graphite, formed on the targets. It is not known whether this deposit came from the surface of the lid or diffused through it (or the orifice) from the interior of the crucible. It is unlikely that it came from the surface of the lid since such a phenomenon would lead to 67 an increase in the orifice size and in those instances in which the orifice size did change it was observed to become smaller. If the graphite diffused through the lid, it would seem possible that this material flow could disturb the equilibrium conditions within the cru- cible. However, the agreement between the results of experiment A, with- out a radiation shield, and experiment B, with radiation shields, shows any effect to have been outside experimental prescision and hence un- detected. 7 The heavy deposition which formed on the walls of the condenser when graphite crucibles were used led to the use of a tungsten crucible v in experiment C. Unfortunately, the induction furnace was not operat- ing properly and it was impossible to appreciably extend the tempera- ture range studied. (b) Test for total condensation It is necessary, in the calculation of vapor pressures from amounts of effusate collected on targets, that any departure from total conden- sation be taken into account. At the outset of this research, quantita- tive condensation was expected because of the use of well-cleaned tar- get surfaces and the relatively low target temperatures, especially since the backless cassettes would permit radiation of heat in the vertical direction. The procedure used to test for incomplete condensation was as fol- lows: A hole was drilled through the centers of both a fused silica target and a circular 5 mil platinum disc of the same diameter, and both were placed in the aluminum cassette with the platinum disc below the fused silica target. By this arrangement, some of the effusate could pass through these targets and strike the target next above in l ": I .1- . h 1 ‘13! *5 - .15. .m-J‘J‘ - -.-'__ -. 68 the magazine. If reflection occurred, some of the reflected molecules 'would strike and stick to the lower fused silica target. The platinum disc protected the lower fused silica target from receiving effusate directly. Two such condensation tests were performed in the course of experiment C. The first was conducted at 2235°K and the lower targets had 0.096-inch diameter holes. The second was conducted at 2361°K and the holes in the lower targets were 0.037-inch in diameter. In both cases, activity was detected on the lower target. At 2235°K this ac- tivity was 1.93 per cent that of the upper target, and at 23610K, 2.22 per cent. The conclusion was that, although "bouncing" of effusate from the targets occurred to a detectable extent, and therefore constituted a small systematic error in the calculated vapor pressures, allowance for this in the final calculations did not seem to be justified. (0) Change in dimensiops with temperature Orifice diameters measured at room temperature were corrected for the expansion due to temperature by use of the values (28) 5.33 x 10-6 deg.1 for the mean linear expansion of tungsten and 3.1 x 10.6 deg-1 for graphite between 0 and 20000. Increase in the length of the effusion crucibles was calculated to be 0.16 and 0.3 mm for graphite and tungsten, respectively. Shrinkage 0f the copper magazine when the Dewar was filled with liquid nitrogen was calculated to be about 0.5 mm with the effusion cell cold. This effect must have been less with the effusion crucible hot since radiation from the crucible may have raised the target temperatures several hun- dred degrees. 69 For the calculation of PE’ the room temperature orifice-to-collima- ; tor distances tabulated with the other experimental data were used. The resultant error is a small systematic one tending to raise the measured pressures of high temperatures more than those at low temperatures. The uncertainty in the orifice-to-collimator distance was estimated to be about i 0.02 cm, an error of about t 0.2 per cent. At liquid nitrogen temperature the decrease in the diameter of the stainless steel collimator was calculated to be about 0.6 mm, and at 8000 the increase was calculated to be about 0.2 mm. The actual temperature was probably nearer room temperature than either of these and the room temperature value was used in the calculation of pressures. The esti- mated uncertainty due to this systematic error was i 0.1 mm, approx- imately 0.5 per cent. C. Treatment of the Data 1. Calculation of PTh and PThCZ fromPB Jackson and co-workers (21) who studied the vaporization of thorium dicarbide mass spectrometrically observed that the two principal reac- tions are ThC = ThC 2(S) 2(g) and Th = . . CZ(s) Th(g) + 2C(graphite) It is necessary that we have some method of converting the measured "effective pressures" PB into the partial pressures of ThC2(g) and Th res ectivel . (g): p y The use of the mass spectrometer as a detector for the molecular beam effusing from a Knudsen crucible is basically as follows. The Sum-“L 'm . sq f1 .3“ an n» ‘ 70 effusing molecules pass through collimating slits and some are ionized, usually by collision with an electron beam. The resulting ions are ac- celerated electrostatically as an ion beam from the ionization region into an evacuated space where the beam is resolved by magnetic deflec— tion or drift time into components whose ions are characterized by dif- ferent charge-to—mass rations. Assume, for simplicity, that all ions are singly charged molecules or atoms which are formed in the effusate without changes in formula. Then the ion current ngdue to the species of molecular weight M1 is related (51) to the partial pressure pi of the corresponding molecules of kind i in the effusion crucible at tempera- ture T by the equation: + IiT - GDiO'ipi. (30) Here Gi is a constant determined by the physical dimensions of the system and the ionizing beam intensity. D1 is the efficiency of the ion detector for ions of molecular weight Mi and CF, is the cross sec- tion or efficiency of ionization for molecules i when bombarded with electrons of the particular energies used. From equation (30) it follows that at any temperature P + ThC . (ThC IThC Z 2 = ...;_Z . (31) P 16’ Th Th ITh Rearrangement and substitution into equation (28) gives, P = . (32) _ .3 :MQtIx-A an... ; a! w .7II' -'—’I " 71 Hence, 6’ 1+ a‘ MT log PTh = log PE + log —¥:§92 — log .2292. + 153292 hcz (33) “'Th 1Th Th lqh and + I G" ThC ThC = __L .— ._.__2 log PThCZ log PTh + log 1+ log q-Th . (31) Th Jackson and co-workers reported values of log (I+ /I+ ) as a ThCz Th function of temperature and a least squares treatment of their data allowed the calculation of IThC /1Th at any temperature in the range 2 studied. These authors reported the values of cr and 0' as 89.5 Th ThCZ . + + and 97.8, respectively. The values of IThCZ/ ITh and G—ThCZ/GTh so obtained and the values of PB determined in experiments A, B, and C were substituted into equations (33) and (31) and the values for PTh and PThC 2 were obtained for these experiments and are listed in Table XI. When the values of log PTh and log PThCZ are graphed against 104/T, equation (6) relates the slope and the intercept to the heats and the entropies of the vaporization processes, respectively. The graph of log PTh against 104/T for the reaction ThC2(s) = Th( + g) 2c(graphite) is shown in Figure 8. The graph of log P against 104/T for the ThCz reaction ThC2(S) = ThC2(g) is shown in Figure 9. The results of a least squares treatment are: For the reaction 72 Table XI. PTh and PThCZ from experiments A, B, and C. Biposure Temperature 104/1.OK PTh PThC NO ’ (0K) (atm) (atm A-lO 2123 1.710 1.803 x 10’11 1.218 x 10‘11 A-9 2195 1.556 1.120 x 10'10 8.793 x 10‘11 c-3 2210 1.161 1.911 x 10‘10 1.639 x 10‘10 c-12 2257 1.131 2.581 x 10'10 2.288 x 10’10 A-8 2291 1.361 3.168 x 10'10 2.997 x 10'10 C-1 2321 1.309 7.898 x 10‘10 7.882 x 10‘10 B-l 2333 1.286 9.961 x 10‘10 1.017 x 10’9' B-2 2331 1.281 9.965 x 10'10 1.019 x 10'9 B-3 2331 1.285 9.113 x 10‘10 9.616 x 10‘10 B-1 2331 1.281 7.113 x 10'10 7.610 x 10’10 1-7 2357 1.212 1.117 x 10'9 1.573 x 10'9 c-5 2359 1.210 1.160 x 10“9 1.559 x 10'9 0.9 2368 1.222 1.679 x 10"9 1.823 x 10‘9 A-1 2120 1.133 3.839 x 10"9 1.516 x 10'9 c-8 2130 1.116 1.106 x 10‘9 5.301 x 10’9 c-6 2151 1.076 6.316 x 10'9 7.906 x 10‘9 A-6 2171 1.011 9.311 x 10’9 1.206 x 10'8 B-5 2186 1.023 8.658 x 10‘9 1.117 x 10'8 c-7 2198 1.001 1.203 x 10‘8 1.615 x 10‘8 A-5 2505 3.992 1.238 x 10'8 1.681 x 10'8 B-6 2516 3.971 1.188 x 10‘8 1.612 x 10‘8 ~8.0 , Log PTh (atm) l \0 O -10.0 Logarithm of Partial Pressure -ll.0 73 Temperature, 0K 953m 990 2390 22:0 <30: bi X‘A ‘\\\\\\x‘ x ZS X \X A ExperimentA A (3 Experiment B x ExperimentC 13 I 1 I I l J l l ‘ 1.0 1.1 1.2 1.3 1.1 1.5 1.6 1.7 Reciprocal of temperature, 104/T (deg'l) Figure 8. The temperature-dependence of the partial pressure of thorium vapor in equilibrium with solid thorium dicarbide. Temperature, 0K 2500 2100 2300 2200 l I 1 l A -8.0 I" a +3 :3 "u of” _ U) .3 . ”~11 N u a -900 I— K 0 $4 0.. H .2 4: 1- A m 0. 9+ ’g\\x O E 40.0 ._ A Experiment A A g (3 Experiment B E" X Experiment C £5 “11.0 I l I I I I I I ’ 1.0 1.1 1.2 1.3 1.1 1.5 1.6 1.7 Reciprocal of Temperature, 104/T (deg-1) Figure 9. The temperature-dependence of the partial pressure of thorium dicarbide vapor in equilibrium with solid thorium dicarbide. 75 ThCZ(s) = This) * 2C(1111mm) AHggg - 176.92 1 3.30 kcal/mole, A5395 - 31.19 1 0.61 e.u. For the reaction ThC2(S) = ThC2(g) AHZQB = 196.21 1 3.30 kcal/mole, 15298 = 12.81 i 0.72 e.u. A least squares solution for the two vaporization reactions, as- suming that ACP = 0, leads to the following expression for the vapor pressure of each species in equilibrium with solid thorium dicarbide: For 111(9), log P(atm) “2% + 7.537(i 0.3062), (35) For ThCZ(g), log p =_.121887%i721.7) (atm) + 9.355(to.3063). (36) From the reported (22) value for the enthalpy of vaporization of thorium metal and the enthalpy listed above for the dissociation reac- tion, the standard enthalpy of formation of solid thorium dicarbide was determined to be Ahgga = - 10.32 t 3.33 kcal/mole. 2. Calculation of Free Energy Functions It was shown in the preceding section that the principal reactions involved in the vaporization of thorium dicarbide are ThC2(S) = ThCZ(g) and ThCZ(S) = Th(g) + 2C(graphite)' We can check the second law values of the enthalpies of vaporization and dissociation obtained from the slope of a graph of log P against l/T by means of a third law calculation based on the equation 76 . 11 - 12.. The necessary free energy functions for ThIg)’ ThC2(g), ThC2(s), and C . are tabulated in Table XII. The thermodynamic functions (graphite) H2 - H398 are listed in Table XIII, and the values of s? for these species are listed in Table XIV. These functions were obtained as . described below. (a) ThE 2 The thermodynamic functions were interpolated from the tabulation of Darnell, McCollum, and Milne (22). (b) Graphite Thermodynamic functions were taken from Stull and Sinke‘(21).X‘ (c) ThCZ(s) The following values of 8298 and C; used in calculating thermo- dynamic functions for ThC2(S) have been estimated by Krikorian (52): 5395 = 15.1 i 3 e.u., and 0° = 12.60 1 1.16 + (2.0010.18) x 10’3T - (2.6210.20) x 105/‘rZ P cal/deg-mole. The calculations of the thermodynamic functions follow from the relation- ships: 0 o T HT ‘ H298 = C CIT, (38) 298 P o o ‘JPT S = S + C dlnT T 298 298 p 3 (39) and o o o o F‘ ' H298 PH~' H290 T (——=f——) = (——T—-) S; - f (10) 40.5 w4.mm ma.mm m2.mm mz.mfl ©m.OH w©.w: OOwN aw.o am.mm mc.mm mm.ms H:.dH mH.oH 0m.w: OONN mo.o ma.mm NH.Nm mm.ma mm.mH mm.m Hm.mq 00cm om.o as.mm oc.Hm so.ws mm.ma ac.m mfi.w: 00mm mm.c s:.mm co.Hm mm.aa 4H.ma mm.m mm.as ooam 7 7 2 a omam mom 8.: moi 2a 2.3 88 mm.m am.Hm am.mm m:.o~ oo.mH mm.m wq.sa ooNN .a m m a a 9 Hence a ooh a 61> a means a a c- a c- A e TIL- Ale- Ale- TIC- 23. N -a -a -9 -a -9 -a -a - oaom oa cam: om oswm ca oamm on we on mm 61 we oa tongue oHosumoM\Hmo uncompoczm xmpoco comm .HHx ofinme Table XIII. Thermodynamic functions, H; - 78 H395, cal/mole Tempigature ThCZ(g) ThC2(s) Th(g) C(graphite) 2200 26281 27956 13332 9715 2300 27752 29661 11191 10360 2100 29217 31386 15018 10980 2500 30686 33132 15900 11600 2600 32160 31898 16610 12230 2700 33631 36681 17388 12860 2800 35105 38191 18200 13500 Table XIV. values of 8%, cal/deg-mole. Tippirature ThC2(g) ThCZ(s) Th(g) C(graphite) 2200 88.12 12.65 58.00 10.35 2300 89.09 13.10 58.37 10.63 2100 89.70 11.11 58.71 10.89 2500 90.31 11.85 59.07 11.11 2600 90.89 15.51 59.38 11.39 2700 91.11 16.22 59.68 11.63 2800 91.97 16.87 59.98 11.86 79 (d) ThCZE ) (l) Translational The translational contributions were calculated in the usual manner using the following equations (53,51): 13° H0 T ' o " (‘—T——) = “15 19M + 25 lnT) — 7.283 cal/deg, (11) S? = R(l-5 lnM + 2.5 lnT) - 2.315 cal/deg, (12) E -_ (H? - H8) = 2.5 RT, (13) l and E C; = 2'5 R- (11) ‘ Here M is the molecular weight of the gas, T the temperature in degrees Kelvin, and R is the molar gas constant. (2) Vibrational For estimating vibrational contributions a set of assumptions was employed similar to those used by Chupka (20) for LaCZ. He assumed a linear assymetric molecule which preserved the C: group. This as- sumption was based partly on the observation that metallic dicarbides appeared to be the predominant species in the gas phase. Also the alka- line earth and lanthanon dicarbides, as well as thorium dicarbide, ap- pear to have C: groups in the solid phase. This suggests that a gaseous metallic dicarbide is likely to have a strong ionic contribution to its bond. This is further borne out by the work of Honig (51) on the elec- tron affinities of gaseous carbon species in which he observed that C2 has by far the highest electron affinity. The Th-C bond distance was taken to be that of Th-O in Th0(g) o (22), 1.932, and the C—C bond distance was taken as 1.31A (55). The 80 force constants were calculated from Badger's rule (56,57): k(r - d.-)3 = C., (15) where k is the stretching force constant in dynes/cm, re is the equi- librium internuclear distance, and dij and Ci' are constants. Taking Cij as 1.86 x 105 and dij as 0.73 for the C-C bond, and Cij as 1.11 x 105, dij as 1.33 for the Th-C bond, the C—C stretching force constant was determined to be 9.533 x 105 dynes/cm.and the Th—C stretching force constant 5.27 x 105 dynes/cm. The bending force constant was taken as 0.20 x 105 dynes/cm. The vibrational frequencies in sec—1 were calculated according to T the following equations (58): 1N(\)i+\) §)=k1(MT-h-:—MM_)+1<2(M), (16) MC 0 + 2M 16n1>i7§ = k1k2°M$Ih M C, (17) Th C and 2 ( )2 k 11 12 11 + 12 12132 = J —- — >, (18) n lilfi (M MC MTh * MC where k1 is 5.278 x 105 dynes/bm, k2 is 9.533 x 105 dynes/cm, kJ is 0.20 x 105 dynes/cm, MTh is 385-131 X 10.14 9; MC 0 o and 11 and 12 are 1.93A and 1.31A, respectively. The fundamental fre- is 19.936 x 10'2‘ g, quencies ('ur = 1)/t) were then calculated to be TLFI = 595.9 cm-1 1172 = 100.0 cm-1 (doubly degenerate) ‘urg = 1767.8 cm’1 If we define a dimensionless quantity u such that (51) u _ hi) _hc'w"_ 1.1388147 (1,9) ‘ W‘Td‘“ —T—’ 81 the thermodynamic functions are given by the following relationships: FO-HO _( TT 0) = - R ln(l-e-u), (50) s; = R( - ln(l-e'u), (51) e -l (Hf; - H8) = RT u” , (52) e -l and 0° = REEL . (53) p (eu-l)Z (3) Rotational 0n the basis of the linear assymetric model used in the cal- culation of the vibrational contributions the rotational contributions were calculated as follows. The diSplacement of atoms from the center of gravity is given by 2; mixi = 0 (51) where mi is the atomic weight expressed in grams and xi is the dis- tance in X of a given atom from the center of gravity. The values of mi for thorium and carbon are 385.131 x 10.24 and 191936 x 10-2‘ 9, respectively. The values ofax, were taken as a, 1.933 - a, and (1.93 + 1.31)K — a, for the thorium and the two carbon atoms, respec— tively, where a represents the distance of the thorium atom from the center of gravity. The solution of equation (51) gives a = 0.2981. The moment of inertia is given by I = Z midiz (55) 82 where di is the corrected value for X1 in equation (5h). The values of di were calculated to be: dTh = 0298.3, 0 (:1C1 = 1.632A, = 2 uzX dc2 .9 . The corresponding moments of inertia were calculated to be ITh = 3h.32 x 10’40 g cm2 IC = 53.06 x 10.40 g cm2 1 IC = 172.19 x 10'40 9 ma. 2 The moment of inertia of the molecule was calculated to be I = 259.87 x 10““ 9 cm2. (56) The rotational partition function is given by Q = l/o’ y (57) where 6', the symmetry number, is unity for an assymetric linear mol- ecule, and the dimensionless quantity y is given by 2 = _h_,, (58) 8fi31kT When h was taken as 6.6252 x 10‘27 erg sec and k as 1.380h5 x 10-16 erg/deg, y was calculated to be 0.15h96/T. When T is large and CF is unity, the rotational contributions to the thermodynamic functions are given by the equations (5h): FO-HO -( TT 0) = -R In y, (59) s; = R(l — ln y), (60) (fig—Hg) = RT, (61) and (b) Electronic The electronic partition function is given by - Eé/kT qe = ‘LJ; 2 . (63) Generallx there is a large separation in electronic energy levels and we need only be concerned with the ground electronic state (53) hence, q = w. e-eel/RT e e, (6b) where we is the degeneracy of the electronic ground state and Ge 1 1 is the energy of that state. If we make the assumption that the ground I state for thorium dicarbide gas is 1: then equation (6h) reduces to qe = l. (65) The value of the free energy function is then given by the relation 0 o F -H T o The electronic contribution to the other thermodynamic functions are also found to be zero, hence there is no electronic contribution to the values tabulated in Table XII. The assumption made above is a valid approximation at low temper- atures; however, at high temperatures a contribution can be expected from the excited states. It may even be that at sufficiently high temperatures the ground state is 311 not '2 . Because no data on the electronic spectra of thorium dicarbide or related compounds were avail- able, it was believed that the assumption made above was as good as any that could be drawn and that at temperatures up to 2500°K the contributions from excited states were negligible. } i 3 1% § , 3' E 3 i a ‘ *1 an 3. Calculation of the Enthalpies of vaporization for Experiments A, B, and C. The values of the free energy functions listed in Table XII.were used to calculate the changes in the free energy functions accompanying the reactions ThC2(S) = ThC2(g) and ThC = Th + 2C . . 2(S) (g) (graphite) A least squares treatment of these values as a function of temperature was performed and changes in the free energy functions for the two reactions were determined for all experimental temperatures. These val- ues and the values of PTh and PThCZ listed in Table XI were substituted into equation (37) and the enthalpy changes accompanying the two vapor- ization reactions were determined. These third law enthalpy values are presented in Table XV. Finally, the mean values of the heats of dissociation and vapori- zation determined by second and third law treatments of the data for experiments A, B, and C are: For the reaction ThC = Th 2c . 2(S) (g) (graphite) Second law, AHZQB = 176.92 x 3.30 kcal/mole, Third law, AHEQB = 175.82 x 0.68 kcal/mole; For the reaction ThC2(S) = ThC2(g) Second law, AHgge = 196.2h i 3.30 Real/mole, H Third law, AHZQB 208.96 1.25 kcal/mole. 9.. ‘2 i .3 W73? (um “I‘m-cor: um?! a, \ I ‘1 I ‘ IIIII. l 'I .' \_ ‘H ‘ ' ' - ' . ‘ e I .- , , ..,.. H7 .‘ ”I: fl II r - 7 I . . " §;__'4'~'ifiii'f..~ ._.- 85 Table XV. Third law values of the enthalpies of vaporization of ThCZ Temgi§ature ThC2(S) = Th(g) + 2C(graphite) ThC2(S) = ThC2(g) AHZQB kcal/mole AHZQB kcal/mole 2123 176.06 208.97 2195 178.22 203.20 2280 175.55 208.55 2257 175.50 208.57 2291 177.38 206.83 2321 175.51 205.78 2333 175.38 208.86 2338 175.83 208.51 2338 175.66 208.78 2338 176.63 208.71 2357 175.82 208.60 2359 175.60 208.70 2368 175.69 208.80 2820 175.62 208.77 2830 175.72 208.87 2858 175.78 208.71 2878 175.39 208.59 2886 176.52 205.72 2898 175.81 205.02 2505 176.19 208.81 2516 177.17 206.39 Mean value 175.82 i 0.68 208.96 1 1,25 w i L .3 . ... .- I: -3. .I i" pl!- Jr-‘. ' lvé.r 1. .4 Eh!!- 8.6 The standard enthalpy of formation of solid thorium dicarbide was calculated to be - 80.32 i 3.33 kcal/mole and - 39.22 t 0.88 Real/mole from the second and third law results, respectively. D. Analysis of Errors in the Measured "Effective Pressures" One should be able to show from the errors in the various experiment- ally determined quantities whether or not the scatter in the data plot- 1 ‘ 'rI- 1" u ted in Figure 7 can be ascribed solely to random errors in the measure- ments, or whether or not there were other factors involved. This eval- uation may best be done by considering the errors involved in one “1‘5."ir'Vs .4 '- amm'qidrfy if representative datum, and that chosen for treatment was exposure No. 5 from Series c at 2359°K, for which 104/7 1 8.280; The observed scatter arises from two sources. One is the random errors in the quantities expressed in second term in the equation for PE: P = (constants) [(lgHE-Z—i-QEH t E r2 in which w represents the amount of thorium on the target,)p the orifice diameter, r the collimator radius, d the orifice-to-collimator distance, and T and t represent duatemperature and the time of the ex- posure, respectively. The second source of scatter is the displacement of the experimental points above and below the log PE 22° 104/T curve due to errors A109/T in the reciprocal temperature. Consider the first effect. The various values and measured or estimated standard deviations for the experimental quantities for exposure c-5 are the following: w = 2.687 : 0.136;V‘T = 88.535 x 0.021; ‘joz = 0.877 t 0.028; t = 180 r 0.02; (r2 + dz/rz) = 125.070 1 0.123. 87 From the theory of the propagation of errors it was calcualted that PE = (constants) x (103.32 1 2.536). The contribution of random errors is thus 2.855 per cent and the expected standard deviation in 10g FE is log (1.02885) = 0.0105. The contribution of the second effect is as follows. For an error ET in the measured temperature the corresponding diSplacement amounts to A104/T x slope“! slope x (AT/T2) 104. The estimated standard devia— tion in measured termperatures is i 2 degrees, as was discussed previous- ly. From the slope of equation (29) we find, at the exposure tempera- ture, 2359°K, for target C-5, an expected uncertainty in log P of . E i 0.017. The corresponding multiplicative uncertainty in P is 1.080; E the expected standard deviation in PE resulting from the uncertainty in 104/T is thus i 8.0 per cent. Combining the two parts of the calculated standard deviation, we have for exposure C-5, Std. dev. in log PE = :Af(0.017)2 + (0.0105)2 = : 0.01997. The corresponding estimated standard deviation in the measurement of the absolute value of the "effective pressure" of thorium dicarbide was i 8.7 per cent. In the neighborhood of 104/T = 8.28, about three-fourths of the points may be expected to lie within i 0.02 of the value of log PB ob- tained from equation (29). Examination of Figure 7 shows this criterion is satisfied for the points from experiment C, but that some of the data from experiments A and B have larger residuals than expected. In the discussion of experiment B it was pointed out that the orifice size de- creased during the course of that experiment. This phenomenon would 52" d ,3- ? _ifa I' J h-mtfl'B m-r. mu "IEK 88 account for the apparent low values obtained for exposures B-8, B-5, and B-6. The scatter at the lowest temperatures, Specifically points A-7 and A-8, is not understood. It is concluded that there are no random experimental errors unac- counted for in the measurement of the total rate of effusion except at the extremes of the temperature range. B. Other Investigations 1. The Results of Lonsdale and Graves Lonsdale and Graves (19) who studied the vaporization of thorium dicarbide over the temperature range 2300 to 2900°K obtained a second law enthalpy of vaporization of 172.0 i 8.6 kcal/mole. From this, they calculated the heat of formation of the solid dicarbide to be AHgge = - 86 i 6 heal/mole. However, they based their calculations on the assumption that the only reaction occurring was ThC = Th + 2C . . 2(S) (g) (graphlte) From the study of Jackson and co-workers (21) it is obvious that the reaCtion ThCZ‘s) = ThC2(g) must also be taken into account. The data of Lonsdale and Graves were converted to values of P and P Th ThCZ by assuming that their reported values for the vapor pressure of Th(g) in equilibrium with ThC2(S) were actually "effective pressures" p0 calculated from equation (21) based on an effusing species of molecular weight 232.038. In order to compare the "effective pressures" determined by these authors with those measured in this investigation the values determined by Lonsdale and Graves were 89 multi lied b the factor ( )1/2 to convert the data to "effec- p y MTh/MThc2 tive pressures" PE based on the average molecular weight of the effusing Species being 256.0603. From these values of P the values of PTh and E) PThC were calculated in the manner described above in Section C. The 2 values of P and PTh calculated from the data of Lonsdale and E’ PTh’ c2 Graves are presented in Table XVI. Third law values of the enthalpies of dissociation and vaporization of ThC2(s) were calculated from these partial pressures and are listed in Table XVII. For the sake of com- parison, the values of PE calculated from the data of Lonsdale and Graves, together with the values determined in experiments A, B, and C are graphed against 104/T in Figure 10. In this figure, the straight line was obtained from a least squares treatment of the data from experiments A, B, and C. The enthalpy values listed in Table XVII show a temperature-de- pendence and Figure 10 shows that the values of PE calculated from the data of Lonsdale and Graves do not increase linearly with temperature. There are several possible explanations for this behavior. (a) One explanation could be that the values calculated for the changes in the free energy functions were in error. However, the fail— ure of the third law heats calculated from the data obtained in exper- iments A, B, and C to exhibit this dependence indicates that the changes in the free energy functions vary linearly with temperature and that the temperature dependence was related to the measured values of the vapor pressure. (b) A heat capacity effect could cause the value of the slope of the curve in Figure 10 to decrease at higher temperatures. When vapor ~11- } 3“- 90 Table XVI. Vapor pressures calculated from the data of Lonsdale and Graves. Temperature 104/TOK PE PTh PThC (OK) (atm) (atm) (atm; 2278 8;390 7.1 x 10‘10 3.6 x 10‘10 3.3 x 10'10 2355 8.286 3.0 x 10‘9 1.8 x 10‘9 1.5 x 10‘9 2826 8.122 7.8 x 10'9 3.3 x 10‘9 8.0 x 10'9 2871 8.087 1.7 x 10’8 7.3 x 10‘9 9.8 x 10‘9 2531 3.951 3.6 x 10'8 1.5 x 10'8 2.1 x 10‘8 2583 3.871 8.7 x 10‘8 1.8 x 10'8 2.8 x 10‘8 2617 3.821 7.5 x 10'8 3.6 x 10‘8 5.8 x 10‘8 2673 3.781 1.5 x 10'7 5.5 x 10'8 9.5 x 10‘6 2673 3.781 3.0 x 10‘7 1.1 x 10‘7 1.9 x 10‘7 2723 3.672 6.8 x 10'7 2.8 x 10‘7 8.8 x 10‘7 2785 3.683 8.3 x 10'7 1.8 x 10'7 2.8 x 10‘7 2750 3.636 6.3 x 10'7 2.1 x 10‘7 8.1 x 10‘7 2779 3.598 8.6 x 10"7 2.8 x 10‘7 5.6 x 10‘7 2815 3.552 1.3 x 10‘6 8.2 x 10‘7 8.8 x 10’7 2858 3.899 2.0 x 10‘6 6.2 x 10‘7 1.8 x 10‘6 2897 3.852 2.8 x 10‘6 7.1 x 10‘7 1.6 x 10‘6 91 Table XVII. Third law values of the enthalpies of vaporization of ThC2(S) calculated from the data of Lonsdale and Graves Tampgfiature ThC2(s) =0Th(g) + 2C(graphite) Thgz(s) - ThC2(g) AHzge kca1/'mole AHZQB, heal/mole 2278 175.71 208.75 2355 175.36 208.86 2826 176.83 205.98 8" x. 2871 176.31 205.50 S 2531 177.21 206.85 2583 179.91 209.17 2617 178.78 208.09 E, 2673 180.50 209.88 2673 176.98 206.32 2723 177.20 205.39 2785 180.19 209.60 2750 178.85 207.86 2779 178.81 208.28 2815 178.91 208.37 2858 179.61 209.10 2897 181.31 210.83 Mean Values 178.25 i 1.58 207.50 i 1.98 92 -5.0 \ \ "x\ g\ _ ._ \ 6 0 “x \ X \ x \ x \ I \1 O l X / I 00 O I I To 0 l Logarithm of effective pressure, log PE(atm) o -10 0 _ o This Investigation X From the Data of Lonsdale and Graves -ll.0 I 1 l l I 1 3.8 3.6 3.8 88.0 8.2 8.8 8.6 _8.8 Reciprocal of Temperature, 10€/T(deg 1) Figure 10. The temperature-dependence of the effective vapor pressure of thorium dicarbide. 93 pressures are calculated from equation (6) the tacit assumption is made that the difference in the heat capacities of the solid and gaseous phases is constant in the temperature range studied. The fact that the data for experiments A, B, and C do not show this effect and the fact that Lonsdale and Graves did not attain the melting temperature of ThC2(S) (29280K) would seem to indicate that the assumption that AC.p is zero in the temperature range studied is valid. Nevertheless, a phase change in which thorium dicarbide attains a new structure may occur and the possibility of a heat capacity effect cannot be ruled out. (c) At the highest temperatures attained the vapor pressure of graphite is appreciable and the effusion process could be changing from molecular to viscous flow. Such a phenomenon, however, should cause a positive change in the slope of the curve in Figure 10. (d) Considering the rather large scatter in the points at high temperatures it is probable that the cause of the decrease of the slope lies in experimental errors. It was demonstrated in eXperiment C of this investigation that complete condensation of effusate on the targets is not attained and that the amount of "bouncing" increases as the tem- perature is increased. Because Lonsdale and Graves used graphite rather than fused silica targets it is probable that the temperatures of their targets were higher than those for the targets used in this investiga- tion. These authors did not test for total condensation of the effusate on the targets and the effect of "bouncing" is not known. 2. The Results of Jackson and CQrworkers Despite the lack of precision in the values of the vapor pressures determined at the higher temperatures, the data of Lonsdale and Graves are in much closer agreement with the data from experiments A, B, and C .Eli' 98 than are those of Jackson and co-workers. The second and third law values of the enthalpies determined by these authors are (21): For the reaction ThC2(8) = Th(g) + 2C(graphite) Second law, Ange, = 160.3 x 3.2 kcal/hole, Third law, AHgge = 188.7 t 1.5 kcal/mole; For the reaction ThC2(S) = ThC2(g) Second law, AHgge = 188.1 i 3.8 kcal/mole, Third law, AHgge = 212.8 i 1.5 kcal/hole. The standard enthalpy of formation of ThC2(S) was calculated to be — 23.7 i 3.5 kcal/mole, and - 88.1 t 2.0 kcal/mole from the second and third law results, respectively. This discrepancy between the second and third law enthalpies is disturbing. Upon examination of these author's data it was found that they had made an arithmetic error in the calculations of the free energy functions for the ThC2(g), but this error was not large enough to ac— count for the large difference in enthalpies. Also, this error would not affect the calculation of the enthalpy change in the dissociation is formed. When the values of P and P 9) Th ThCZ were compared with those obtained in the current investigation and reaction in which Th( those calculated from the data of Lonsdale and Graves, they were found to be lower by a factor of about 5. Because the sensitivity calibra— tion of the mass spectrometer for absolute pressure measurements involves the use of secondary standards, the pressures determined by this tech— nique are more likely to be in error than are those determined by the 95 effusion method. Another possible cause for the discrepancy lies in the measurement of temperatures. The standard technique in mass spec- trometric investigations is to graph IT against 1/T. Here I is the relative intensity of the gaseous species and the quantity IT is related to the vapor pressures. Possible uncertainties in the temperature scale are accentuated in this method. It whould be noted that while errors in the measurement of temperature will greatly affect the calculation of the partial pressures of the vapor species, the effect on the measured ion intensity ratio, I+ThCZ/1Th’ is much less and the values listed by Jackson and co-workers Should probably be considered as re- liable. In summary, considering the lack of precision in the data of Lonsdale and Graves and the low vapor pressures determined by Jackson and co-workers, it is believed that the partial pressures of Th(g) and ThC2(g), in equilibrium with ThCZ(S), are best characterized by the present investigation. F. Suggestions for Further Research l. The Thorium-Carbon System The phase diagram shown in Figure 1 is only a tentative one and a more complete study of the system should be made. One method of ac- complishing this end would be to prepare samples of Tth with varying mole ratios of carbon-to-thorium in an arc melter and studying the com- position as a function of temperature by X-ray diffraction techniques, including the use of a camera designed to operate at high temperatures. A calorimehflc study should be made and the heat capacity of solid thorium dicarbide determined as a function of temperature. 96 The mass spectrometric investigation of the vaporization process should be repeated and the temperature range covered should be extended. This study would involve problems basic to mass Specrometric investiga- tions, i;g., the calibration of the mass spectrometer for absolute pres— sure measurements, and the theoretical calculation of the ionization cross sections of individual gaseous species. The Knudsen effusion study should be extended to higher tempera- tures, and the effusion from non-carbon crucibles investigated; in the present study, the crucibles used led to an excess of carbon being present at all times. Finally, the system thorium-oxygen—carbon has not been studied and the effect of oxygen on the vaporization process and on the stabilities of the solid phases should be investigated. 2. Determination of Thermodynamic Functions for Vapor Species At the present time the literature contains little information per- taining to the spectroscopic data for the vapor species of refractory inorganic compounds. The thermodynamic functions, such as the free energy functions and the entropies, are usually viewed as being separable in the following manners: 0 e: S¥=SE+SS+83+S where t, r, v, and e refer to the translational, rotational, vibrational, and electronic contributions, respectively. The translational contri- bution can be unambiguously calculated for any gaesous molecule provided that its molecular weight is known. The rotational and vibrational contributions may be estimated with fair accuracy if the molecular structure is known. This may be determined in many cases by electron 97 diffraction techniques. Micro-wave studies can yield very precise structural information if the molecule has a permanent dipole. In some instances it may be possible to determine the rotational and vi- brational spectra by means of matrix isolation techniques. However, the determination of the structure of triatomic and more complex gas- eous molecules remains a difficult problem and much remains to be done in this area. Perhaps the most difficult to assess are the electronic contribu- tions. In the first place, there are few, if any, spectroscopic data for most triatomic molecules and the investigator must make use of an assumed ground state. In the second place, the idea that excited electronic states make negligible contributions is based on the tacit premise that only moderate temperatures will be of interest. At tem— peratures of 2000°K and greater, excited electronic states may contri- bute significantly to the thermodynamic functions. Compilation of electronic energy levels would be of great value in calculating thermo- dynamic functions for gaseous molecules, but the determination of these data remains a formidable problem. 10. ll. 12. 13. 18. 15. 16. 17. l8. 19. . K. Lonsdale and J. N. Graves, Thermodynamics of Nuclear Materials LITERATURE CITED Troost, Compt. rend., 888, 1229 (1893). . Moissan and A. Etard, Compt. rend., 822, 573 (1896). A. Wilhelm, P. Chiotti, A. I.Snow, and A. H. Daane, J. Chem. Soc., Suppl. Issue 2, S318 (1989). . A. Wilhelm and P. Chiotti, Trans ASM, 8g, 1295 (1950). Hansen, Constitution of Binary Alloys, Second Edition, MCGraw— Hill Book Company, Inc., New York, N.Y. (1958). von Stackelberg, Z. physik. Chem., 82, 837 (1930). B. Hunt and R. E. Rundle, J. Am. Chem. Soc., 13, 8777 (1951). E. Rundle, Acta Cnyst., 8, 180 (1988). J. Modic, private communication to E. B. Hunt and R. E. Rundle, appearing in J. Am. Chem. Soc., 12, 8777 (1951). . Lebeau and A. Damiens, Compt. rend., 858, 1987 (1913). B. Engle, W. V} Goeddel, and C. S. Luby, J. Am. Ceram. Soc., 85, 136 (1962). . P. Kempter and N. H. Krikorian, J. Less Common Metals, 8, 288 (1962). . J. Palenik and J. C. Warf, Inorg. Chem., 8, 385 (1962). H. Prescott and W. B. Hincke, J. Am. Chem. Soc., 82, 2788 (1927). A. Rath and G. Beeker, Z physik. Chem., A159, 1 (1932). H. Krikorian, Univ. of California Radiation Laboratory Report UCRL - 2888 (1955). Meslan, Brookhaven National Laboratory Report BNL - 583 (1959). . Brewer, L. A. Bromley, P. W. Gilles, and N. L. Lofgren, I83 Chemistgy and Metallurgy of Miscellaneous Materials-Thermo- gynamics, edited by L. L. Quill, McGraw-Hill Book Company, Inc. New York, N. Y. (1950). ’ ) Proceedings of the International Atomic Energy Agency, Vienna (1962). 98 99 LITERATURE CITED (Cont.) 20. 21. 22. 23. 28. 25. 26. 27. 28. 29. 30. 31. 32. 33. 38. 35. 36. 37. 38. 39. 80. 81. W. A. Chupka, J. Berkowitz, C. F: Giese, and M. G. Inghram, J. Phys. Chem., 8g, 611 (1958). D. D. Jackson, G. W. Barton, Jr., 0. H. Krikorian, and R. S. Newbury, A. Thermodynamics of Nuclear Materials, 10c. cit. J. Darnell, W. A. McCollum, and T..A. Milne, J. Phys. Chem., 88, if.’ L381 (1960). National Bureau of Standards, Circular 500 (1952). G. R. Stull and G. C. Sinke, Thermodynamic Properties of the Ele- ments, American Chemical Society, Washington, D. C. (1956). Knudsen, Ann. Physik., g8, 75 (1909). Knudsen, ibid., 999 (1909). D. Carlson, Argonne National Laboratory Report ANL-6156 (1960). Bockris, J. L. White, and J. D. Mackenzie, ngsicochemical Measurements at Hi h Temperatures, Butterworth.Scientific Pub- lications, London 1959). Mayer, Z. Physik., 52, 235 (1928). Mayer, ibid., 58, 373 (1929). Knauer and O. Stern, Z. Physik., 82, 768 (1926). . H. Johnson, Phys. Rev., 28, 103 (1928). Clausing, Physica, 2, 65 (1925). . Clausing, Z. Physik., éé,9871 (1930). . D. Freeman and.A. W. Searcy, J. Chem. Phys., 22, 1137 (1958). . G. Wahlbeck, Dissertation Abstr., 82, 2896 (1959). . 0. Adams, Dissertation Abstr., 28, 3683 (1961). . C. DeMarcus, U. S. Atomic Energy Commission Report K1302, Parts I and II (1956); Parts III and IV (1957). H. Spinar and J. L. Margrave, Spectrochem.Acta” 88, 288 (1958). . Hoch, M. Nakata, and H. L. Johnston, J. Am. Chem. Soc., 18, 2651 (1958). . Hoch and H. L. Johnston, J. Am. Chem. Soc., 19: 8833 (1958). /. e - .-/ ,‘I . . : - d _i_ '. 1'.” ' 'xm' ‘ 100 LITERATURE CITED (Cont.) 82. 83. 88. 85. 86. 87. 88. 89. 50. 51. 52. 53. S8. 55. 56. . 57. 58. R. . Motzfeldt, J. Phys. Chem., g9, 139 (1955). .._ . Sasaki, F. Ichikawa, H. Imai, and S. Uruno, Nature, 828, 267 F J. Ackermann, R. J. Thorn, and P. W. Gilles, J. Am. Chem. Soc., Zé. 1767 (1956). A. Chupka, J. Berkowitz, and M. G. Inghram, J. Chem. Phys., 38 1207 (1957). L. Winterbottom and J. P. Hirth, J. Chem. Phys., 21, 788 (1962). 9 I. Whitman, J. Chem. Phys., 29, 161 (1952). W. Lohse, Catalytic Chemistny, Chemical Publishing Company, New York, N. Y. (1985). (1962). ’ : J. Ackermann, P. W. Gilles, and.R. J. Thorn, J. Chem. Phys., gg, 1089 (1956). H. Fletcher and R. G. Milkey, Anal. Chem., g8, 1802 (1956). . E. Honig, J. Chem. Phys., gg, 126 (1958). H. Krikorian, Univ. of California Radiation Laboratony Report UCRL-6785 (1962). L. Hill, An Introduction to Statistical Thermodynamics, Addison- Wesley Publishing Company, Inc., Reading, Mass. (1960). S. Pitzer and L. Brewer, Revision of G. N. Lewis and M. Randall, Thermodynamics, Second Edition, McGraerill Book Company, Inc., New York, N. Y. (1961). Herzberg, Molecular Spectra and Molecular Structure, 1. Spectra of Diatomic Molecules, Second Edition, D. VanNostrand Company, Inc., New York, N. Y. (1950). . M. Badger, J. Chem. Phys., 3, 128 (1938). . M. Badger, ibid,, ;, 710 (1935). Heererg, Molecular Spectra and Molecular Structure, II. Infra- red and Raman Spectra of Polyatomic Molecules, D. vanNostrand Company, Inc., New York, N. Y. (1985). APPENDICES 101 Is. 1 l i . in. “'"4" .‘1 1' ‘1 a. m .3 APPENDIX A SUPPLEMENTARY EXPERIMENTAL DATA Individual Preparations of Thorium Dicarbide 1. First Attempt Powdered graphite and thorium dioxide in the molar ratio 5.6:1 graphite to thorium dioxide were mixed and loaded into a graphite crucible which was placed in the vacuum system and heated for one hour at about 2260°K. After heating was terminated, the system was opened to helium, and then to the atmosphere and a small portion of the brit- tle, sintered product was ground to a powder, loaded into a 0.3 mm diameter capillary, and an X-ray powder diffraction photograph was taken (film A-989). Because only two lines showed on the film, the sample was reheated for one hour at 1870°K, then for one hour at 2500°K. During this heating a graphite radiation shield was placed around the crucible to decrease the deposition of graphite on the walls of the con- denser. The sample did not change in appearance during this second heating. Another X-ray powder diffraction photograph was taken (film A-960) and, although the film was of poor quality, the sample was identified as thorium dicarbide. 2. Series P-l to P-9 This series consisted of nine preparations in which varying amounts of graphite were heated with thorium dioxide. After the product had been formed, the temperature was raised and the samples were annealed for varying lengths of time. Sample sizes ranged from 0.1 to 2.0 grams and the samples were used either to test analytical methods or for ef- fusion experiments. In all analyses performed on this series of samples, 102 103 the thorium was precipitated with oxalic acid. The data for this series are summarized in Table AI and each preparation is discussed briefly below. P—l. Nitric acid was used to hydrolyze the sample and the amount of free graphite found was higher than expected. The empirical formula determined by the chemical analysis was ThC1.47, but the X—ray diffrac- tion pattern indicated that the sample was ThCZ. It was decided to use hydrochloric acid in the hydrolysis of sample P-2 to see if more con- sistent analytical results could be obtained. P-2. In this, and in all subsequent preparations in this series, a graphite radiation shield was employed to decrease the deposition of graphite on the walls of the condenser. Hydrochloric acid was used to hydrolyze the sample and the empirical formula was found to be ThCIOQB. The X—ray powder diffraction pattern indicated the sample to be ThCz. P-3. Nitric acid was used in the hydrolysis and the analysis in- dicated the unrealistic stoichiometry, ThCo.65, however, the X-ray powder diffraction pattern was that of ThCZ. The amount of free carbon found was far in excess of that expected and it was decided that nitric acid oxidized some of the combined carbon to free graphite. Hydro- chloric acid was used in all subsequent hydrolyses. P-8. No X—ray powder diffraction pattern was taken, The analysis indicated the stoichiometry to be ThC2.o7. P-5. Since this sample was used in a preliminany effusion ex- periment E—l, no analysis was performed and no X—ray powder diffraction pattern was taken. P—6. The chemical analysis indicated the empirical formula, Thcz.°6 and the X—ray powder diffraction pattern was that of ThCz. To test the 108' Table A1. Data for series P-l to P—9 Sample Mole Ratio Annealing Conditions Formula X-ray Results N0. c/‘rho2 T(°K) Time(min) (analysis) Film No. Phases P-l 5: 1 2190 75 Thcl,47 A-922 ThcZ P—2 5: 1 2800 70 Thcl, 58 A-993 ThCZ P-3 5: 1 2358 280 Thco,65 A—998 Thc2 P-8 5:1 2366 120 Thcz,o7 None --- P-5 5:1 2353 60 --- None --- P-6 8.8:1 2367 210 Thczooa A-1005 ThcZ P-7 8.5:1 --- 280 --- None --- P-8 8.5:1 2216 90 --- None --- P-9 8.5:1 2218 85 --- A—lO66 ThCZ 105 determination of thorium.by precipitation with oxalic acid, a portion of the sample was ignited directly to thorium dioxide to determine the thorium content. The weight percentages of thorium found by precipita- tion and by direct ignition were 85.81 and 85.02, respectively. P-7. In the last three preparations in this series the re- actants were heated in the form of pellets which had been.pressed for ten minutes at 10,000 p.s.i. During the preparation the veeco ioniza- tion gauge on the vacuum.system failed to function, and the sample was discarded. P—8. Thkssample was used for effusion experiment E-2 and analysis and X-ray diffraction pattern of the sample are described in the discussion of this experiment. P—9. The pray diffraction pattern was that of ThCZ, however, due to a sample spill during filtration, no chemical analysis was obtained. 3. Series P-10 to P-15 This series consisted of six preparations in which vanying amounts of graphite were heated with thorium metal to produce throium dicarbide. Because no carbon monoxide was produced as a reaction product it was possible to attain the desired temperatures quickly. Sample sizes ranged from 1.2 to 2.8 grams. The analysis of samples P-10 and P-ll involved the use of oxalic acid to precipitate the thorium; in all other analyses the thorium.was precipitated with aqueous ammonia. The data for this series are summarized in Table AII. And each preparation is discussed briefly below. Table AII. 106 Data for series P—lO to P-15 Sample Mole Ratio Annealing Conditions Formula. X-ray Results No. c/Th.- T(°K) Iime(min) (analysis) Film No. Phases P-lO 2.86:1 2313 180 ThC2.el A-lO86 ThC2 P—ll 2.18:1 2800 60 ThCz.°o A—lO5O ThC2 P-12 , 2.36:1 1970 120 ThC1.91 A-lO68 ThcZ 2000 60 ThC1.93 P-13A 1.90:1 2000 90 Thcl.£32 A-1078 ThCZ P-13B 1890 280 ThC1.51 P-l8 1.96:1 1850 300 ThC1.3o A-lO77 Thc2 and ThC P-15 2.50:1 1950 80 Thea.o7 A-lO78 ThC2 - -|'-'-.'-’u. "in 1 . f 107 P—lO. The X-ray powder diffraction.pattern was that of ThCZ and the chemical analysis were as follows: Expected, thorium 88.69%, graphite 2.13%, and combined carbon 9.18%; found, thorium 88.71%, graphite 2.07%, and combined carbon 9.22%. P-ll. This sample was prepared at a somewhat higher temperature than the others and there was a veny heavy deposit of graphite on the walls of the condenser. The X-ray powder diffraction pattern (film Ar1050) was that of ThCZ and the analysis indicated the formula to be ThC2,oo- A portion of the sample was exposed to the air for one hour and an X-ray powder diffraction pattern (film.A-1051) which indicated the presence of two phases, ThCZ and ThOZ was taken. P-12. This was the only preparation in this series in which the reactants were heated in powder form, in the others the samples were heated as pellets which had been pressed for ten minutes at 10,000 p.s.i. After the sample had been heated for two hours at 1970°K.a portion was taken for analysis, which indicated the stoichiometny ThC1.91. The remainder of the sample was heated for another hour at 2000°K.and the analysis indicated the empirical formula to be ThC1.93o The X-ray powder diffraction pattern was that of ThCZ P—13. In most previous preparations the amount of excess graphite in the product was greater than that desired. Therefore, it was decided to attempt a preparation in which an excess of thorium was used. Two pellets were pressed from the same reactant mixture and heated together for ninety minutes at 2000°K. One pellet was analyzed and the stoichi- ometry found to be ThC1.82 with 3.61% excess graphite. The X—ray pow- der diffraction pattern was that of ThCZ. The second pellet was reheated for four hours at 1890°K and analyzed. Although the stoichiometry was 108 found to be nearly the same, ThC1,81: the amount of excess graphite had been reduced to 1.29%. P-l8. In this preparation the reactants were heated at a lower temperature than usual and the chemical analyses indicated the empir- ical formula to be ThC1,3o. The X-ray powder diffraction pattern re— vealed that the sample consisted of both ThCZ and a new phase of cubic symmetry which was identified as ThC. P-15. Two pellets were pressed from the same reactant mixture and heated together. One pellet was used for effusion experiment E-3. The other was analyzed and the empirical formula was found to be ThC2.o7. 7. The X-ray powder diffraction pattern, as usual, was that of ThCZ. 8. Series P—16 to P-28 This series consisted of nine preparations in which thorium and graphite were heated together to produce thorium dicarbide samples to be used in calorimetry experiments by E. F. Westrum at the University of Michigan, Ann Arbor, Michigan. In sample P-16 the reactants were heated in powder form, in all others the reactants were heated as pel- lets which had been pressed at 10,000 p.s.i. After each preparation the sample was stored in a dry box under a helium atmosphere. Samples P-18 and P-19 were inadvertently exposed to the atmosphere and dis- carded. The remaining samples were ground together with an agate mor- tar and pestle in an inert atmosphere and the entire product was heated in vacuum for five hours at 2800°K. A portion of this resultant pro- duct was taken for an X-ray powder diffraction pattern (film A-1132) which indicated the sample to be ThCZ. Since any excess graphite would interfere in calorimetry measurements, the sample was twice more ground 109 under an inert atmosphere and heated in vacuum for five hours at 2800°K. The final product consisted of sintered yellow chunks and chemical anal- ysis indicated the empirical formula to be ThC1.995 and another X-ray powder diffraction pattern (film A-1133) again showed the product to be ThCz. A 26.7 gram portion of the sample was loaded into a sealed con- tainer, in a drybox and taken to Ann Arbor, Michigan for heat capacity measurements. 5. Preparation P—25 This sample was used in effusion experiment E-8 and is described in the discussion of this experiment. APPENDIX B TABULATION OF PHYSICAL CONSTANTS R = 1.98726 cal/deg-mole h = 6.6252 x 10‘27 erg sec k = 1.38085 x 10'16 erg/deg c 2.99793 x 1010 cm/Sec hc/k = 1.8388 cm deg Rln x = 8.5758 loglo x cal/deg-mole Mass of atom of unit atomic weight = 1.65979 x 10‘24 9 Atomic weight of thorium = 232.038 Atomic weight of carbon = 12.01115 Atomic weight of oxygen = 15.9998 Mass of thorium atom = 385.138 x 10-24 9 Mass of carbon atom = 19.936 x 10-24 g 110 APPENDIX c Table AIII. Temperature measurement for exposure no. 8, experiment B T°c T°C T°K 104/T0K -1104/'T0K T°K (observed) (Corrected (true) for Pyrometer) 2001.0 2018.00 2287.16 8.3722 8.2821 2335.30 1999.75 2012.75 2285.91 8.3786 8.2885 2333.99 1999.20 2012.20 2285.36 8.3756 8.2855 2333.85 2000.50 2013.50 2286.66 8.3731 8.2830 2338.81 1999.25 2012.25 2285.81 8.3755 8.2858 2333.50 2000.50 2013.50 2286 66 8.3731 8.2830 2338.81 1998.80 2011.80 2288.96 8.3768 8.2863 2333.01 1999.50 2012.50 2285.66 8.3751 8.2850 2333.72 2000.00 2013.00 2286.16 8.3781 8.2880 2338.27 2338.10 1 0.87 111 bill-III .llln u. m. .F- .. imam-.7 LIBRARY "171111111881111115