THE VAPORIZATION THERMODYNAMICS- 0F SAMARIUM DICARBIDE AND THULIUM DICARBIDE Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY ROBERT LANE SEIVER 1971 3'?! {$8333 gimmar Michigan S‘ute. Univets'ty This is to certify that the thesis entitled The Vaporization Thermodynamics of Samarium Dicarbide and ThuTium Dicarbide presented by Robert Lane Seiver has been accepted towards fulfillment of the requirements for '7 ib/ /Z7 “£61 Majgr professor Date—Afllfili—LLM. 0-7639 ' amomc or g “in , "MB 81 SUNS' 3' 5% RIM" INC. ARY BINDERS SPIIIGPOIT, IICIIGII - Hug-5,6 ABSTRACT THE VAPORIZATION THERMODYNAMICS OF SAMARIUM DICARBIDE AND THULIUM DICARBIDE By Robert Lane Seiver ’ Several investigations of the vaporization of SmC2 have been reported. The reported values of the equilibrium decomposition pressures are in only fair agreement and some workers report a variation in the enthalpy of decomposition of SmCz with the amount of free carbon present. The present study was undertaken to examine this apparent composition dependence and to study the previously unreported vaporization of TmCz. The dicarbides were prepared by direct combination of the elements under argon in sealed tantalum ampoules. Chemical analysis indicated that the products were generally metal-rich, 1.785C/M52.02. X-Ray powder diffraction patterns showed only the body centered tetragonal CaCz-type structure for SmC2 preparations and those TmC2 preparations which were cooled quickly. Preparations of TmCZ which were cooled slowly yielded the black low-symmetry modification previously reported. Preliminary single-crystal X-ray diffraction data indicate that this modification is actually a mixture of a hexagonal phase, _a = 3.19 H- 0.01 A,.gr= 16.74 i 0.07 A; and an orthorhombic phase, H- .g = 3.68 0.01 A, h_= 12.40 i 0.04 A, and g = 13.58 i 0.03 A. The Robert Lane Seiver mixture quickly reverted to the tetragonal structure on heating in vacuum. Mass spectrometric observation of the effusate of TmCZ vapor; ization with a 30 or 55 ev ionizing electron beam showed only TmT. Its appearance potential was 5.7 ev. Limits were set for carbide vapor species at ITmC2+ < 0.005 ITm+ and ITmC+ < 0.02 Irm+° Vapor pressure measurements were made by target collection Knudsen effusion. The effusate was condensed onto chilled aluminum targets which were analyzed quantitatively by X—ray fluorescence. Metal-rich samples of SmC2 or TmCZ initially showed high erratic pressures. Calculations from weight loss data indicated that stable pressures were achieved very close to the M02000 composition. Carbon-rich samples (3 .oomm mom: scamsmmo scamHOH .HHoo umwuofi .ommm mom: .uomm mmmz .ummm mmmz .omam mom: .HHoo umwuma scene: H magma. commas .Hm um .usoum .Hm um .Suoaouamm .Hm um .%uo>< .Hm um .uuonsuso H0£ud< msow>oum mo muHSmom mm mm HN mm «N moamummom 6 Reasons for disagreement among the other workers are not so apparent. No study of the decomposition pressure of thulium dicarbide has been reported. 2. Formation of Gaseous Molecules The dicarbides of the less volatile lanthanides vaporize by two modes, giving both gaseous metal atoms and carbide molecules. Both the dicarbide and tetracarbide have been observed. The equilibria of these molecules with the gaseous metals are pressure-independent reactions and can be studied by mass spectrometry Without extensive calibration. Dissociation and atomization energies have been reported for the gaseous carbides of L338,39, Ce22,39-41, Pr39,uo, Nd39,u1—u3, Gduu’ Than, Dy33,3u, H033i3“:”0, and Er36. Gaseous molecules have been found to be absent in the vaporization of SmC22“’26:”5, EuC224,4S, and YbC237. 3. Calorimetric Measurements Baker et al.‘+6 measured the enthalpy of formation of CeC2 by oxygen bomb calorimetry and got results in reasonable agreement with those from vaporization studies. No heat capacity measurement has been reported. D. Other Investigations The dicarbides are considered to be ionic salts of acetylide, C2’, with the metals, which are usually trivalent. Considerable interest arose concerning the character of the third electron. Magnetic measure- manta“,1+8 and eray absorption edge studies“9 showed that the metals are indeed trivalent and the extra electron is delocalized in a conduction band. Neutron diffraction workll'18 confirms this conclusion for the commonly trivalent metals and gives an oxidation state of +2.7 for Yb in YbCZ. Neutron diffraction data for EuC2 and SmC2 are not yet available. 7 Hydrolysis studies of the lanthanide dicarbides under controlled conditions have been reportedSO’SI. E. Other Relevant Dicarbides Since no heat capacity data have been reported for the lanthanide dicarbides, it is necessary to estimate thermal functions to reduce , . thermochemical data to standard conditions for comparison purposes. The isostructural compound CaC2 has usually been chosen as a basis for such estimates. Its standard entropysz, high temperature heat capacity53, and enthalpy of the tetragonal to cubic transformation have been compiled by Wicks and Blocks”. A more reliable standard entropy is available for thorium dicarbideSS and its high-temperature heat capacity has been estimated56 by use of Krikorian's method57, but ThCZ is not isostructural58 with the lanthanide dicarbides. Uranium dicarbide is isostructural”,60 with CaCZ and LnC2, and its low temperature“,62 and high temperature63'65 heat capacities have been measured. However, this compound is metastable and significantly substo- ichiometric (C/U - 1.91-1.93) and not as suitable a basis for estimation. CHAPTER III THEORETICAL CONSIDERATIONS PERTINENT TO THIS INVESTIGATION A. Phase Relationships and Thermodynamic Behavior 1. The Phase Rule Conditions necessary for equilibrium in a vaporization study are given66 by Gibb's phase rule (III-1). The number of degrees of freedom, F = C - P + 2 III-l F, is expressed in terms of the number of components, C, and the number of phases, P. Number of components is defined as the smallest number of independently variable constituents needed to define the system. Two general categories describe most vaporization processes in terms of this rule. In the first, congruent vaporization, the composition of the vapor is the same as that of the single condensed phase. This composition restriction makes it possible to define the system.with only one component, and since there are two phases, F - 1. Fixing the temperature removes all degrees of freedom and fixes the pressure. Incongruent vaporization of a condensed phase gives a second condensed phasepand a vapor of different composition. Here there are three consti- tuents, but because of the chemical reaction relating them the system may be defined with two components. There are three phases, so again the system is univariant and fixing the temperature defines the pressure. 9 Systems involving condensed phases of variable composition or vapors with more than one constituent require a more detailed analysis. 2. The Thermodynamics of Equilibrium Under conditions of constant temperature and pressure, the thermo- dynamic statement of equilibrium for the general reaction (III-2) is AG = 0. vaA + vbB + ... : ch + vdD + ... III-2 Substituting into the mass action equation (III-3)67 and noting that AGT - as; + RT 1n (aC)"C(aD)"d... 111-3 at equilibrium the mass action coefficient is the equilibrium constant gives equation (III-4). Normally in effusion studies the condensed phases 0 AGT = -RT 1n KT III-4 are considered to be present in pure form, at unit activity, and the vapor consists of a single species. Since the vapor is dilute enough to be considered ideal, equation (III-5) results. Thus measurement of the vapor 0 ACT -RT 1n PT III-5 pressure at a series of temperatures yields the standard free energy change and its temperature dependence, from which a variety of thermo- dynamic functions may be calculated as described in section III,C. B. Physical Methods of Measurement 1. Vapor Pressure Measurements The compounds studied are quite refractory, with vapor pressures of 10-9 to 10-3 atm in a conveniently attainable temperature range. Such pressures may be measured68 by either Langmuir free evaporation or Knudsen effusion methods. The method chosen for this study was Knudsen effusion, which is based on the rate of effusion of the vapor through an orifice into vacuum. Determination of this rate may involve microbalance, torsion, 10 target collection, or mass spectrometric measurements, or some combination of these. Mass spectrometry gives information regarding the nature of the gaseous species, but a spectrometer is difficult to calibrate for absolute pressures. Spectrometry was used to identify the effusate vapor and the target collection procedure was employed in the vapor pressure measurements. 2. Theory of Knudsen Effusion The theoretical treatment.of molecular effusion was first described by Knudsensg’70 and more recently, in a general review by Cater68 and in more detail by Ward71. The derivation is based on the kinetic theory of dilute gases and in particular on the Maxwell-Boltzmann distribution of molecular velocities in such a gas. From this dis- tribution it can be shown that the number of molecules which pass through an infinitesimal plane area 68 from one side to the other in time interval St is given by equation (III-6), where n is the N = 93 as (St III-6 4 density, molecules per unit volume, and v is the average speed. If GS is a portion of the container wall, inclusion of the momentum transfer per collision gives the kinetic theory derivation for the vapor pressure. Alternatively, if 68 is an orifice in that (infin- itesimally thin) wall, equation (III-6) gives the rate of effusion through the orifice. For a finite orifice,So,and time interval, t, provided that the loss of molecules through the orifice does not significantly alter the equilibrium or velocity distribution, the effusion rate is given by equation (III-7). This equation may be N a n-VSot III-'7 4 11 combined with v = (8RT/1rM)l/2 from kinetic theory and with the ideal gas law to give equation (III-8) in which W is the mass of the effusate. P = w 2nRT 1’2 III-8 set M 3. The Target Collection Method The rate of effusion can be determined by collecting and analyzing a known fraction of the effusate. To determine the fraction collected it is necessary to know the angular distribution of the effusing molecules. The fraction of molecules from an ideal orifice passing through the solid angle increment dw is given by the cosine rule, (III-9). EE.= n‘lcos e dw III-9 N Here 6 is the angle between the normal to the orifice and the axis of dw. Integration over the solid angle subtended by a circular collector of radius r, coaxial with the orifice and at distance d from it, gives for the fraction collected r2/(d2+r2). This factor is combined with equation (III-8) to give (III-10) where W now refers to the mass of the P = 3.760xio‘4w[r]1/2[d2+r2] III-10 set M r fraction of effusate which strikes the target. Dimensions are P in atm, 2, t in min, and W in g. So in cm 4. Theoretical Limitations of the Knudsen Method a. The Non-Ideal Orifice In practice the orifice cannot be located in an infinitesimally thin wall, but is instead a channel of some finite length. Molecules which enter the orifice and strike the wall of the channel are re-emitted according to the cosine rule, and may be returned to the inside of the cell. The calculation of the decrease from the ideal effusion rate was first carried out by Clausing72 for channel 12 orifices and the correction term is called the Clausing factor. A conical orifice behaves more nearly ideally, especially at small values of 6. Effusion probabilities for conical orifice geometry have been evaluated by Freeman and Edwards73. b. The Steady State Approximation The derivation of the Knudsen theory requires that the equilibrium in the cell is not disturbed by the introduction of the orifice. In fact, it is, and the system is not in equilibrium but in a steady state with material continually being transferred from the sample, through the cell, and out the orifice. This transfer may result in measured pressures some- what lower than the saturated value. Theoretically, this steady state may be treated by considering the cell itself as an orifice, with its own Clausing factor. Motzfeldt7l+ has calculated the pressure gradient in real cells due to orifice loss, and 5 confirmed his work. a more rigorous treatment by Carlson7 Experimentally, large deviations from equilibrium result in the so- called "orifice effect," in which a large change in orifice area is accompanied by an inverse change in the measured pressure at a given temperature. Carlson et al.76 have suggested an empirical expression to correct the observed pressure to the equilibrium value, using the orifice area and sample area as parameters. c. Viscous Flow Another requirement of Knudsen theory is that loss of effusate does not alter the molecular velocity distribution in the Vicinity of the orifice. This is true if the mean free path is large compared to the orifice diameter; that is, if there is negligible chance that a molecule will experience a collision in the vicinity of the orifice. At higher pressures, collisions produce a cooperative effect, the ideal gas 13 assumption (molecules of zero diameter) breaks down, and so-called "viscous flow results. Knudsen70 arbitrarily set the upper limit of "molecular flow" at a mean—free-path/orifice-diameter ratio of 10, but in practice it has been difficult, if not impossible, to predict a_priori the onset of viscous flow for a given vapor and crucible design68. d. Small Knudsen Cells In many cases the large mean free path necessary for molecular flow is larger than the dimensions of the Knudsen cell. In this case most molecules leave a surface and go through the orifice without experiencing gaseous collisions, and the concept of an "equilibrium gas" is rather strained. Fortunately, the cosine rule holds for molecules scattered from a wall or emitted from the sample, so some degree of randomness is main- tained, although weak specular components of scattering have been observed in some special cases77’78. This problem is considered in more detail by Ward79. e. Vaporization Coefficient The vaporization coefficient, a, is defined as the ratio of the rate of evaporization of’a sample to the rate of collision on its surface from its equilibrium vapor. Values of a may vary from 0 to l, and are usually assumed to be unity unless there is evidence to the contrary, although cases of very low vaporization coefficientseo’el’82 have been reported. Low coefficients are characteristic of a potential energy barrier to vaporization, usually due to markedly different molecular geometry in the vapor and condensed phases. The low rate of evaporation leads to undersaturation and a more marked "orifice effect", but all but the most severe cases may be treated using a small orifice and a finely divided samp1e83. 14 f. Surface Diffusion In general a molecule striking the wall of a Knudsen cell does not immediately bounce off, but is absorbed, migrates some distance, and is then re-emitted according to the cosine rule. Molecules which strike near the orifice may migrate to the outside of the cell and be re-emitted, adding a spurious component to the effusate. This effect has been observed in some cases8” and treated theoretically by Winterbottom and Hirth85’86. Unfortunately, parameters necessary to make corrections using this theory are not available. The effect is least significant for species whose.residence time absorbed on the walls is short. 5. Practical Limitations of the Knudsen Method a. Characterization of Condensed Phases In assigning to the equilibrium constant the value of the vapor pressure, the assumption is made that all condensed species are at unit activity, that is, pure. There are several cases in which this assump- tion is not valid. In an incongruent vaporization, there is always some degree of mutual solubility of the two condensed phases. The container may interact with the sample, either raising or lowering the apparent pressure. Small amounts of dissolved impurities, especially oxygen87'89, have been shown to have drastic effects on vapor pressures, and such contaminants may even be produced in situ by reaction with residual gases if the system pressure is not kept sufficiently low. Extreme care must be exercised to assure that such effects are either absent or properly accounted for. b. Diffusion-Limited Vaporization In an incongruently vaporizing system the second phase tends to form on the outside of the vaporizing species, which must then migrate through it to the surface to enter the vapor phase. If the migration is slower 15 than losses through the orifice, undersaturation will result. This phenomenon is usually experienced as a trend of vapor pressure with time or particle size. c. Container Losses In some cases it has been shown that a significant fraction of the vapor molecules striking the container wall are permanently absorbed. Ward, et al., in experimentalgo’91 and Monte Car1092’93’79 studies have shown that this absorption leads to a pressure gradient in the cell and marked deviation from the distribution predicted by the cosine law at high angles. However, in most cases the effusate collected on targets coaxial with the orifice vaporizes directly from the sample and if the vaporization coefficient is unity such losses appear not to affect this form of Knudsen effusion. d. Collection Losses For meaningful measurements it is important to analyze all molecules which leave the orifice within the solid angle defined by the target, and only those molecules. Implementation involves several requirements: (1) The mean free path outside the cell must be considerably larger than d, the orifice-to-target distance, so that no significant number of molecules undergo collisions and are scattered away from the target. Residual vacuums of 10'5 torr or better are required. (2) A11 effusate striking the target must adhere. Experiments have been designed9‘+ to measure the sticking coefficient. (3) Any effusate not striking the target must be permanently removed from the system. It must not be re-emitted from the vacuum chamber walls. Re-emission is particularly a problem.when the condensed effusate is a conductor, ngL, a metal, and induction heating is employed. 16 e. Other Limitations There are several other problems encountered in converting Knudsen theory to practice. Temperature gradients within the cell and their effects95 must be avoided. Just as important, the tempera- ture must not drift with time as a sample is collected. Thermal expansion of the orifice must be considered, but Kent96 has shown its effects to be negligible. Mass spectrometry has made character- ization of the vapor phase much more straightforward than characterization of the comdensed phase (section III,B,5,a) but the spurious effects of fragmentation still must be considered. 6. Temperature Measurement The International Practical Temperature Scale of 1948 defines97 temperatures above 1336 K by the intensity of radiation by a black— body according to the Planck Radiation Law. This intensity is measured by optical comparison with the filament of a standard lamp in an optical pyrometerge. Corrections must be applied for absorption and reflection of light by the optical elements in the system. The correction is derived99 from Wien's law and given by equation (III-11), _1_ 1 _, A 1n 1 _ AH III-ll where Ta is the apparent temperature, T is the transmissivity of the optical elements, c2 (1.438 cm K) is the second fundamental radiation constant and A is the effective wavelength at T. Use of filters and the normal cutoff of the human eye makes A, and thus A(1/T), nearly independent of T. Values of A(1/T) for various components are additive as a consequence of Beer's Law. Correction for a non-black body may be made by including the emissivity e at wavelength A, as in equation (III-12). l 1 A 1n rs III-12 l7 7. X-Ray Fluorescence Analysis Atoms in excited electronic states may return to lower states by filling the vacancy from an outer orbital and emitting electromagnetic radiation of an energy characteristic of the element. Primary radiation results when the excited state is created by an electron beam. If it is created by a gamma ray or X—ray, secondary or fluorescent radiation results. Fluorescent radiation involving inner orbitals is in the eray region of the electromagnetic spectrum, and is simple and practically insensitive to chemical environment. Highly sensitive, non-destructive quantitative and qualitative analysis may be accomplished100 by energy analysis of this radiation. Wavelength-dispersive analysis uses the principle of Xeray diffraction as given by the Bragg equation, (III—13)., With the interplanar distance d nA = 2d sin ¢ . III-13 fixed for a given analyzing crystal, photons of different wavelength, A, and hence energy, are diffracted at different angles ¢. C. '-.Thermodynamic;Data Reduction 1. Second Law Calculations The Gibbs free energy is defined67 by equation (III-14), so at G = H - TS III-l4 constant temperature equation (III-15) will hold. Combining (III-15) AG§ v AH§ - TAS§ ' III-15 with equation (III-4) and rearranging gives equation (III-l6). To the =— O o _- ln KT AHT + AST III 16 RT R ‘ extent that AH; and A8; are independent of T, this is the equation of a straight line in 1n KT and l/T. Treatment of experimental 1n KT versus 1/T data by linear least squares gives the slope,_§, and intercept, b, 18 from which AH} = -Ra and ASE = Rb may be obtained. If the heat capacities of the reactants and products are known or can be estimated, the thermochemical values may be corrected to the reference temperature 298 K by equations (111-17) and (III-18). The . g 298 _ AH298 AH§ + 4 AdeT III 17 o = . 298 _ A8298 AST + f ACPdT III 18 T T term ACp is the heat capacity difference between the products and reactants. Although the value of T to which the line (III-16) corresponds is not well establishedIOI, the experimental median temperature Tm is usually used. Also, since ACP for the reaction over the temperature range of the measurements is generally non-zero, the data should exhibit slight curva- ture. Both these difficulties are overcome by the Z-plot treatment, which 7 or tabulated thermodynamic data102 incorporates heat capacity equations6 and gives AH§98 directly. 2. Third Law Calculations The free energy function (fef), as defined in equation (III-l9), is fefT = (G; - H398)/T III—l9 a smooth function of temperature and may be extrapolated with a high degree of precision. The function can be calculated directly for gases 67 when the spectroscopic energy levels are known . Rewritten as in equation (III-20), it may be calculated from tabulated or estimated fefT = H§ - H298.” (Sf - Sfigg) - S298 III-20 T entropies and heat capacities with the aid of equations (III-l7) and (111518). For a reaction Afef is the difference between the fef of the products and that of the reactants. The definition can be combined with equation l9 (III-4) and rearranged to give equation (III-21). Each experimental AH§98 = -T(Afef + R 1n KT) III-21 vapor pressure measurement may be treated by the third law method to give a value of AHfigg. The individual third law values may be examined for consistency and trend, either with temperature of chronological sequence. A temperature trend indicates a systematic error in temperature or pressure measurement or in the thermodynamic functions employed. Agreement between second- and third—law enthalpies is also used as a check of the measurements, the definition of the vaporization process, and the thermodynamic values. Such agreement ensures only internal consistency, not absolute accuracy, and should be used with care since the two measures of enthalpy are slightly-correlateleI. 3. Derived Thermodynamic Quantities The results of vaporization measurements may be used to obtain the energetics of formation of the reactant if the values for the products are known. For any reaction equation (III-22) holds, with i and j o _ o _ o _ AH298 ' EViAHf298i gvjAHf298j III 22 referring to products and reactants, respectively, in equation (III-2). Since for a vaporization there is only one reactant, it may be simplified as in equation (III—23). Identical expressions are valid for AGf298 AH£298j '-;l(§“1AHf29si' AH298) III'23 and ASE298. Comparison with AH2298 measured by other methods (Eifia: combustion calorimetry) gives a check on the vaporization results. The second law entropy change AS598 may be compared with the value calculated from absolute entropies if such values are available. Conversely, 20 it may be used to calculate an absolute entrapy for one of the constituents whose low temperature heat capacity has not been measured. Thorn and coworker3103-107 have used absolute entropies and a correlation between experimental enthalpy and entropy to choose a "best" value of enthalpy, but there exists controversyloa'110 whether the correlation is a physical phenomenon or an artifact introduced by the mathematical treatment. If AG§298 are known, they may be compared with the results of the vaporization, but no more information is gained than from come parisons of AH%298 and ASE298 directly. CHAPTER IV EXPERIMENTAL METHODS A. Materials Chemicals and materials used: (a) samarium and thulium metal, 99.9%, Michigan Chemical Corp., St. Louis, MI; (b) samarium sesqui- oxide and thulium sesquioxide, 99.9%, Michigan Chemical Corp., St. Louis, MI; (c) graphite powder, Grade No. 38, Fisher Scientific Co., Fair Lawn, NJ; (d) graphite rod, spectrographic grade, Becker Brothers Carbon Co., Cicero, IL; (e) tantalum seamless tubing, Fansteel Corp., North Chicago, IL; (f) molybdenum powder, 325 mesh, Fansteel Corp., North Chicago, IL; (g) molybdenum rod, Kulite Tungsten Corp., Ridgefield, NJ; (h) catalyst R3-ll, Badische Anilin und Soda Fabrik, AG, Ludwigshafen am Rheim, Germany; (1) Ascarite, A. H. Thomas Co., Philadelphia, PA; (j) hydrochloric acid, reagent; and (k) potassium chloride, reagent, annealed at 350°. B. Preparation Samples for effusion experiments were prepared by direct combination of the elements in sealed tantalum ampoules. Seamless tantalum tubing was outgassed in vacuum at >2000° for at least two hours, then one end was crimped and sealed by arc welding in an atmosphere of argon or helium. The graphite was also outgassed at >2000° in vacuum before use. Samarium metal was handled in a glove box, but this was not necessary for thulium. The metals were chipped from the ingots and weighed into the ampoule with a 5-10% 21 22 excess of graphite over that required for the dicarbide stoichiometry. The other end of the ampoule was then crimped and welded in the same manner. The welding chamber was evacuated twice to <0.2 torr and flushed with the welding gas before each weld, and then a zirconium button was melted to remove any remaining traces of oxygen. The sealed ampoules were heated inductively in vacuum to 1400- 1600° for 2-6 hours, then cooled and transferred to the glove box. C. Sample Handling All tantalum ampoules were opened in the argon-filled glove box. For early experiments this box was dried using open dishes of phosphorus pentoxide. For SmCz vaporization experiments 16A, 16B, and 16C it was dried by recirculating the argon through activated alumina and deoxygenating catalyst R3-ll. The two towers of alumina were alternately regenerated at 425°. Knudsen crucibles were placed in a ground glass weighing bottle for transfer to the vaporization apparatus, which was flushed with argon during the time required for assembly. After vaporization experiments the evacuated system was filled with argon and the same techniques were used to return the crucibles to the glove box port. Samples for Guinier eray powder diffraction or for mass spectromr etry were coated with light paraffin oil to prevent hydrolysis during transfer. D. Chemical Analysis 1. Free Carbon Analysis Analysis of unreacted graphite was effected by direct weighing of the residue of hydrolysis. Samples were hydrolyzed and dissolved 23 in 20 ml 3! hydrochloric acid, digested, and filtered into constant weight sintered glass crucibles. The precipitate was dried at 110° and weighed. 2. Thulium and Samarium Analysis Metal content was analyzed gravimetrically by direct conversion to the sesquioxide. Samples were weighed into constant weight crucibles in the dry box. Some were charred with a bunsen burner and then ignited at 950° in a muffle furnace. Others were slowly heated to 950° in a tube furnace under a flow of pure oxygen. Attempts were made to analyze for metal content with the solutions left over from determination of free carbon. They were adjusted to pH 4 with sodium hydroxide and the metal oxalate was precipitated by adding saturated oxalic acid solution. The oxalate precipitate was filtered into constant weight alundum cruc- ibles and fired to the sesquioxide. This method gave lower results and poor precision. 3. Total Carbon Analysis When metal analysis was performed in the tube furnace, the gaseous products were passed over CuO and CeOZ at 750° to catalyze conversion to C02, dried by passing over MgClO4, and collected on Ascarite. The total carbon content was determined gravimetrically as carbon dioxide. 4. Oxygen Analysis For the samples on which both metal and total carbon analysis were done, oxygen content was determined by difference. 24 E. XeRay Diffraction Samples were examined by eray powder diffraction before and after vaporization experiments. Debye-Scherrer (Cu K5) and forward-focussing Guinier-Hagg (Cu Kal) cameras were employed. Methods for aligning the Guinier camera are outlined in Appendix I. Sample preparation and film measurements were essentially identical to those described by Haschke9l+ and Stezowskilll. Annealed potassium chloride (a0 = 6.29300 1 0.00009 A)112 was used as an internal standard. Diffraction data were reduced with the aid of the linear regression program of Lindquist and Wengelein113. F. Mass Spectrometry A Bendix Model 12 time-of-flight mass spectrometer modified to include a Knudsen source was used to identify the species in the vapor over TmCZ. A tantalum crucible with a channel orifice, of the design described by Pilatoze, was heated by electron bombardment.~ Both continuous and pulsed ionization modes were used, with ionizing potentials of up to 55 ev. Appearance potential data were obtained by a linear extrapolation technique using mercury and nitrogen as internal standards. Since it is well documented2L*-26’L‘5 that Sm(g) is the only vapor species in the equilibrium with SmCi, no mass spectrometric investigation was made of the SmCZ vaporization. G. Target Collection Techniques The target collection apparatus used in these measurements has been described previously by Kent96 and Haschke9°. The targets were aluminum discs with a recessed collection surface, which was polished with 600 mesh emery paper, then cleaned with dilute HCl and distilled water before use. The target magazine was liquid nitrogen cooled. Haschke9° has shown that monatomic metal vapors have unit sticking coefficient on such targets. 25 Crucible to target distances were measured with a cathetometer after the magazine was cooled. They varied from 10.4 to 12.3 cm. Effusion cells of the two designs described by Haschke9° were fashioned from molyb- denum. Areas of the nearly knife edge orifices were measured with a compensating polar planimeter (Keuffel and Esser Co.) from 100x photo- micrographs made with a Bausch and Lomb Dynazoom metallograph. A 20-kva Thermonic high-frequency induction generator was used to heat the effusion cells. Targets were exposed with both increasing and decreasing temperatures. By replacing the target magazine with an optical window it was determined that the temperature gradient between the upper and lower black—body cavities was less than 5 degrees. H. X-Ray Fluorescence Analysis 1. Spectrometer Operation Exposed targets from effusate collection experiments were analyzed by eray fluorescence by use of a Siemens goniometer with 4b spectrometer attachment, LiF analyzing crystal, NaI(Tl) scintillation detector, and a tungsten anode eray tube powered by a Siemens Kristalloflex 4 generator. Operation parameters were optimized for Sm L81 and Tm Lal radiation according to the criteria set forth by Neff11°. Impurities in the aluminum targets gave a peak which interfered with the Sm Lal radiation. Counting and scanning procedures developed by Haschke115 were used. 2. Spectrometer Calibration Standard targets were prepared from solutions of the sesquioxide. Calcined Tm203 or Sm203 was weighed on a semi-micro balance, dissolved in a minimum of 6M HCl, and diluted volumetrically to give solutions containing 50 to 150 ug metal/ml of solution. These solutions were placed on targets identical to those used for effusate collection, with 26 an ultra-precision micro buret (Kontes Glass Co.). The targets were dried over phosphorus pentoxide and counted in the usual manner. Least squares analysis of the counts was used to obtain the sensitivity per microgram of rare earth metal. The calibration was linear between 0.5 and 15 ug. I. Temperature Measuring Equipment Temperature measurements were made with a National Bureau of Standards-calibrated Leeds and Northrup disappearing filament optical pyrometer (serial number 1572579). Prism and window transmissivites were measured by observations of a tungsten strip lamp powered from a constant voltage source. Corrections were made using the average value of A(1/T) from observations at several temperatures. Temperature measure- ments for preparative reactions in tantalum bombs were corrected for the emmissivity of tantalum (0.49 at 650 mu). J. Specific Experimental Conditions Pressure measurements were made at successively increasing and decreasing temperatures in the range 1630-2050 K for SmC2 and 1660-2130 K for TmCz. Orifice areas ranged from 7.2X10'” to 39.2X10'l’cm2 for the Sm—C measurements and from 11.8Xl0'° to 64.OXI0'5 cm2 for the Tm-C measurements. Under these conditions 3.0 - 15.0 ug of metal was collected on each target in times ranging from 2.0 to 60 minutes. The cells were charged with 0.25 - 0.65 g samples. Residual pressure in the system was maintained at 10'5 to 10'6 torr with a mercury diffusion pump and mechanical forepump. High-carbon compositions were studied by mixing weighed amounts of outgassed graphite with the dicarbide before loading it into the cell (runs 11, 15, 16A, 16B and 16C for Sm; l3 and 14 for Tm). Tests for container 27 interaction were made by placing the sample in a graphite cup inside the molybdenum cell (run 12 for Sm) or by using an equimolar mixture of SmCz, graphite, and 325 mesh molybdenum powder to charge the cell. A test to confirm contaminant interaction was made as follows. In experiment 16 a sample of SmCz was mixed with graphite and vaporized (16A) in the normal manner. It was then stored with the special handling tech- niques described in section IV, C, for the minimum time required to prepare the apparatus for a new experiment (16B). After experiment 163, it was stored again.with the same precautions, for a similar minimum time, but this time, 17 mg calcined Sm203 was added. This intentionally contaminated sample was used for experiment 16C. CHAPTER V RESULTS A. Preparative All preparations of SmC2 yielded a golden-colored powder, which was sometimes slightly sintered. This product was extremely hygroscopic, and produced the sharp odor associated with acetylene when it decomposed to a grey powder in the presence of traces of moisture. In spite of the precautions described in section IV,C, attempts to store this material for more than a few weeks were generally unsuccessful. Preparations of TmC2 yielded a similar golden-colored product when cooled quickly, or a black powder when cooled over a period of more than two hours. Both these preparations were quite hygro- scopic, but not to the degree of SmCZ. B. Analytical 1. Chemical Analysis Samples of both SmC2 and TmCZ were found to be generally metal- rich, 1.785C/M52.02, even though all samples also had unreacted graphite present, in amounts which varied from 1.2 to 1.7 weight per cent. Combined metal and total carbon analysis typically recovered around 99.2% of the sample, so contamination, considered to be oxygen, was about 0.8% by weight. 28 29 2. XrRay Powder Diffraction Analysis The X—ray powder diffraction patterns of the golden-colored forms of SmC2 and TmCz showed them to be body centered tetragonal, isostructural with CaCZ, as reported by Spedding et al.‘+ The black form of TmC2 gave an Xeray powder diffraction pattern which matched that of the low temperature modification of the dicarbides reported by Krupka et al.19 The very complex diffraction pattern of the black form of TmCZ has not yet been indexed satisfactorily on the basis of a single phase. An attempt was made to prepare single crystals by annealing and to determine the crystal structure. The resulting crystals were not sufficiently well formed for structure determination purposes, but examination of their Weissenberg eray photographs indicated that two phases were present. One phase, indexed on orthorhombic symmetry, has a much smaller volume than the cell proposed by Krupka et a1. and accounted for most of the powder diffraction lines. The other phase, indexed on hexagonal symmetry on the basis of single crystal diffraction data, showed the rather stringent reflection requirements hki, h + k i 2 - 3n; 001, 2 - 6n. This phase accounted for seven more of the powder diffraction lines, the only lines allowable under the aforementioned restrictions. Six of the remaining ten lines matched the strongest lines from the known impurities, graphite, tetragonal TmCZ, and TaC. The remaining four lines, all weak, were accounted for by relaxing the k + 2 - 2n restriction indicated by the single crystal eray photographs of the orthorhombic phase. The lattice parameters of these phases, along with the observed lattice parameters of the tetragonal SmC2 and TmCz structures, are listed in Table 2. The observed intensities, 30 interplanar d-spacings, and their assignments are listed in Appendix II. The black mixture of phases converted immediately to the tetragonal dicarbide upon heating in vacuum. Table 2 Observed Lattice Parameters of Phases Prepared in This Study Compound .3 b_ .2 Tetragonal SmC2 3.79 i 0.02* A 6.37 i 0.04 A Tetragonal TmC2 3.6026 i 0.0004 6.056 r 0.001 Orthorhombic "TmCz" 3.68 i 0.01 12.40 i 0.04 A 13.58 i 0.03 Hexagonal "TmC2" 3.19 i 0.01 16.74 i 0.07 *The indicated uncertainties are calculated standard errors. C. Mass Spectrometry Results 1. Vaporization Mode In the mass spectrometric investigation of the TmC2 vaporization, TmT (at m/e - 169) was the only shutterable peak in the region 160 s m/e s 210 when a 30 or 55 ev ionizing electron beam was used. Limits were set for carbide vapor species at ITmC2+ < 0.005 ITm+ and ITmC+ < 0.02 ITmf. The presence of a background peak at m/e = 181 decreased the sensitivity for TmC+. These observations indicate that TmCz vaporizes according to reaction (V—l). It has already been indicated in section IV,F that SmC2 vaporizes TmC2(s) : Tm(g) + 2C(s) k V-l by the analogous reaction (V—2). Second law treatment of seven (T’ITm+) SmC2(s) Z Sm(g) + 2C(s) V-2 data points in the range 1855-2150 K gave AH§2000 = 64.0 i 2.7 kcal/gfw. 2. Appearance Potential From the ionization efficiency curves for TmI, Hg+, and N; shown in 31 Figure l, appearance potentials of 10.1 volts for Hg+, 15.2 volts for N3, and 5.4 volts for TmT'were obtained. The literature values”6 : of 10.44 ev for Hg+ from Hg and 15.56 ev for N5 from N2 allow correction to a value of 5.7 ev for TmT with an estimated error of $0.2 ev. This value is in good agreement with the literature reports which vary from 5.81 to 6.51 ev for Tm(g) as the parent species, further confirmation that reaction (V—l) represents the vaporization mode of TmCZ(s). D. Vaporization Results 1. Behavior of Metal-Rich Samples No unusual vaporization behavior was noted for samples with C/M < 3. Metal rich samples first showed high erratic pressures which stabilized part way through a run. From the rate of metal loss and the chemical analysis of the sample it was possible to calculate the composition at any time. These calculations indicated that stable pressures were achieved very close to the MCZ.OO composition. For samarium, the measured pressures were within the range reported by earlier workers. 2. Behavior of Carbon-Rich Samples When excess graphite was added to the effusion samples (3 < C/M < 12) the behavior was different from that reported by earlier workers. Pressures were first high, then decreased after 2-3 hours of heating. Data collected during the first part of these experiments exhibited the lower enthalpy reported by earlier worker82192°:25. The second part of the experiment, however, gave pressures identical to those measured from samples which contained little excess carbon. A typical example is experiment 11 (Figure 2) in which the data points are numbered in the order in which they were taken. Additional experiments showed that the behavior was dependent on elapsed time, not ascending or descending temperature. 32 X r. X LI. Q L. HUD r- L. E L s I a 1.13”” T- T e T- t' t +- ~J 5.2» +- 800 +- >~\ e e H Ln .- E l" P“ EI/Ufll' ‘1 7711* t- X H’I' T- 0 Na“ 0.1—4.4. 1 1 gymnivi Li L 1 L_L [.7 ID ED 30 u IDNIZINE POTENTIAL Figure 1. Ionization Efficiency Curves 33 x R... II ”:5 DE' 0 PM [El H:‘I -ID- s R... 153 ”:4? '3’ D Run ’5: ”:0 _II '1 J l L l 1 J l l 1 J 9.3 5.1.7 5.5 5.0 //T x IU" (K") Figure 2. Vaporization Behavior of Carbon-Rich Samples 34 3. Container Interaction The X-ray diffraction patterns of the samples after effusion were examined carefully. In two instances the three strongest lines of the MoZC pattern were observed, but even when 50% of the sample had been depleted these were among the weakest lines in the pattern. Effusion of SmC2 from a molybdenum cell fitted with a graphite liner (Run 12) gave results almost identical to those of experiment 11 (Figure 2) in which a high carbon content sample was effused from an unlined cell. The two experiments in which molybdenum powder was added to the sample did not show the initial high pressures. These samples had little excess carbon (3 < C/Sm < 4) and gave the same pressures, within experimental error, as the near-stoichiometric samples discussed in section V,D,1. It was concluded that container interaction, although present, does not significantly affect the vapor pressure of the metal in equilibrium with the dicarbide. No change in pressure was observed when the orifice area was varied by a factor of six. This observation indicates that the cell lid was impervious to the diffusion of metal and that significant undersaturation (3:; III,B,4,b) was not present. Vapor pressures were kept below 0.6 torr to avoid the effects of viscous flow (g§_III,B,4,c). 4. Evidence of Contaminant Interaction Two significant features were observed during the first part of high-carbon effusion runs, that is, the part where the measured pressures were higher than expected. First, the residual pressure in the vacuum system was also somewhat higher than usual. Second, for TmCz-C samples, 35 the duration of the first part of the run was related to the duration of storage of the sample, and this initial high pressure region could nearly be eliminated by using freshly prepared TmC2 and freshly outgassed graphite. It has already been noted (Section V,A) that TmC2 was observed not to be as susceptible to hydrolysis as SmCz. In one experiment with a high carbon content sample the crucible was heated rapidly, and a very high system pressure resulted. A Tesla coil was used to excite a discharge in the residual gas. The color of the discharge - light blue - was attributed to carbon monoxide. Presence of this gas indicated contamination by an oxygen-containing species, which was reduced by the graphite. When the mass spectrometric experiment was done, such a contamination effect was just beginning to be suspected, and the m/e - 28 peak was moni- tored during initial heating. When the system pressure rose, the m/e - 28 peak increased and the H20+ peak at m/e . 18 did not. However, it was not confirmed (2:81, by fragmentation to c+) that this increase was due to CO and not to N2. Appearance potential data for N2 were taken well after the pressure returned to its base value. 5. Confirmation of Contaminant Interaction The results of series 16 (9f;_IV,J) are shown below those of experi- ment 11 in Figure 2. The line with each set of points indicates the pressure finally assigned for the equilibrium vaporization of SmC2(s). Experiment 16A was qualitatively similar to experiment 11, although the scatter was somewhat greater than usual. Points 5, 6, 7, and 8 are within 2.50, or 99% confidence level, of the line, while points 1, 2, 3, and 4 are all above the line by 3.5-4.50. A high residual system pressure (girga IXl0-“ torr) was observed during the exposure of targets 1-4. 36 The sample used in experiment 16B was still in the same composition range, but extreme care was taken to insure that no more oxygen reacted with it. There was a brief pressure surge in the system as the cell was heated to about 1350°, but it lasted less than the time normally allowed for equilibration. The measured vapor pressures were in excellent agree- ment with those represented by the line. In experiment 16C the only difference from 16B was the intentional contamination with 17 mg Sm203. The residual system pressure was high throughout experiment 16C, and all pressure data from it deviate positively from the equation finally assigned, five of them by >2.50. Thus the effect noted in the first part of the high-carbon content experiments is identical to that which results from addition of small amounts of oxide. 6. Vapor Pressure Equations for SmCz A11 SmC2 target collection data points shown in Figure 3 were collected when oxygen contamination was absent. The linear least squares equation which describes the 62 data points (1630 §_T §_2050K)is given by equation (V—3), where the uncertainties are calculated standard errors. 1n Psm(atm) - [(-32’740 i 460)[T] + (8.84 i 0.25) V-3 The pressures represented by equation (V-3) for the vaporization of SmC2(s) are in very good agreement with the values reported by Faircloth et al.21, whose work was done by target collection on almost stoichiometric samples, and that portion of the work of Cuthbert, et al.2° done by target collection. Oxygen contamination was undoubtedly present both in their work and in the portions of this study done on nearly stoichiometric samples, but its effect of high initial pressures and low enthalpies is similar to the effect of sesquicarbide usually present in dicarbide prepar- ations, an effect which was recognized and allowed for. 37 -Ln Pm“, (at m) V I0- 5.o 5T5 6.0 VT 3: IO4 (K") Figure 3. Equilibrium Pressure of Samarium Vapor Over Samarium Dicarbide 38 Since these three independent measurements of the Sm pressure in equilibrium with SmC2(s) are in such good agreement, the best expression would be derived by combining all three studies. Such an equation (V-4), was derived by combining into one set the data 1n Psm(atm) . [(-3l,520 r 3oo)/T] + (8.15 i 0.20) V-4 collected in this study, the 56 data points reported by Faircloth et al., and a data set constructed with a random number generator to duplicate the equation, standard error, temperature range, and number of data points reported by Cuthbert, et al. This expression is believed accurate to within r 0.20 in 1n P throughout the temper— ature range of 1400-2080 K. From equation (V-4) and the relationships in section III,C,1 the following thermodynamic values are calculated for reaction (V—2): AH§1740 - 62.63 i 0.60 kca1/gfw and AS$1740 - 16.19 i 0.40 eu. 7. Vapor Pressure Equation for TmCZ For TmC2 (Figure 4) the linear least squares line which describes the 46 data points (1660 5 T 5 2130 K) collected when oxygen contam- ination was absent is given by equation (V-5), where the uncertainties 1n PTm(atm) 8 [(-35,570 1 340)/T] + (8.98 i 0.18) V-5 are calculated standard errors. From equation (V-5) and the relationships in section III,C,1 the following thermodynamic values are calculated for reaction (V-l): AH31895 - 70.68 i 0.68 kcal/gfw and A831895 - 17.85 i 0.36 en. E. Thermodynamic Data Reduction 1. Thermodynamic Values Employed a. Heat Capacity Functions Measured values of the heat capacity of graphite5° and values of the heat capacities of the gaseous metals calculated from spectroscopic 39 ’ RUN 3. ~"I . D 2 A' A5 v V 8 . 0:2 0 IS a- 45' 9" Vl4 s 3 I O 33 '. 5 I0- ¢_ 0. " I: v ..I a g 0 II- , o,- O 0 l2" 0° 0 l l I 5.0 5.5 6.0 Figure 4. I/T x IO4 (K") Equilibrium Pressure of Thulium Vapor Over Thulium Dicarbide 40 data117’118 were available. The heat capacities of SmCZ and TmC2 were assumed to be that of CaC2 of the same crystal modification (cf. II,E). The AS° trans for the tetragonal to cubic conversion was assumed to be the same for all three carbides. From the enthalpy of transition for CaC2 (1.33 kcal/gfw)5° at 720 K, calculated values were AH° = 2.16 trans kcallgfw for SmCz and AH° trans - 2.50 kcal/gfw for TmC2 at their transition temperatures10 of 1170 and 1355 K, respectively. From these heat capacity relationships, enthalpy and entropy increments were calculated using equations (III-l6) and (III-l7). b. Absolute Entropies Literature values were employed for S298 of graphite5°, samarium 17 vaporl. and thulium vaporlla. An estimate of 8398(MC2) was made from 8398(Ca02) - 16.8 euSL+ by subtracting Latimer's estimate119 of the calcium lattice contribution and adding the lanthanide lattice contri- bution120 and a magnetic contribution N 1n (2J+1). This calculation gave 8398(SmC2) - 25.2 eu and S§98(TmC2) - 25.8 en. The estimating procedure is considered accurate to r 1.5 eu. c. Free Energy Functions From the enthalpy and entropy increments and values of absolute entropy, free energy functions were calculated according to equation (III—20). The difference in free energy of the reactants and products, Afef, was calculated for reactions (V-l) and (V—2) over the temperature range of the measurements and the results are tabulated in Appendix III. d. Additional Thermochemical Values In order to calculate enthalpies of formation of the dicarbides, the enthalpies of formation of the metal vapors were taken from Hultgren's compilation121. For calculations (section V,F) of the effect of oxide contamination on the apparent vapor pressure, the thermodynamic values 41 for the sesquioxides as reported by Holley, Huber and Baker122 were employed. 2. Results of Second Law Treatment The thermodynamic values derived (3:; V,D,6 and V,D,7) from the pressure equations for reactions (V—l) and (V-2) were reduced to 298 K by use of the approximated heat capacity data. For the vaporization of SmC2(s), AH; 298 = 66.9 i 1.0 kcal/gfw and A3; 298 - 21.4 i 1.0 eu. For the vaporization of TmC2(s), AH; 298 - 79.1 i 1.3 kcal/gfw and A8; 298 - 27.5 r 1.3 eu. The error values indicate a composite of standard deviation and estimated error in the thermodynamic functions. The values of AH; 298 have been combined with the enthalpies of formation of the gaseous metals121 at 298 K according to equation (III-23) to give AH; 298 (SmC2(s)) = -l7.5 r 1.3 kcallgfw and AH; 298(TmC2(s)) = -23.6 r 2.0 kcal/gfw. The experimental entropy of vaporization of SmCZ compares well with the value calculated from the absolute entropies, 21.3 eu. The entropy value calculated for vaporization of TmCz, 22.3 eu, is not in satisfactory agreement with the experimental value. 3. Results of Third Law Treatment The independent third law enthalpies, along with the pressure and temperature data from which they were calculated by equation (III-21), are shown in Appendix IV. The average value for SmC2 was AH; 298 - 66.5 i 3.0 kcallgfw, with no significant temperature dependence in the values. The values for TmC2 show a temperature trend of 2.3 kcal/gfw over the temperature range of the measurements, and their average, AH; 298 = 69.1 i 4.0 kcal/gfw, is not in satisfactory agreement with the second law value. 42 4. The Absolute Entropy of Thulium Dicarbide It has been shown in the preceding two sections that the results for the vaporization of TmCz do not form a consistent set. Since it was believed that the disagreement was larger than could be explained by possible systematic errors in vapor pressure measurement, considerable attention was given to the thermochemical values and to other schemes for estimating them. From this study it was found that the discrepancy can be isolated in the SE98(TmC2) term. In particular, if this entropy is estimated by Latimer's method (gf; V,E,1,b), but no contribution for magnetic entropy is added, the following results are obtained: (1) The calculated entropy of vaporization is As; 298(TmC2) - 27.4 eu, in good agreement with the experimental second law value of 27.5_eu; (2) The average third law enthalpy is AH; 298(TmC2) - 78.7': 3.0 kcallgfw, in good agreement with the second law value of 79.1 i 1.3 kcal/gfw; and (3) there is no discernable temperature dependence in the third law data. Appendices III and IVB include the values calculated for TmC2 both with and without a magnetic contribution to the estimated entropy. . Such internal consistency alone is not substantiating evidence for lack of a magnetic entropy cOntribution inTmCz, but independent confirmation is available. As has been indicated earlier (3:; II,B) Atoji17 has found by neutrdn diffraction that TmCz is the only lanthanide dicarbide studied which does not undergo an antiferromagnetic transition at low temperature. It is the entropy of this transition which is not observed in the vaporization results. Taken together, these observations strongly suggest that in the dicarbide environment the Tm+3 ion has a non-degenerate ground state, and that S§98(TmC2)I 20.7 i 1.2 eu. The results of thermodynamic data reduction are summarized in Table 3. 43 am m.H n m.- as m.H A m.m~ zuw\amos o.e A H.mc cowuanfiuucoo haouusm ofiuocwma Saws .NUEH so ~.H H s.e~ am m.H am ~.H a h.oN so m.H 3mm\flmua o.~ H e.m~- 3mw\amuah m.H 3mw\Hmux o.m H a.m~ 3em\amox o.m so m.H H m.n~ so o.H am sm.o A mw.aa no os.o smw\flmux m.H_H H.m~ smw\amus o.H 3mm\amox ms.o A mo.o~ suw\amox oo.o e mama M Gena coausnfiuucoo %aouuam oauocwma uaonuws .NuaH Noam muasmom afiemazvoauony mo unmeasm m mHan +| +l +| +| H H +| +l m.H~ AuHmUmeN awe ~.m~ Amozvmsmm m.ean Amozvmmm we QQDHN> U0>HHOQ mosam> 3mg unfiny e.H~ Aaxmvmequ mH.oH a Wme a.oo mam was mo.~o a ”ma ousumuoneoe owsmuvfiz moaam> 3mg vacuum 44 F. Thermodynamic Treatment of the Contaminant Reaction 1. The Reactions Involved It has been proposed that the anomalous vaporization behavior of high carbon content samples was caused by the reduction of oxide—bearing contaminants by the graphite and the resultant increased metal pressures. It would be valuable to ascertain if such a reduction is thermodynamically feasible. Although the oxygen bearer may well have been one of the oxide carbides 123‘125, it is informative to consider the thermodynamics of reduction of the lanthanide sesquioxide, reaction (V-6). The dicarbides Ln203(s) + 3C(s) : 2Ln(g) + 3C0(g) V-6 can be prepared by reaction (V-7) (9;; II,A), and microscopic examination Ln203(s) + 70(3) + 2LnC2(s) + 3co(g) v-7 of quenched reaction mixtures revealed free metal. Since the sesquioxide can be expected to have higher oxygen activity than an oxide carbide, its reduction thermodynamics, as discussed in the next three sections, will indicate the highest possible metal pressure in such a system. 2. A Kinetically Controlled Vaporization If under Knudsen conditions equation (V-6) has a higher equilibrium Ln(g) pressure than reaction (V-l) or (V-2), then reaction (V-8), the Ln(g) + 2C(s) + LnC2(s) V-8 reverse of the vaporization, can be expected to take place, and will lower the pressure of the lanthanide vapor. The observed pressure will not be an equilibrium value at all, but will depend on the relative rates of reactions (V-6) and (V-8). The pressure corresponding to (V-6) will be an upper bound on the Observed value, and that corresponding to (V-l) or (V-2) will be a lower bound. 45 3. The Phase Rule Reaction (V-6) is an example of vaporization of a ternary system, that is, C - 3. Since there are three phases, two solid and one gas, application of the phase rule leads to F - 2, and a vapor pressure equation will be meaningless unless another condition can be imposed. Fortunately, the mass balance requirement leads to a condition concerning the composition of the vapor. According to equation (V-6), two moles of metal vapor are produced for every three moles of carbon monoxide. Then at steady State, for every three moles of CO effused through the orifice, two moles of metal must either be effused or be consumed according to reaction (V-8). The principal loss is by effusion through the orifice, so equation (V-9), coupled with the Knudsen equation (III-7), gives for wLn . wco v—9 2MLn 3Mco the composition of the gas phase equation (V-lO). Again, due to the . 1/2 _ PCOCg) _3_[Mco] PLMS) v10 2 MLn fact that Ln(g) is also consumed by reaction (V-8), this equation represents an upper limit to PLn(g)’ in agreement with the kinetic arguments presented in section V,F,2. 4. Results The thermodynamics of reaction (V-6) can be considered in terms of equation (III-22) as a sum of the thermodynamics of formation of Ln203(s), CO(g), and Ln(g), all of which are well characterized specie8121’122’126. The AH§98 and Afef for reaction (V-6) have been calculated for Ln = Sm, Tm and the third law procedure was used with equation (V-10) to calculate the Ln pressure. The results for Sm are shown in Figure 5, along with the various reported values of PSm over SmCZ. The equilibrium pressure over the oxide Ln P517169) [n+mJ 46 l‘Calc . for Sm203-C h Avery, gt a1.25 --Cuthbert, et a1.2° Pilat026+ ’ This Work- Composite Stout, et alg7- L 11' 5.0 5.5 5.0 I/Txm" (K") Figure 5. Equilibrium Samarium Pressure Reported for SmCZ and Calculated for Sm203-C 47 mixture is higher than that over the dicarbide. Pressures observed over contaminated samples would be intermediate between the two values (2:; section V,F,2). Likewise the results for Tm (Figure 6) show the same relationship. Thus it is thermodynamically feasible that oxide contamination of SmCZ and Tmcz caused the observed anomalies in the vaporization. 5. Extension to Other Lanthanide Dicarbides The calculations described in the last section have been carried out for the other lanthanide elements to predict which other systems might be similarly affected by oxide contamination and to establish a criterion for evaluating conflicting reports of the decomposition pressures of other dicarbides. The results fall into three classes. The calculation of AH298 for reaction (V-6) is predominated by the enthalpy of formation of the lanthanide sesquioxide, which is relatively independent of the identity of the lanthanide. Thus PLn for reaction (V-6) is of the same order of magnitude for all the lanthanides. For the first class, the very refractory carbides, all CO(g) would be removed well before the temperature necessary for dicarbide vaporization was attained. No difficulties should be encountered in the vaporization of these dicarbides, with the possible exception of HoC2, which might be volatile enough to behave like SmCz and TmC2 in the presence of oxide. Haschke37 has noted that the enthalpy of vaporization of H002 is not in line with those of the other dicarbides. The second class includes the single carbide, YbCZ, which is so volatile that its metal pressure is clearly greater than the pressure over a graphite-oxide mixture. This is shown in Figure 7. It should be noted that the higher Yb pressure will not drive reaction (V-6) to the left because there is no significant source of CO(g). Thus Yb203 in a YbCz-C 48 \ \ c. for Tm203-CJ\ Ln F’Tm(’)[n+mJ This Work+ \\ l I L 5.0 5.5 5.0 //Txl[7"’ (K‘U Figure 6. Equilibrium Thulium Pressure Reported for TmC2 and Calculated for Tm203-C 49 r‘ E .3. -3 . \ ’3. E \ UL _ s \ .lc7 — \ Haschke and Eick37 + I- \Calc. for Yb203-C . .\ J , 5.0 5.5 7.0 7.5 I/Tx/0" ((0 Figure 7. Equilibrium Ytterbium Pressure Reported for YbCz and Calculated for Yb203—C 50 vaporizing mixture is an inert contaminant. The last class is that of EuC2. The results are shown in Figure 8. There is a considerable discrepancy in the reported pressure of EuCZ, but this calculation cannot unambiguously resolve it, since part of Gebelt's line lies above the upper limit set by the oxide reduction line. There is a large uncertainty in this particular upper limit, because the low temperature calorimetric work on Eu203 is unsatisfactory and there is a 2.0 eu uncertainty in 8598(Eu203). When better thermodynamic values become available, they may place the pressure of (V-6) for Eu greater than Gebelt's pressure and suggest that his experiments involved an oxide-graphite reaction ratherthan the dicarbide equilibrium decomposition. ,. . tun-_1' 51 Ln PE» (I) [aim] \rCalc. Cuthbert, et a1.2”+ \ i l Faircloth, et S31. 21 Gebelt and Eick30 L 5.0 5.5 7.0 0.0 ”7.10” (K'l) Figure 8. Equilibrium Europium Pressure Reported for EuCZ and Calculated for Eu203-C TKH", CHAPTER VI DISCUSSION A. Evaluation of Experimental Conditions 1. Sample Handling Even the stringent procedures adopted for keeping the dicarbide samples free of moisture were not totally successful, as was evidenced by the momentary pressure surge on heating (2:; V,D,S) in experiment 163. It has been suggested that instead of building glove-boxes in wet rooms, we build dry rooms and let the scientists wear glove suits. Until this procedure becomes practical, it seems necessary to accept and account for inevitable contamination of such extremely hygroscopic materials in the course of handling. 2. The Attainment of Knudsen Conditions The attainment of most conditions required for Knudsen effusion (5f; III,B,4 and III,B,S) is evidenced by consideration of the trends in the experimental data. The use of the target collection method minimized the effect of the adverse cell length to mean-free—path ratio, the slightly non-ideal orifice, and possible wall losses. The invariance of measured pressures with change in orifice area indicates that there was no serious effect from undersaturation, non-unit vaporization coefficient, or surface diffusion. Other investigators have attributed the low enthalpies of vapor- ization observed in the Ser system to diffusion limitations in samarium deficient samples, but the oxide reduction reaction is a 52 53 more satisfactory explanation, and no other indications of diffusion limited vaporization were observed. Container-sample interaction was demonstrated to have negligible effect. In any incongruent vaporization, the two solid phases will exhibit some mutual solubility and thus are not truly at-unit activity. As long-as this solubility is small and not strongly temperature dependent, it will not affect the consistency of the thermodynamic data. A more subtle effect on the activity of the condensed phases, and on the collection efficiency, is discussed in the next section. 3. An Improved Target Collection Apparatus In the discussion (section V,F,l) of the oxide reaction it was assumed that all oxygen would eventually be removed from the condensed phase by evolution as CO(g). After the oxygen was gone, the Ln(g) pressure would be that of pure TmCz. In actuality, it is not possible to remove all the oxygen from the solid because it is impossible to remove all the CO(g) from the system. The CO(g) pressure will be determined by the residual oxygen pressure in the system according to equilibrium (VI-1). Thus it is quite valuable to lower the C(s) + 1/2 02(g) I CO(g) VI-l residual pressure in the system far beyond the limits set by free path arguments (sf; III,B,5,d). Since these experiments were completed, the author has designed and constructed a vaporization apparatus capable of a much lower residual pressure. This feat was accomplished through three design features: (1) A11 glass walls and grease-sealed ground-glass joints were replaced by water-cooled stainless steel walls and OFHC copper gaskets. To permit the metal encasement, the induction coil was placed inside the vacuum chamber. Two frequently opened seals are 54 fitted with Viton O-rings. (2) The system is pumped by a four-inch diffusion pump charged-with Convalex-lO, a polyphenyl ether of extremely low vapor pressure and backstreaming characteristics. (3) The chamber is pumped through a straight six inch diameter tube, as short as was practical, to give a high conductance and make full use of the pump speed. The resulting system operates at 1><10"8 torr base pressure, and as low as 3><10'8 torr with the sample at 2000°. This is an improvement of two and a half orders of magnitude over the glass system. In the partic- ular case of the dicarbides it is not expected that this lower residual pressure would result in significantly different vapor pressures, but in future studies it will result in increased confidence in the data. Other advantages of the system include the removal of a safety hazard by making the high-voltage induction coil less accessible; more ideal collection efficiency, both due to the lower scattering of the beam and permanent removal of the wide angle effusate by condensation on the chilled, conducting walls; direct mechanical linkage to the target changer; and installation of a thin film monitor in the molecular beam to give immediate indication of orifice clogging, sample depletion, and other similar features. 4. Fluorescence Analysis XeRay fluorescence analysis is a very convenient technique for target collection effusion studies. It is non-destructive, sensitive, and requires no preliminary treatment of the sample. The major disadvantage was the tedium of the counting procedures. Recently acquired equipment, including voltage— and current-stabilized power supply, vacuum spectrometer, and high diffraction efficiency graphite analyzing crystal, has reduced analysis time while drastically improving counting statistics. Suggested new methods of standard target preparation, including coulometric deposition of the metals on the targets, should improve the accuracy of the technique 55 even further. 5. Temperature Measurement The systematic error in temperature measurement due to the limitations of the pyrometers is quoted to be 14° in the National Bureau of Standards certification. Temperature gradients from the top to the bottom of the crucibles were also around 14°. The random error introduced by observer fatigue was estimated to be 52° as determined from a number of successive :f -1 V. 1.5.1. at v "lb 5. i- reading of the standard lamp's temperature. In this study these errors I'L"'.é 1" were comparable to the errors in pressure measurement, but with the new .‘l‘. target collection and eray fluorescence equipment in use, it is antici- pated that temperature measurement may be the most significant source of L j errors in future vaporization studies. More accurate temperature measuring techniques need to be found for further improvement of the target collection technique in this laboratory. B. The Effects of Oxide Contamination l. Explanation of the Anomalous Behavior In view of the known hydrolysis behavior of the dicarbides, it is believed that the anomalous pressures observed over carbon-rich carbide samples results from oxide contamination, with the excess carbon reducing any oxygen bearing species to form CO(g) and Ln(g). It has been demon- strated that thermodynamically, such a reaction could give a higher lanthanide pressure, and the mechanism also accounts for the higher residual system pressure. The evidence for the presence of CO(g), although not conclusive, supports this hypothesis. All reported lower enthalpies of vaporization from high carbon content samarium dicarbide samples have involved experiments conducted with a mass spectrometer. Since several hours are required for complete evolution of 56 CO(g), these experiments could have been completed before the oxide which caused the high szpressure had been removed. Presence of oxygen in near- stoichiometric samples would have been interpreted as presence of excess metal, which causes similar higher pressures. Experimenters would have waited until the pressure stabilized, whether they were using a mass spectrometer or other methods. Failure to observe an oxide species in X-ray diffraction patterns is not disturbing. First, it would not be present after a vaporization; second, experiment 16C shows that the sesquioxide contamination required is so small that it would be unobservable by this technique; and third, oxide formed by hydrolysis has very poor crystalline structure and would have to be annealed before it could be observed by powder diffraction, even if present in large amounts. 2. The Kinetics Involved As was shown in section V,F,2, the samarium pressure observed over an oxide-contaminated samarium dicarbide vaporization sample is dependent on the relative rates of the two competing reactions, (V-6) and (V-8). The observation of free metal in quenched preparations of the dicarbide from the oxide indicates that the rate of reduction (V-6) is at least comparable to the rate of formation of the dicarbide. Examination of Figure 5 shows that in some cases it can clearly predominate. Avery, et a1. quote results which are in better agreement with the thermo- dynamics of reaction (V—6) than of (V-2). This observation suggests that the contaminating species is probably one of the oxide carbides which have carbon and oxygen in close proximity in the crystal lattice and not sesquioxide, whose rate of reaction with graphite would be dependent on the low mdbilities in the solid phase. ,- . ,. 'F' ‘ ‘41.... . 57 3. The Reaction Trend The slight variation in lanthanide properties, particularly the volatilities of the dicarbides, has led to a complete reversal of reaction paths in the instance of oxide contamination. The effect of this contamination ranges from nil for YbCz, to so great as to be unmistakable for the commonly trivalent metals. Only in the intermediate range of volatility does the oxide contamination seriously interfere in a vaporization study. This conclusion illustrates that interpolation, as well as extrapolation, of the properties of the lanthanide compounds must be done with reservation. 4. Observations Concerning the Preparation of YbCZ and EuC2 Since the pressure of Yb over YbCZ is higher than that over Yb203-C, one would expect that YbCz could not be prepared from the oxide and graphite, at least under conditions resembling those in‘a Knudsen crucible. No report of such a preparation has been found, although most of the other dicarbides have been prepared in this manners. In contrast, a recent report127 indicates that EuCz can be prepared by graphite reduction of the oxide. This observation suggests that oxide contamination in EuC would 2 have the same effect as that in SmCz and TmCz. C. Evaluation of Thermochemical Results 1. Comparison with Previous Work This work extends and confirms (cf. V,D,6) the vapor pressure values reported for SmC by Faircloth, et a1.21 and that portion of 2 the work of Cuthbert, et al.2° done by target collection. Both these studies used techniques which were not likely to be affected by oxygen contamination. The pressures reported by Stout, et a1.27 agree with the composite line (V-4) to within experimental error 58 at the higher end of the temperature range and those of Pilato26 agree at the lower end. Avery,et a1.25 and Cuthbert'sz° mass spectrometric results are both significantly higher and both show the composition dependence noted previously. 2. The Low Temperature Modification of TmC2 No correction has been made for the enthalpy of the tetragonal- 9 At present it low symmetry transformation of thulium dicarbide.1 is believed that the "low-symmetry-modification" consists of two phases. Apparently tetragonal TmC disproportionates on cooling, 2 and until some method is developed to prepare the phases in pure form, neither can be characterized satisfactorily. In.some respects the behavior of TmC2 resembles that of UCZ' Below 1514° UC2 is unstable with respect to sesquicarbide and graphite, but it is not uncommon to find the non-equilibrium mixture: UC, U C3, UC 2 2’ and graphite as the reaction product.128. It is possible that one, or both, of the thulium-carbon phases may be oxygen stabilized; Krikorian'slg.results with other heavy.lanthanide dicarbides preclude tantalum stabilization. It is interesting to note that the tetragonal form of LuC2 has been prepared only from Lu metal samples which contained 2% Ta.11 Krikorian, who used high purity Lu, reports only the "low symmetry modification" of LuC .Since this modification is 2. apparently diphasic, the dicarbide of.lutetium may not exist. It should be understood that the value of AH; 298(TmC2(s)) herein reported refers specifically to the tetragonal.modification. 3. . Validity of the Thermodynamic Approximations The methods used for estimating the thermal functions are generally fairly accurate. If.CaC2uis.sufficient1y similar to 59 SmC2 and TmC2 to be used as a model, the estimated thermodynamic values should be quite adequate.. If CaC2.is not a suitable model, there is no way to assign an error magnitude to the estimations. It is characteristic of the methods that the second-law enthalpy is dependent primarily on the experimental data, with a small correction from the thermal parameters, whereas the third law method weights data and thermal functions about equally in determining AH; This weighting is reflected in the much larger- 298' error estimates assigned to the third law values of AH; 298' Because the experimental data were considered less likely to contain serious systematic error than the thermodynamic function estimates, the O 0 second law AHv 298 alone was used to calculate AHf 298’ even though use of an average or the third law value alone is more common. D. The Electronic Ground State of TmC2 In.section V,E,4 it was concluded that the ground'state of Tm+3 in TmC2 is non-degenerate. The freesion.ground state-is a 3H6.term, and no other free ion term is low.enough to be considered as an alternative ground state in.the crystal. Therefore in TmC2 the crystal field must split the free ion term to a chemically significant degree. At room temperature magnetic susceptibility measurements17 are consistent with the 3H6 state, so the splitting must.be less than kT at this temperature (200 cm-l), and all the 3H states are thermally 6 populated. However, in the region of 50 K, where antiferromagnetic transitions occur for the other lanthanide dicarbides, kT is only 35 cmfl. The splitting in TmC -must.be greater than this, so that at 2 this temperature the Tm+3 ion is already in a nondegenerate state and there is no driving force for.the.antiferromagnetic transition. This small crystal field effect is in the range observed for splitting of ‘iv. ‘47—‘— I. 6O fn configurationslzg, but it is thermodynamically very significant: it results in a change of 1n P over TmC2(s) of 2.5 units. Tm E. The Correlation in Vaporization of the Lanthanide and Alkaline Earth Metals and Their Dicarbides Figure 9 shows Haschke's37 correlation between the enthalpy of vaporization of the lanthanide and alkaline earth dicarbides and the vapor pressure of the pure metals at 1500 K. Those points designated by asterisks have been indicated by Haschke to be in question. The vapor pressures121 of samarium and thulium at 1500 K and the enthalpies from this study have been included. It is seen that they extend well the linear relationship expected from theoretical considerationsl30. 61 _l I I l I' N ’\ .. \E" 2 ’\ \‘2 — 2 'N .. ’5 qJ: 5 E .. '\ _ qt \3‘ d FL; \, as " 'E'us lLPE LAM Le a r r- :2 T at a“ 3‘ b .. QB ‘~J g 0 U L l L l s s a e Figure 9. The Correlation of the Metal and Metal Dicarbide Vaporizations "n I'II'- .. .-_. CHAPTER VII SUGGESTIONS FOR FUTURE RESEARCH This investigation has indicated several topics which should be investigated to develop a unified body of knowledge concerning the lanthanide dicarbides. Low temperature heat capacity measurements of tetragonal TmC2 should be carried out to confirm the standard entropy indicated in this study. Theoretical calculations of the crystal field splittings of the Tm+3 ground state in the tetragonal symmetry field would also be valuable, and might indicate other lanthanide compounds in which the crystal field splitting effect could be expected.tolbe chemically significant. The equilibrium vaporization of EuC2 should be repeated with special attention paid to the effects of oxygen contamination on the vapor pressure. Alternatively, the calculations performed in section V,F,5 should be repeated as better values become available for the standard entropy of Eu203. ,The.vaporization of..HoC2 is also suggested as a significant topic of future study. 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W. M. Latimer, "Oxidation Potentials," 2nd Edition, Prentice Hall, Englewood Cliffs, NJ, 1952, Appendix III. E. F. Westrum, Jr., "Advances in Chemistry Series, No. 71, Lanthanide/Actinide Chemistry," R. F. Gould, Ed., American Chemical Society, Washington, D. C., 1967, pp 25-50. R. Hultgren, "Supplement to the selected Values of Thermodynamic Properties of Metals and Alloys," Private COmmunication (AH; 298 = 49.4 i 0.5 kcal/gfw [Sm] and 55.5 r 1.0 kcallgfw [Tm]). C1 E. Holley, Jr., E. J. Huber, Jr., and F. B. Baker, Prog. Sci. Technol. Rare Earths, 1968, 343. A. D. Butherus, R. B. Leonard, G. L. Buchel, and H. A. Eick, Inorg. Chem., 5, 1567 (1966). A. D. Butherus and H. A. Eick, J. Amer. Chem. Soc., 90, 1715 (1968). 125) 126) 127) 128) 129) 130) 71 J. M. Haschke and H. A- Eick,.Inorg. Chem., 9, 851 (1970). "JANAF Interim Thermochemical Tables," D. R. Stull, Project Director, Dow Chemical Co., Midland, MI, 1960. N. N. Matyushenko and O. P. Svinarenko, Ukr. Fiz. Zh., 13, 1083-(1968); Chem. Abstr.,.69,-11296lv (1968). E. K. Storms, "The Refractory Carbides," Academic Press, New York, NY, 1967. F. A. Cotton and G. Wilkinson, "Advanced Inorganic Chemistry," WileyrInterscience, Inc., New York, NY, 1966, p 1058. J. M. Haschke, University of Michigan, personal communication, 1971. 7 APPENDICES APPENDIX 1: Instructions for Realigning the Guiner Cameras It is assumed that the operator is familiar with the geometry and basic operation of the Guiner camera and with good X-ray safety techniques. CAUTION: During the alignment process the X—ray generator will frequently be energized without the usual shielding material in place. The lead apron should be worn at all times. ‘When checking with the fluor- escent.screen, a lead-glass plate should be placed over the box. For making adjustments with the beam on, wear the lead gloves. A. Preliminary Setup (1) Remove and identify each piece of the camera as shown in Figure A-l. If the crystal is not to be changed, figungg take apart the mono- chromator assembly; omit part B. (2) If X-ray tube has been moved, optimize as follows. If only the box has been moved or if the other camera Hasalready been realigned, omit (a) and (b)- (a) ’Move box to center of its motion (three bolts on bottom) with respect to forward-back, sideways, and twist motions. (b) With Azaroff beam tunnel in place, glassplate over top of box, lead apron on, and a fluorescent sdreen in front of window in box, turn the generator on to 25 KV, 5 mA. Turn off room lights and open shutter.) Slide the eray tube back and forth in the dovetail until the image in the fluorescent screen is a full circle of maximum intensity. Lock the tube in position with the Allen head set screw. 73 (3) (4) (5) 74 (c) Put the main base plate in the box and mount the monochromator vernier base plate on it with the two long screws, again with it in the center of its motion. (d) Move the box sideways until the pin on the vernier plate is 9 cm from the tube anode (center of the tube housing), without disturbing the forward-back position; or, if (b) was omitted, move box forward or back at this time to meet the conditions of (b). (Note: This pin marks the exact center of the monochromator crystal.) Remove the vernier plate. Using a small level adjust the three leveling screws until the main base plate is parallel to the top face of the tube mount-shutter assembly. Turning all three screws the same amount to maintain this level, raise or lower the main base plate to 1-1/8" below the center of the window in the box. Recheck the level, then lock the leveling screws. Plotting The Beam Path - With the beam on (25KV, 5mA) use the fluorescent screen to find the center of the beam at several distances from the tube (8-25 cm) and mark it on the main base plate. Scribe a line through these points. Replace the vernier plate so that: (a) The pin lies exactly on the line just scribed. (b) The pin is 9.0 cm from the anode. (c) Within these limitations, the plate is as far counter- clockwise as possible (for the right camera; for the left, clockwise). B. Unless the crystal has to be changed, do not disassemble the monochromator 75 Replacing the Monochromator Crystal assembly. Omit this section. (1) (2) (3) (4) (5) Remove the knurled bolt and the monochromator slit from the assembly. Carefully remove the four spring-loaded bolts from the back of the monochromator assembly and lift offxthelbaCk and crystal. Remove the crystal from the back by soaking in petroleum ether or other solvent suitable for rubber cement (be patient). Clean the monochromator housing. Lay a thin bead of rubber cement along both supporting edges of the back of the mono- chromator. Carefully rub both sides of the crystal with EB pencil and then clean off. With curvatures matching lay the crystal on the assembly back so that it touches both alignment pins and is centered length- wise. Press lightly to contact the cement well. CARE-BREAKAGES ARE COSTLY NOTE-If crystal breaks it is still possible to use the bits. Lower the assembly front over the alignment pins, carefully invert the assembly, and put in the spring-loaded bolts, tightening evenly and carefully to just fingerétight. Replace the slit and knurled bolt - it is impossible to tell which side (6) is up at this time. C. Aligning the Monochromator (1) Mount the monochromator on its base plate and put the assembly over the pin on the vernier plate, with the adjustment bar between the supports for the vernier screw and spring. (2) (3) (4) (5) (6) 76 Place the fluorescent screen.about 3 cm from the assembly 86 that the primary beam will just show in the back edge of the screen. Put on the cover.glass and turn off the room lights. With the generator at 30 KV, 12 mA, use a screwdriver on the adjustment bar to rotate the monochromator back.and forth. At the right angles both Ka and K8-diffracted beams will appear near the front of the screen as bands about 1 cm wide. The Kc reflection can be distinguished because it is much brighter and occurs at higher angle, igggg, adjustment bar further from the.tube housing. Adjust roughly to maximum intensity for Kc. .Slide the fluorescent screen back.away from the monochromator until.the diffracted image appears as a sharp line. This will occur with the screen either.5.cm or 14 cm from the monochromator. .If the focus is at 5 cm, the monochromator is upside down. .Remove the monochromator,.take out the knurled bolt and monochromator slit, take off the.base plate and-put it on the other side. Replace the slit (fully open) and bolt. Repeat sections C-(l), -(2) and —(3). Put adjustment screw in.vernier plate and tighten until it .just touches adjustment.bar. Remove the monochromator and insert the spring-loaded pin-(It may be necessary to loosen the screw; count the turns and retighten it after monochromator is back in.) Replace:the.monochromator. .With.the X-rays on again, Ka.should still appear in the fluorescent screen, or should appear with slight adjustment. Tighten the adjustment screw until the reflection just dis- appears, then loosen it to the other extinction.- This should require about a 360° rotation of the adjustment screw. 77 (a) For K5 radiation, tighten the screw 180° from extinction. (For routine identification and examination for presence of minor phases.) (b) For Kcl radiation, tighten the screw 240° from extinction. (Around 50% as intense but sharper lines with more precise wavelength; for accurate lattice determination.) Install the secondary beam base plate with its notch around the pin on the underside of the vernier plate. Put in the With X—rays on move this plate until the pin on it (marking the center of the sample) is in the exact center of the diffracted beam. Tighten the bolts temporarily. Place a celluloid millimeter scale firmly along the long front edge.of this plate with masking tape, so that it can be moved parallel to the beam without disturbing the adjustment just Place the triangular cassette support plate over the pin on the secondary beam plate.and.insert the short bolt loosely. Mount the cassette on it with the leather strap swung back out of the way and the primary beam shutter open. Rotate the triangular plate fully toward you and place the fluorescent With XErays on, rotate.the plate slowly away. Image will disappear, then reappear in the primary beam opening. Rotate plate back and forth to center image in this opening. D. Aligping the Cassette Mount (1) two medium-length bolts loosely. (2) (3) made. (4) screen just behind it. (5) (6) Turn off X-rays, carefully remove cassette, and tighten bolt. Replace cassette. (7) (1) (2) (3) (4) (5) (6) (7) 78 Check this alignment by closing the primary beam shutter with the beam on. The image shou1d4disappear when the shutter is about halfway closed. .If it.is not fairly close to halfway, repeat D-(S) and -(6). Focussing Loosen the bolts holding the secondary beam base plate and move it against the millimeter.scale all the way toward the tube.. Load the cassette with a short piece of film (3-5 cm) in black paper, so that the film is in the path of the primary .beam.. Primary beam shuttermshould be open. .Expose the film for one second at 18 KV, 1 mA. (May have to be varied slightly for best results.) .Develop.as usual, scrubbing off the back emulsion, and label with the scale reading at the outside edge of the secondary beam plate. Move the secondary beam plate out one millimeter. Repeat steps (2) through.(5) until the secondary beam plate is at the ether limit of its motion. (Usually 5-10 exposures) Place the film strips on a light box in order and examine with a hand lens. For Kol, there should be a single.line which goes through a maximum sharpness. ~.Set the secondary-beam plate at the optimum.distance and tighten.securely. For Ka, there .should.be two lines, separated by about 0.1 mm, with the line . furthest from the diffraction area (Koz) lower in intensity .by about a factor of four.-.These should be optimized with Arespect.to both sharpness and resolution, and the secondary beam plate set as above.- If the intensity ratio is too far 79 from 1:4, the adjustment screw should be rotated clockwise slightly to enhance Kai or counterclockwise to enhance Ka2 and all steps from D—(l) must be repeated. Position the sample holder 5.25.mm.from the flat face of the cassette using the specially machined spacing insert that fits in the sample holder. It should be centered in its travel perpendicular to the beam.. Remove and store the-spacing insert. Install the entrance slit assembly with the slits fully Open .and the side slits loose. With.erays on, (25 KV, 5 mA) close the side slits until the bright green portion of the image of the primary beam in the fluorescent screen (the beam.not diffracted by the monochromator) just disappears on each side (see below). Image of crystal .in direct beam Remove the entire assembly on its base plate and place it on a table. Adjust the top and bottom entrance slits until they are just below and above the top and bottom edges, respectively, of the Opening in the crystal holder.“ Measuring with a vernier caliper from the base plate is a convenient method. F. Slits and Sample Holder (1) (2) Slits fully Open: Slits properly adjusted: (3) (4) With a strong light coming through the crystal and sample holder, and an empty steel target in the holder, sight through the primary beam opening of the cassette and close the sample slits until none of the steel disc will be in the beam path, as shown on the next page. 80 Steel sample disc (viewed at an angle and thus foreshortened to an ellipse) (5) Replace the unit in the box and.p1ug in the sample motor. (6) Put in the stray radiation shield. G. Checkout (1) Take a one hour exposure of KCl (35 KV, 18 mA).. Read the film vand calculate a correction factor-from the tables in the Guinier manual.- (Note separate tables for K5 and Kal.) -For our cameras the correction factor is usually 0.985 r 0.010.. For K5, there will be a slight decrease in S- /SO 1 - with increasing 8 calc o bs be; for K01 this trend should not be present. (2) With an empty steel disc mounted,.take a 24 hour exposure (35 KV, 18 mA). If no metal parts are struck by the beam, a diffuse film with ng sharp lines should be obtained. Excessive darkening at low angles can be reduced somewhat by moving the monochromator slit in about 3/4 of the way, with no serious loss in intensity. 81 Levelling Screw Handle QO 0 O C :1 ('1’ (ED (D l": 00 D" n Cassette Main Base Plate Adjustment Bar 0 O 9 o Monochromator Menochromator Monochromator Secondary Beam Vernier Plate Base Plate Assembly Base Plate Stray Radiation Shield (to / Spacing Insert Entrance Slit Triangular Assembly Cassette Support Plate (Right Camera shown - Left is a Mirror Image) Figure A-l. Parts of the Guinier Camera APPENDIX II: Black Form of TmC The Observed X-Ray Powder Diffraction Pattern of the 2 Relative.--sin2¢ d—value. . . Assignment - Intensity*w (A) Orth. Hexagonal Other 2 0.00312 13.79 001 5 0.01278 6.813 002 2 0.01582 6.124 020 ’ 3 0.01862 5.645 021 3 0.02825 4.583 022 6 0.04443 3.654 100 2 0.04713 3.548 101 5 0.05024 3.436 111 4 0.05147 3.395 004 4 0.05263 3.357. Graphite 00:2 2 0.05541 3.272 014 4 0.05986 3.148 120 5 0.06188 3.096 040 6 0.06239 3.084 Tetragonal TmC2 101 5 0.06514 3.018. Tetragonal TmC2 002 10 0.06703 2.975 024 I 5 0.07469 2.818 042 i 7 0.07618 2.791. 00°6 7 0.07866 2.746 10-1 4 0.07923 2.736 130 2 0.08064 2.712 005 5 0.08281 2.677 131 82 APPENDIX II: 0.08600 0.08872 0.09064 0.09570 0.09871 0.10108 0.10757 0.11175 0.11604 0.12075 0.12776 0.13034 0.13154 0.14230 0.14843 0.15219 0.15680 0.16330 0.16554 0.16847 0.17342 0.17629 0.18146 (continued) 2.627 2.586 2.558. 2.490 2.452. 2.423 2.348 2.304, 2.261 2.217. 2.155 2.134. 2.124 2.040 1.999 1.974 1.945 1.906 1.893 1.877 1.850 1.835 1.808 83 104 051 133 006 115 026 151 054 062 144 017 116 153 126 200 10°2 10°3 10-4 10'5 10°7 TaC 111 Tetragonal TmC TaC 200 2 110 *Visually estimated APPENDIX III: Values of Afef For.Reactions (V-l) and (V-2) Afef, vaporization Afef, vaporization Afef, vaporization T, K of SmC2 of TmC , with no .of TmC , with magnetic contribution magnetic contribution 1600 -18.69 -22.80 -l7.70 1700 -l8.55 -22.53 -17.43 1800 —18.43 -22.29 -17.19 .1900 —18.30 -22.07 -16.97 2000 -18.18 -21.84 -16.74 2100 -18.08 -21.65 -16.55 -2200 -21.46 -16.36 84 APPENDIX IV: Equilibrium Pressure and Third Law Enthalpy Data APPENDIX.IVA: Samarium Dicarbide T, K — 1n P (atm) AH; 298(kcal/gfw) 1656 10.9705 66.92 1744 .9.9728 66.81 1838 8.9103 66.32 1925 7.9331 65.52 1908 8.2058 66.01 1857 8.7272 66.28 1795 9.4522 66.79 1725 10.2512 67.08 1717 10.1279 66.37 1782 9.4932 66.49 1865 8.6788 66.37 1988 7.5816 66.13 1914 8.2037 66.20 1851 8.7833 66.29 1767 9.6885 66.65 1631 11.2951 67.02 1916 8.3315 66.754 1882 8.7037 67.03 1804 9.3770 66.84 1770 9.8868 67.45 1690 10.5158 66.69 1792 9.1908 65.76 1853 8.7012 66.05 85 APPENDIX IVA: 1935 1899 1827 1765 1696 1708 1799 1717 1821 1872 1945 1896 1860 1772 1720 1914 1861 1829 1788 1726 1772 1834 1944 1986 1879 1797 (Continued) 8.0409 8.5660 9.2338 9.8334 10.5503 10.2832 9.3475 10.0864 8.9226 8.4577 8.0568 8.4747 8:7999 9.6636 10.2239 8.1769 8.7485 9.0593 9.4468 10.0743 9.5719 9.0691 8.1018 7.7522 8.6182 9.3334 86 66.25 67.08 67.12 67.08 67.03 66.57 66.56 66.23 65.79 65.78 66.63 66.63 66.65 66.73 66.81 66.09 66.50 66.55 66.53 66.51 66.41 66.76 66.77 66.74 66.61 66.44 87 APPENDIX IVA: (continued) 1712 10.3783 67.04 2009 7.5073 66.48 1967 7.9339 66.85 1893 8.1988 65.50 1745 9.7553 66.10 1788 9.5776 67.00 1896 8.5792 67.03 1975 7.8348 66.72 2026 7.3175 66.24 2053 7.0919 66.15 2025 7.2765 66.05 1935 8.0805 66.40 1829 9.0498 66.52 APPENDIX IVB: Thulium Dicarbide T, K - 1n P (atm) . A ° (kcallgfw) with magnetic without magnetic contribution contribution 1664 12.5053 70.51 79.00 1748 11.3329 69.63 78.55 1808 10.6263 69.22. 78.44 1886 9.7908 68.74 78.36 1926 .9.3703 68.42 78.24 1876 9.9268 68.92 78.49 1832 10.3218 68.93 78.27 APPENDIX IVB: 1761 1688 1751 1798 1860 1913 1950 1879 1840 1948 2006 2066 2125 2080 1968 1792 1758 1712 1676 1907 2013 1871 1806 1745 1824 1899 1992 (continued) 11.2421 11.8857 11.1825 10.6897 10.0639 9.6322 9.2739 9.8816 10.3087 9.2276 8.8139 8.1593 7.8580 8.2360 9.1079 10.9415 11.2581 11.9031 12.2289 9.6658 8.6356 9.9698 10.7067 11.3927 10.5499 9.7424 8.8670 88 69178. 69.35 69.22 69.11 68.91 69.01 68.79 68.85 69.15. 68.55. 68.70. 67.82 68.24. 68.54 68.70 69.80. 69.73. 70.29 70.05 68.94 68.20 68.92. 69.44 69.73 69.49. 68.98 68.49- 78176 77.96 78.15 78.28 78.40 78.76 78.74 78.44 78.53 78.49 78.93 78.35 79.08 79.14 78.74 78.94 78.69 79.02 78.60 78.67 78.46 78.46 78.65. 78.63 78.79 78.66 78.65 APPENDIX IVB: 2035 2127 2063 2012 1875 1698 1724 1784 1856 1809 1770 1710 (continued) 8.4437 7.8916 8.2034 8.6931 9.9856 11.9632 11.7668 11.0494 10.1470 10.7607 11.1951 11.9991 89 68.08 68.44 67.91 68.40 69.11 69.98 70.26 69.91 69.09, 69.74 69.93 70.54 78.45 79.29 78.43 78.66 78.67 78.64 79.06 79.00 78.55 78.97 78.96 79.26 llllHllllflillNlH 0145700 IHII "2 H 1 MI3