RARE EARTH BORIDES: THE SAMARIUMJORON SYSTEM 7 Thesis for “a Dean; of DB. D. MECHIGAN STATE UNWER‘SITY- George Dennis Sturgeon.- = ,1964‘ WES-‘9 1"" 1-. 1...: 1:" 4:: X4 :R Y M 1C? 3-;- Sta te Ugiwersi ty i' "VH‘F- 51:4? 1-: ”rm-z. MiCH‘GAN STATE UN‘NERSITY DEPARTMENT OF CHEMlSTRY EAST LAN51NG, MlCHlGAN RARE EARTH BORIDBS: THE SAMARIUM-BORON SYSTEM By George Dennis Sturgeon A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1961; ACKNOWLEDGMENTS The author is very pleased to acknowledge the guidance of Dr. Harry A. Eick and to thank Dr. Gordon L. Galloway and Mr. Paul Nordine for their illuminating comments and personal interest during the course of this research. The financial assistance provided by the Atomic Energy Commission has been very welcome. Finally, the author would like to take this opportunity to ex- press his deep appreciation to the multitude of people who, willingly or unwittingly, have had a hand in making this thesis a reality. ii TABLE OF CONTENTS I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . A. Literature Concerning Rare Earth Borides B. The Structures of the Rare Earth Borides C. Bonding in the Rare Earth Borides . D. The Specific Purpose of This Research . II. THEORETICAL CONSIDERATIONS A. Thermodynamics . 1. Relationships Arising from the Second Law of Thermodynamics . . . . . . . . 2. Estimation of Heat Capacity Change . . 3. Third Law Determination of Standard Enthalpy Change . . . . . . . . . . . . . B. The Knudsen Effusion Method . . . . . . . . . . . l. The Knudsen Effusion Equation . . . . . . . . . 2. The Cosine Relationship . 3. Limitations and Restrictions in the Knudsen Effusion Method . . . . . . . . a. Equilibrium vapor Pressure and the vapor— ization Coefficient . b. Non-ideal Orifices c. Extraneous Chemical Reactions Within the Effusion Cell . . . . . . . . . d. Pressure Considerations in the Effusion ‘ Method . . .-. . . . . . . . 1) Molecular Flow Limitation . . 2) Residual Pressure of the vacuum.System e. Collection of Effusing Species . . . . f. The Molecular Weight of the Effusing Species 9. Cell Temperature . . . . . . . . . III. EXPERIMENTAL METHODS A. Synthesis of Borides . . . 1. Starting Materials and Containers . . . . . . 2. Induction Heating Experiments . . . . . ... . 3. Arc-melting Experiments . . . . . . . . . b. Analysis of Reaction Products . . . . . . 5. Product Boride Purification . . . . B. Effusion Experiments . . . . . . . . . . . . 1. Apparatus . . . . . . . . . . . . . . a. vacuum Assembly . . . . . . . . . . . . . b. Effusion Cell . 2. Measurement of Dimensions . . . . . . . . . .1. 3. Exposure Procedure . . . . . . . . . . h. Coll.ection Efficiency; ”Bouncing" Experiments . iii IV. VII. TABLE OF CONTENTS (Cont.) C. Temperature Measurement . . . . . . . . . . D. Quantitative Samarium Analyses 1. Preparation of Standards . 2. Neutron Activation of Samarium Samples . . . . . 3. Identification of Species Present in Activated Samples b. Counting of Activated Samples . E. Molecular Weight of Samarium Vapor Species RESULTS . . . . . . . . . . . . A. Synthesis Experiments . l. Hexaborides 2. Samarium Tetraboride . . . . . . . . . . . . 3. Europium Tetraboride . . . . . . . . . . . . . . h. Thulium Diboride . . . . . . . . . . . . . . . B. Knudsen Effusion Measurements . . 1. Comparison of Individual Runs 2. Collection Efficiency Determination . . 3. Calculated values for Enthalpy and Entropy Changes (Second Law). . . . . . h. Calculated values for Enthalpy Change (Third Law) C. Determination of Molecular Weight of Effusing Species CONCLUSIONS . . . A. Reports of Hexaborides of Erbium Thulium Lutetium and Scandium . . . B. The Effect of Metallic Size on the Stability of the Cubic Hexaborides . . C. The Preparation of New Rare Earth Borides . . . . . . D. Samarium Tetraboride Stability . . . . . . . . . . . E. The Problem of Europium Tetraboride . . . . . . . . ERROR ANALYSIS . . . . . . . . . . . . . . . . . . . . FUTURERESEARCH............ REFERENCES . . . . . . . . . . . . . . . . . . . . . . . APPENDICES iv 57 59 61 63 6b 69 71 75 ‘ LIST OF TABLES Table Page I. Reaction resume listing reactants, containers, temperatures, time, products and identifying X-ray photograph number . . . . . . 35 II. X-ray diffraction data for an erbium sesquioxide—boron carbide reaction product . . . . . . . . . . . . . . . . 51 III. Observed d values for a thulium-boron reaction product ” with calculated d values for thulium borides . . . . . . 53 IV. Alternative interpretations of X—ray diffraction data for lutetium boride . . . . . . . . . . . . . . . . . . . 58 V. Observed boron—boron distances in those types of borides exhibited by the rare earths . . . . . . . . . . 60 VI. Lattice parameters for known rare earth borides . . . . . 62 VII. Standard deviations of parameters measured for use in ' the Knudsen effusion equation . . . . . . . . . . . . . . 6S Figure la. lb. 2a. 2b. ha. 9. LIST OF FIGURES The unit cell structure of binary metal diborides . The structure of binary metal borides showing alternate layers of boron and metal atoms . The boron environment of the central metal in cubic hexaborides . The structure of the cubic hexaborides showing the boron lattice The structure of the metal tetraborides; a projection of the structure on the (001) plane . . . . . . The structure of the metal dodecaborides showing the boron environment of the metaliatom . . . . . . . . . . The structure of the binary dodecaborides showing the boron lattice .‘. . . . . . . . An element of a solid angle through which a gaseous particle effuses . . . . . . . . . . . . . . . . . . Schematic diagram of vacuum system used for effusion‘ experiments . . . . . . . . . . . . . . . . . . . . . Pictorial representation of the Knudsen effusion cell . Gamma—ray spectrum of neutron irradiated samarium— bearing quartz disc Graphical representation of Knudsen effusion data vi Page ll 12 2h 38 b0 b7 Sh LIST OF APPENDICES Appendix I. II. III. IV. VII. VIII. Source and Purity of Materials Employed Compilation of Corrected Linear Parameters for Individual Effusion Runs . Data Concerning Collection Efficiency for Knudsen Effusion Target Discs . . . . . . . . . . . . . . Data Concerning Standard Samarium Solutions and Quartz Discs Bearing Samarium Deposits Possible (n,y) Reactions for Naturally Occurring Samarium Isotopes . . . . . . . . . . . . . . . Samarium Assays . . . . . . . . . . . . . . . Log Pressure and Temperature Data for Individual Effusion Exposures . . . . . . . . . . . . . Third Law Standard Enthalpy Change Calculated at Various Temperatures . . . . . . . . vii Page 76 77 77 78 79 80 8h 88 I. INTRODUCTION Rare earth borides are not thoroughly characterized physically or chemically, but recent years have witnessed a large increase in knowl- ecige of these borides, particularly with regard to the preparation of previously unknown compounds. The specific interest in materials for high temperature applications together with the unusual electrical and thermal properties exhibited by many binary metal borides have been the primary forces behind much of the research in this fertile area. But the properties of binary * borides: high melting points, high boiling points, hardness, inert— ness and the difficulty of classifying these borides in terms of chem— ical and metallurgical bonding rules, compounded by the problems con— fronted in conducting research in this area are sufficient to arouse the interest of the scientist. While it is generally true that the properties of the rare earths and their compounds are uniquely similar, the student of rare earth chemistry is concerned primarily with the differences in the behavior of these metals. The common educational practice of considering the rare earths as an isolated group among the elements seems to have re- sulted in a dearth of attention to the problem of relating and unifying the properties of the lanthanons with the properties of the metals lying outside this classification. In the case of the rare earth borides, the relationship between these and the borides of the outer transition metals is compounded by the fact that the rare earth metals and the outer transition metals 2 exhibit borides of quite divergent stoichiometries with relatively few instances of the same stoichiometry and structure appearing for borides of both groups of metals. For example, typical stoichiometries of the transition metals are M4B, M3B, M783, MZB, M1188; M583, M382, M4B3, MB, M3B4, M2B3, MBZ, M2B5 and MB;, whereas typical stoichiometries of the rare earth borides are MBX where x is 2, h, 6, or 12. The difficulty in obtaining pure samples of the rare earth metals‘ and their compounds, long a barrier to rapid and substantial progress in rare earth chemistry now largely has been removed. At the present time, the problems confronting the chemist dealing with binary rare earth compounds are very frequently those of high temperature technology, 1:3. achieving, controlling and measuring high temperatures, containing reactive mixtures at high temperatures and determining one or more properties of such systems. The importance of the element boron in any discussion of borides can hardly be over-stated. It is time that the interest in the heavy metal* in binary borides be balanced with corresponding emphasis on boron’s contribution to the chemistry of these compounds. Boron which is positioned on the edge of the metallic elements of the periodic table, has properties which make it fascinating and at times unique. Foremost among these properties are the propensity of boron atoms to form bonds with other boron atoms whenever possible, the ability to form five or KIt would be tedious to preceed the word "metal” with the adjective ”heavy” when referring to the non—boron member of binary borides. There- fore the word "metal” will be used alone unless clarity demands further specification. 3 more bonds per boron atom even though boron is in the first eight— member period of the table of elements, and the striking rigidity of three dimensional boron structures such as are found in many binary borides. A. Literature Concerning Rare Earth Borides The literature on binary rare earth borides, firmly rooted in the work of Andrieux (l), Allard (2) and of von Neuman and Stackleberg (3), only recently has begun to expand. The publication of several review papers and compilations of crystallographic data (h—9) have been of ‘ great benefit to workers in the area. Unfortunately, the literature has not been so exclusive as to prevent the appearance of suspect and un— substantiated reports. The list of borides of the lanthanons is being lengthened almost constantly as reports of new compounds appear (7—28). Such reports generally contain information concerning the preparative method, the rough stoichiometry of the product boride and X—ray powder diffraci tonetry data demonstrating the structure. B. The Structures of the Rare Earth Borides It should be noted immediately that, in general, X—ray data provide only information concerning the arrangement of the metal atoms so that the positions of the boron atoms in a unit cell must be assigned on the basis of symmetry and geometric arguments. The diborides of the rare earths are of simple structure with hex- agonal unit cells of space groups Po/mmm with one formula weight per unit cell. The metal atom is at the origin of the unit cell (0,0,0) h with the boron atomz'positions at (1/3,2/3,1/2) and (2/3,1/3,1/2) (Fig. 1). The metal and boron atoms thus occupy alternate planes with the boron atoms forming hexagonal networks in the (0,0,1/2) plane. The cubic hexaborides have a cesium chloride type lattice of space group Pm3m with one formula lHTLt per unit cell. The metal atom may be considered to be located at the center of the cell (l/2,l/2,l/2) with the boron atoms located at (t x,0,0), (0,ix,0) and (0,0,ix) (Fig. 2). The only variable position parameter, x, has not been determined because of the difficulties associated with the location of light atoms in the- presence of heavier atoms. Generally the boron atoms are considered to form octahedral groups centered on the point (0,0,0) with each of the six boron atoms at one of the vertices of the octahedron. The boron positions are easily established by simple geometric considerations if all boron—boron bond distances are assumed to be equal. The validity of this assumption can be asCertained only by very precise X~ray dif- fraction studies. The tetraborides are tetragonal containing four formula units‘ per unit cell; the space group is Ph/mbm. The metal atoms are arranged in planes, each metal having five iso—elemental neighbors. In the spaces between metal atoms, the boron atoms are arranged in planar groups where the boron atoms have an arrangement much like 'that of the diborides or in octahedral groups much like those of the hexaborides (Fig. 3). The boron atoms of either type are in contact and form a continuous three— dimensional network, but with the majority of the atoms in the z = l/2 plane. Thus, the tetraborides may be viewed as hybrids of the diborides and hexaborides in terms of structure as well as stoichiometry. O s _ H \ @ BORON METAL Figure la (9). The unit cell structure of binary metal dibOrides. .mEObw Hmbos cam copop .Ho 88ka obmcoofim @539? mopwuonmc :1.me \Cmcwb (Ho 9350?“? mg .Amv a. 933m ® 233 .352 . .x \ vIII/ \ Figure 2a (9). The boron environment of the central metal in cubic hexa- borides. :BORON METAL Q) Q BORON METAL 9 7 \\\ Figure 2b (9). The structure of the cubic hexaborides showing the boron lattice. O V (I. 1’ .» C 5 3. 11D l . . . a WWII!!!“ Figure 3 (9). The structure of the metal tetraborides; projection of the structure on the (001) plane. 10 The dodecaborides are also cubic of space group Fm3m with four formula units per unit cell. The structure may be visualized in terms of a modified sodium chloride type structure with the metal atoms in place of the sodium and cubo—octahedral groupings of twelve boron atoms in place of the chloride ions (Fig. h). Alternatively, the structure can be described as consisting of larger regular cubo—octrahedral groups with bdron atoms at each of the twenty-four vertices and a metal at the center. Very little information is available concerning higher borides. Phases with a composition of about seventy boron atoms to one metal have been reported for yttrium, holmium, terbium, ytterbium, erbium, samarium, and gadolinium (9,28). Most, but not all, reports refer to a cubic phase; chemical analyses have not been definitive. It may be that the higher borides include more than one type of structure and more than one stoichiometry. C. Bonding in the Rare Earth Borides 0f the four known stoichiometric boride types of the rare earths, the diboride is the only one having an obvious distribution of electrons. The surrender of two electrons by the metal atoms leads to a closed shell structure, the borons having gained enough electrons to possess a gra— phitic electronic structure as well as graphitic geometry. It is more surprising to find that the best available calculations and experimental data indicate that the metal atom is required to donate two and no more electrons to the boron lattice no matter which boride is involved (29-33). Because the hexaborides are most familiar and because quantum mechanical calculations are simplest for a cubic structure, the hexaborides l2 The structure of the binary dodecaborides showing the boron Nb (9). Figure lattice. 13 have been studied more thoroughly than any of the other borides. Several separate discussions of the bonding in the hexaborides have concentrated on the internal orbitals of the B6 octahedral group with six external bonds to other, like octahedra. The electron requirement is the sum of the six electrogs used for the external orbitals and seven pairs of electrons used for internal bonding orbitals amounting to twenty electrons per Octahedron. Hence, two electrons must be provided by the metal since the six boron atoms supply eighteen.* Lipscomb and Britton (33) have studied the electron requirements of the boron atom groupings in the tetraboride unit cell which includes four metal atoms and sixteen boron atoms. Twelve of the boron atoms are members of octahedra like those in the hexaborides. Since each octahedrdirequires twenty electrons to fill the orbitals of its external and internal bonds, a total of forty electrons are needed for the boron octahedra. The other four boron atoms are grouped into two pairs joined internally by an ethylenic bond which requires four electrons per pair or eight electrons. In addition, each boron atom in the ethylenic group is joined externally to two other boron atoms (which are part of octahedra) by single bonds for which one electron is needed. The four such boron atoms with two single bonds each therefore require eight electrons for external orbitals. 0f the sum of fifty—six electrons (forty plus eight plus eight) required, the boron atoms themselves “There is evidence that the B6 group does not require a full two electrons from the metal since a Group I metal, sodium, has been sub— stituted for the Group II metal calcium in its hexaboride to the extent that only 1.6 electrons are statistically available to each 86 group (11). it provide forty-eight so that each of the four metal atoms in the unit cell must supply two electrons to make up the eight additional electrons. Lipscomb and Britton also have usedemiLCAO molecular orbital ap- proach to calculate the electron requirements for dodecaborides; the cubo-octahedra require twenty-six electrons for internal orbitals and one electron for each of the twelve boron atoms for a single bond to a like boron in an adjacent cubo-octahedron. 0f the total of thirty eight electrons required (twenty-six plus twelve), thirty-six are available from the twelve boron atoms themselves leaving a deficienqy of two electrons to be made up by the metal atom. These models previously suffered from a lack of experimental sub- stantiation. However, experimental data reported by Johnson and Deane (3h,35) support these models. 0n the basis of electrical conductivity and Hall Effect measurements on CaB6, SrB6, BaB6, YBZ, YB4, YB6, and YB12 they report results which are in agreement with the models invoked above. Thus the alkaline earth borides were found to be semiconductors while the yttrium di—, hexa- and dodecaborides were found to have one free electron per yttrium atom in each compound. In the case of the tetraboride, it was impossible to obtain a calculated value for the Hall coefficient to compare with the experimentally determined value, but the measured value does not contradict the model discussed above, and the electron requirements of the octahedral boron units in the tetra- borides have been established from the work on hexaborides. 15 D. The Specific Purpose of This Research The state of knowledge of rare earth borides was summarized by Eick in a paper presented at a seminar at Lake Arrowhead, California in October 1960 and subsequently published as a chapter in the book Rare Earth Research (8). Because of the very limited amount of data more than qualitative in nature, some speculations and tentative con- clusions were drawn from the information then available. In Eick's discussion of the rare earth hexaborides appear the fol- lowing comments: Although the lattice parameters of lutetium, thulium, and erbium hexaborides are probably in error by a small amount, it is readily noticeable that they do not decrease in size proportionally to the other members (of the series of rare earth hexaborides). This very small decrease may indicate that the boride lattice can contract no further and the smaller metal atoms are simply held, as it were, rather loosely in a boron cage. Other non-rare earth hexaborides have larger lattice parameters. and ” ..... ErB6 may not be prepared readily because of the instability of ErB6 with respect to ErB4 and boron at the temperatures necessary for the reaction (of Er203 with elemental boron).” In work reported in another place, Eick and Gilles (36) determined precise lattice parameters of some rare earth borides. In that work, the smallest rare earth metal for which a hexaboride could be prepared was holmium. Two important observations were thus gleaned: that formation of rare earth hexaborides becomes progressively more difficult to induce as the metallic radius of the metal involved becomes smaller and that the lattice parameters reported for the hexaborides of erbium, thulium and lutetium are not entirely consistent with those of the other rare earth hexaborides. 16 In the face of continuing reports emanating from the Soviet Union (6,12—16,18-2l,2h,25), on the preparation of the hexaborides of erbium, thulium, lutetium and Scandium, investigations into the preparation of these hexaborides were reopened with the intent of obtaining information about the products--precise lattice parameters and thermodynamic stabil- ity data. Another section of the rare earth boride review by Eick predicts that in those cases where rare earth tetraborides are less stable than the corresponding hexaboride, a sufficiently high temperature should cause the occurrence of the disproportionation reaction 3m4<¥~—_—> 2MB6(3) * 11(9). Such a tetraboride is formed by samarium—-indeed, the preparation of samarium tetraboride rather than the more stable hexaboride constituted a minor project in itself——and since the free energy change accompanying this reaction should reflect the relative stabilities of the two borides, experiments were planned which would allow the determination of the equilibrium vapor pressure of gaseous samarium over a mixture of the two borides at various temperatures, and, from this equilibrium vapor pres— sure data, calculation of the standard thermodynamic quantities of enthalpy and entropy for the reaction. For these vapor pressure measure— ments, the Knudsen effusion method was chosen as being most adaptable to the system. II. THEORETICAL CONSIDERATIONS A. Thermodynamics Because of the natural limitations on physical systems at equilib- rium summarized in the familiar phase rule, F = C—P + 2, where F is the number of degrees of freedom, P the number of phases present and C is the minimum number of components necessary to describe the system. A system (such as that under study) containing three phases (vapor, hexaboride and tetraboride) and two components (samarium and boron) must have a unique equilibrium vapor pressure at any given temperature. By recording the equilibrium vapor pressure at various temperatures, and calling upon other thermodynamic data, the value for the standard free energy change accompanying the conversion of tetraboride into hexa- boride and samarium vapor can be obtained. 1. Relationships Arising from the Second Law of Thermodynamics For the reaction SmB = 2 SmB + S l 3 4 6(s) . m ‘ ) at temperature T0 K., O :: O _ O :: _. fi’ ‘ :: .. AGT AHT T AST RTaneq RTlnPSm(g) (2) where Keq is the equilibrium constant-wfor this reaction the vapor pressure of samarium. For the case where the change in the constant pressure heat capac- ity is constant, the expressions for AH% and AS% are given by equations (3) and (h) respectively. 17 18 T 1H8 = 1H3 +1r AdeT = AH: + ACp (T - e) (3) e 0 o T l 0 T AST = ASe +1): ACp T dT = Ase + ACpln(6) (t) G is a reference temperature; in this work 298.160K.will be used. Combination of the above equations (2), (3) and (h) leads to -RT1nKeq = — RTlnP AGO = AH: + ACp(T — o) - TASg - TACp1n(g),(5) Sm(g) = T If the value of ACp should be so small as to be negligible, equa— tion (5) simplifies to O_ O -RTlnPSm(g) AHe 1156 (6) and 0 -AH° AS log P = -2-- + .__2__ (7) Sm(g) 2.303RT 2.303R where R is the molar gas constant and the number 2.303 arises from the conversion of natural to base 10 logarithms. From equation (7) it can be seen that numerical values of AH: and AS: may be obtained from the slope and intercept respectively of an equation in which log PSm(g) is a function of l/T. 2. Estimation of Heat Capacity Change The method used to estimate the value of ACp for the reaction under study first assumes that, at high temperatures, the ACv (which is further assumed to approximate ACp) amounts to 3R (R is the gas constant) for each atom in a solid compound (32) (hence 21R for samarium hexaboride and 15R for samarium tetraboride). Treating samarium as an ideal, monatomic gas with no electronic contribution to the heat capacity results in a value of 5/2 R for its heat capacity. These assumptions 19 lead to an estimated minimum of —l/2 cal/deg. for the heat capacity change for the reaction. (An electronic contribution to the heat capacity of samarium gas would result in the algebraic addition of a positive term to the estimated minimum.) If the absolute value of ACp is less than 1.0 cal./deg.,the maximum values for ACp(T-e) and ACp ln(T/B) are 2.0 kilocalories and b.25 calories respectively. Should ACp equal zero, the plot of loglOP versus l/T must Sm(g) be a straight line; the observation of such a straight line relation— ship would provide eloquent testimony that the true value for ACp is very close to zero in the temperature range studied. 3. Third Law Determination of Standard Enthalpy Change Because of its use of absolute entropies and heat capacities, this method is fundamentally related to the Third Law of Thermodynamics. In order to corroborate the results from the treatment of data by the Second Law method, it is useful to obtain a value for the standard enthalpy change by employing the Third Law method since it is relatively insensitive to errors in temperature measurements. The Third Law method makes use of the free energy function (here— after abbreviated fef) defined by _ T e _ T e _ o fef - ( T ) — (———Tr——) sT . (8) Tabulations of free energy functions usually adopt 298.160K.as a reference temperature leading to o o o 0 G ‘ H298 H ‘ H298 T T o (-—--=,--——— = <-——-,=——— -sT. (9) 20 which is related to the free energy function at 00K. by the relation o o o o o 0 GT ‘ H298 GT ‘ Ho H298 ' H0 . (10) __—T-__—— _ ——TT_-_ 7 ——-’—T——— For a reaction 0 0 o 0 o O f _ GT ‘ H298 GT ‘ H29a _ AGT AHzge A 8f — —T—-— - T— - -—T— - T (11) products reactants and, making substitution for AG? from equation (2) gives 0 _ R l P AHzge Afef — - n Sm — T (12) , i which rearranges into i 1113,, = -T Afef — RT ln Psm (13) or Go _ Ho T 295 AHgse = - T[A(—-—T———)] — 2.303 RTlog PSm. (111) It can be seen from equation (1h) that an independent value for the standard enthalpy change for a reaction may be calculated from each pair of pressure and temperature measurements provided that the free energy functions are available. In the absence of tabulations of the free energy function, the fef for a substance can be calculated from heat capacities or from spectroscopic data on gases. In those cases where no actual spectroscopic or heat capacity data of any sort are available, estimates must be made; even so, the caluclated standard enthalpy change is still a very useful check on the values obtained via calculations based on the Second Law treatment of the vapor pressure data. 21 B. The Knudsen Effusion Method The Knudsen effusion method ofcttamuning equilibrium vapor pressures within a container by measuring the number of molecules effusing through a small orifice of known area in a thin wall of the container is now well established. In 1909, Knudsen first showed that the number of molecules passing through an orifice of a container in unit time is the same as the number of molecules which strike a section of the wall having an area equal to that of the orifice, so long as the wall is very thin and the vapor phase within the container is behaving as an ideal gas (37). Therefore, measurement of the number of molecules effusing through a small orifice in a cell allows the determination of the pressure within the container. 1. The Knudsen Effusion Equation The number of molecules striking a unit area of a container wall, Ze’ is fiE/l per unit time, where n is the density of the gas in molecules per unit volume and E is the average molecular speed. Since n = N/V, N = R/k and V = RT/P, we may write I 28 = 1/t (PE/k1) (15) where N is Avagadro's number, k is the Boltzman Constant, V the volume, P the pressure and T the absolute temperature. The net rate of transfer of molecules out of the container is simply the number of molecules effusing per unit time, which is propor- tional to the internal pressure, less the number returning which is proportional to the external pressure of the species. Hence the effective effusion rate is 22 Pl? PZE Ze = l/A (“fi- - fi- ) (16) where P1 is the internal equilibrium pressure and P2 is the external partial pressure of the species. If P2 is zero or P, >> P2, equation (16) becomes P13 28 = l/LLW . (17) Making use of the Maxwellian velocity relationship 1/2 - R C _ ,VRT _ \ WM) (18) and multiplying both sides of equation (17) by M/N where M is the molec- ular weight of the effusing species leads to Ze M/N = % fi—AB—fi—bl/Z =m (19) and P = m (2%)1/2 : §II_:_€(2TTIVFI{T)l/2 (20) where R, the gas constant, is expressed in ergs/deg.~mole, m is the rate of mass effusion in g/emz—sec, and w is the weight of material effused through an orifice of area SO cm? during time t sec. Equation (20) is the basic Knudsen equation. 2. The Cosine Law Relationship Although it is possible to determine the total number of grams of material effused from a cell by determining weight loss or by collecting the total effusate material, neither of these methods is universally applicable. The determination of weight loss is insufficiently accurate to measure extremely low pressures involved in some systems and requires 23 large samples. Total collection of an effusate is sometimes desirable; it is experimentally cumbersome and often unnecessary. \ 3e; that the geometric distribution of ef— It has been shown (37, , fusate molecules escaping from an ideal, ”knife—edged” orifice is governed by the cosine law represented by d2 = ZP(l/h)dSo cos 0 doidt (21) which indicates that the number of molecules escaping from the orifice, d2, passing through an element of area dSO and through a conical section of elementary solid angle dis oriented at angle 0 from the normal to the orifice plane (Fig.53) is a function of the time, t, and the total ef— fusion rate, Ze’ Integration of equation (21) for which the reader is referred to the work of Carlson (38) indicates that the rate of molecular flux through an area unit located on the surface of a large sphere tangent to the orifice plane is everywhere equal. For this reason, the frac- tion of effusate striking a target located above an effusing orifice can be calculated so long as the distance from orifice to target and the orientation of the target are known. Hence, if a circular target of radius r is coaxial to the orifice at a distance d, the pressure P with- in a cell is related (37,38) to the number of moles, A, striking the target according to the equation _ A 1 r2 + d2 P — a? (2mm) /2(——-;2-—) (22) or, when SO, t, and T are expressed in units of square centimeters, seconds and degrees Kelvin respectively, the pressure in atmospheres, P = 0.022557%.E x/TM (53-3113) (23) r2 i 2b Figure 5. An element of a solid angle through which a gaseous particle effuses. ‘25 3. Limitations and Restrictions in the Knudsen Effusion Method a. Equilibrium Vapor Pressure and the Vaporization Coefficient The Knudsen method requires that the amount of material escaping through the effusion orifice have no significant effect on the equilib- rium vapor pressure within the cell. The vapor preSSure of the evaporating species within an effusion cell where the rate of departure of particles from the solid phase is not sufficiently great to compensate for the loss from the vapor phase via effusion-4hence to maintain equilibrium-~15 dependent upon the rate- of evaporation of the effusing species rom the surface of the solid (37,39). In these cases, the Knudsen effusion equation (23) must be further altered to include a, the vaporization coefficient which may be defined as the ratio of the actual number of particles leaving the solid phase to the number of particles leaving the solid phase under equilib~ rium conditions. The value of a will be seen to be unity when the evaporation rate of the particles is sufficient to maintain equilibrium in the effusion cell. It is possible to detect those cases where the vaporization coefw ficient is not unity by comparing sets of pressure data obtained by using cells with two or more different orifice sizes. Smaller orifices restrict the material loss from the effusion cell to smaller absolute amounts. In many cases, for a properly constructed effusion cell, no appreci- able error results in assuming that the experimentally determined vapor pressure is the actual equilibrium vapor pressure (NO). To fashion such 26 a cell, it is necessary that the size of the effusion orifice be very much smaller than the surface area of the solid phase from which evapoa- adion.is occurring. b. Non—ideal Orifices The Knudsen effusion equation (23) was developed with the require- ment that the cell wall aroundthe orifice be very thin; in practice this requirement means that the orifice must have a knife edge, 143. the orifice must be a channel of infinitesimal length. Of course, it is experimentally impossible to fabricate an effusion cell meeting this requirement. In a theoretical study of the transmission of gaseous mole- cudlas through channels of finite length under molecular flow condi- tionS, Clausing (bl) found that the probability of transmission of such molecules through non—ideal orifices of certain geometric configurations is dependent indirectly both on the area of the orifice and the length of the orifice channel. Tabulations of numerical solutions to his equations for various dimensional shapes and sizes are available in the form of "Clausing factors" or transmission coefficients (h2). Further discussions of this correction factor may be found in several reports (38,13-17). c. Extraneous Chemical Reactions Within the Efquion Cell Of course, no other reaction affecting the equilibrium must be tak— ing place within the effusion cell. In general, this restriction re- quires that the products and reactants of the system under study must be analyzed to ascertain that the reaction taking place is accurately described by the chemical equation applied to the system. 27 Possible interaction of the reactants or products with the container must be considered, especially for high temperature systems, and even ’ more e5pecially for borides. Work performed in this laboratory by G. L. Galloway (b8) demonstrated that molybdenum, tantalum and even tungsten, materials in common use for containing high temperature reaction mix— tures, are unsuitable as containers for hot borides because of formation of molybdenum, tantalum or tungsten borides, respectively, accompanied by the release of the metal species of the contained boride. d. Pressure Considerations infithe Effusion Method 1. Molecular Elow Limitation: The Knudsen method requires that the gaseous species within the effusion cell not interfere with one an- other's motion during the effusion process. Knudsen himself reported (37) that at sufficiently high pressures within an effusion cell, hydro- dynamic or fluid flow through the orifice occurs, such flow not conform- ing to the equations for molecular effusion and resulting in the escape of more material than under conditions of strict molecular flow; he pre— scribed the condition that the mean-free-path be 10 times greater than the orifice diameter to insure free molecular flow. However, Carlson (38), who performed a detailed study of the problem found that deviation from the Knudsen flow condition took place when the ratio of mean—free—path to orifice diameter was unity. Furthermore, Habermann and Daane (h?) measured vapor pressures of various rare earth metals at pressuxs up to 10.—1 mm.Hg (corresponding to mean-free—path to orifice diameter ratios as low as 0.5). Wakefield (b9) has measured the vapor pressure of holmium obtaining values as high as 10 mm.Hg without 28 noting deviations from the Knudsen flow condition. The conclusions of various workers concerning this complex problem are not in agreement and no satisfactory theoretical treatment which can be applied with confidence has appeared as yet. Of the measurements reported in this thesis, fewer than one-tenth apply to caSes where the mean—free-path to orifice diameter ratio is less than unity; and further, the value of the ratio is never less than 0.1- The collective findings of other workers together with the appear— ance of the data obtained in this work indicate that db significant complication has arisen due to excessively high pressures within the ef- fusion cell. 2. Residual Pressure of the Vacuum System: Not only must the atmosphere surrounding the effusion cell have an effective pressure of zero for the effusing species as is required for equation (17), but the residual pressure of other gases must not be high enough to react with, scatter or otherwise interfere with the motion of the effusing vapor species toward the collection device. 8. Collection of Effusing Species If the fraction of effusing material which strikes the target and also condenses there is not unity, it must be determined experimentally. The target must be kept as cool as possible to increase the probability of an impinging particle's "sticking". If condensation is not complete, "bouncing" experiments (described later) may be performed to determine the efficiency of collection by the targets. 29 In addition, the species being collected should not arrive at the target from any source or direction other than the effusion orifice. Error could.arise if effusing Species outside the collection angle were to reach the target by bouncing off the wall of the vacuum system and striking the target at the end of their secondary trajectory. The .species being collected might also escape from the effusion cell through another hole in the cell, or by diffusion through the cell lid. f. The Molecular Weight of the Effusing §pecies From equation (23) it will be seen that the molecular weight of the effusing species must be known. The ideal method of verifying the molecular weight of the effusing species is by use of the mass spectro- meter. Mass specrometric data on the equilibrium distribution of molecular weights of the substance effusing from the cell can also be obtained from other.work where the same substance is present in gaseous equilib- rium.- It is.also possible to assume a molecular weight for the effusing -species based on knowledge of the behavior of similar materials, or the same material at different temperatures, but such assumptions should be subjected to the closest scrutiny with actual measurement of the charge to mass ratio being reserved as a truly reliable method of ob— taining the molecular weight. 9. Cell Temperature The observed temperature, determined as precisely as possible, must be related directly to the internal temperature of the cell by a 3O determinable relationship. Gradients in the temperature within the cell generally are to be minimized and the avoidance of such gradients Should be considered in the cell design. The exponential dependence of pressure on temperature makes temper— ature determination the most critical of the physical measurements in— volved in this work. III. EXPERIMENTAL METHODS A. Synthesis of Borides l. Starting_Materials and Containers Starting reactant and crucible materials for this research con- sisted of rare earth metals, rare earth sesquioxides, boron, boron car- bide, graphite, boron nitride, zirconium diboride, molybdenum, and a molybdenum—tungsten alloy. Appendix I lists sources and purity levels for these materials. Boron and the metal oxides were available in the form of powders. Metal powders were sometimes obtained by filing soft metals or by crush- ing hard metals in a diamond mortar. When in the form of powders, re- action mixtures, were mixed thoroughly in plastic containers using a Wig—L-Bug amalgamator (Crescent Dental Co., Chicago, Illinois). The mixed powders were pressed into pellets using a steel die under a hydraulic press (Carver Laboratory Press, Fred S. Carver, Inc., Summit, N. J.) employing a pressure of about b,OOO lbs./in.2. When solid metals were used, it was not always practical to use powders so metal chunks and boron powder were simply placed together in a reaction vessel. The ratios of boron to metal in reactant mixtures varied with ex- periment and were generally chosen to approach that ratio in the desired boride prodUct with allowance being made when boron also reacted with oxygen in the reactant sample. 31 32 2. Induction Heating Experiments The large majority of experiments were conducted in vacuum or an inert atmosphere in various crucibles heated directly or indirectly by' the method of induction. The reaction containers were placed in a glass, vycor and quartz system evacuated by means of a three-stage mercury diffusion pump backed by a Cenco Hyvac lb fore pump. Unless an inert atmosphere was employed, the vacuum system pressure, which generally was in the range of 10“4 to 10‘6 mm. HQJHWas'mgasufgd , :szU by means of a vacuum ionization gauge (Type Rg2lA, Veeco Co., Hyde Park, N. Y.) attached to the system. The actual choice of reaction container depended upon the intended purpose. Graphite crucibles were ideal in terms of availability, ef— ficiency of heating and ease of machining. Boron nitride was easily machined and had the important advantage of showing no interaction with boride reaction mixtures. However, boron nitride is a non-conductor and therefore was heated indirectly by enclosing it in a graphite jacket. At temperaturesabove 16000c, boron nitride becomes useless as a con- tainer because of material breakdown; the boron nitride begins to flake away from the surface of the material while fissures form in the bulk of the material itself. Zirconium diboride was chosen as the primary container for the Knudsen effusion studies. Because of difficulties encountered in at— tempting to machine this material, crucibles were obtained commercially (Borolite Corporation, 3113 Forbes Ave., Pittsburgh 30, Pa.); only cer— tain simple shapes were practically available. The zirconium diboride crucibles as supplied contained large amounts of binder material which 33 was driven from the crucibles by extended heating at temperatures up to 2lOOOC. until binder material ceased to condense on the walls of the vacuum line. Zirconium diboride was tested as a boride reaction container by heating it at high temperatures (above 2lOOOCJ with a samarium hexa— boride pellet inside. Although the boride migrated from the floor to the lid of the crucible, the deposit of the hexaboride came loose cleanly from the zirconium diboride lid after a subsequent heating at about lSOOOC. In general, pellets of hexaboride or powder samples of tetraboride showed no tendency to bond to zirconium diboride even after being in contact with the crucible material for several hours at tem- peratures above lSOOOC. Molybdenum or molybdenum-tungsten allqys were used to fashion bombs when a closed reaction vessel was desired. Molybdenum and tungs- sfien have been shown to interact with boride samples at high tempera— tures (DB), but were still useable since the loss of a small amount of boron from the reaction mixture did not interfere with the formation of the desired product: the tetraboride. 3. Arc-melting_§xperiments A number of samples of rare earth metals and boron pressed into pellets were fused under an argon atmosphere in an arc—melter equipped with a water—cooled, tungsten—tipped electrode and a water—cooled cop- per floor. An electric arc was struck between the sample and the tung— fienrtipped electrode resulting in the rapid heating and'melting of the sample. Once the sample was fused, the arc was broken or moved away from the sample which then almost instantaneously solidified. The sample was then flipped over and remelted to assure a homogeneous product. 3h h. Analysis of Reaction Products All reaction products and some incompletely reacted mixtures were subjected to X—ray powder diffractometry analysis. This method may be expected to detect phases present to the extent of five percent or more in a mixture of phases. It was not always possible to identify all phases shown by X—ray methods to be present in products, but, within the limit of the method, it was frequently possible to ascertain the absence of phases of certain symmetries when the appropriate diffrac— tion patterns were not observed. Since many of the boride reaction products were mixtures of borides of different stoichiometries, or of boride and excess boron or metal, quantitative elemental analyses were unwarranted. The limitations of X—ray powder diffraction analysis made it possible that boride phases were present yet undetected in reaction products, but did not seriously hamper the interpretation of results. The absence of a particular phase, although not directly determined, could usually be concluded on the basis of phase-rule considerations and by observing the course of re- actions by means of quenching reaction mixtures at various time inter— vals during the reaction process. Quenched reaction mixtures were sub— jected to X—ray powder diffnmiion analysis so that the course of a re— action could be followed. A résuné'of reaction mixtures, containers, temperatures, length of time at reaction temperature and products is given in Table I. 5. Product Boride Purification Only in the case of samarium boride products prepared for use in HHoH-< a .amae H onH m wooH1< emae a cmmH «mam oamm + newas a Hx pooH-a a .NHmsu .emsa wH omaH Nmem oemm + moNau a x mooH.HooH-< NHmaeriamee eHez sea so mmH + as a xH oooH-< NHmesiemas eHo: one so me + ea a HHH> amend a .NHmem .amcm pH»: one. so mmH + em a HH> saa-< NHmem,semam eHez ace so me + em a H> mooH-< «mum . H mesH o are inseam am an a 4m ooeH comm + acmcm a > mHa-< Nmem .meem .emcm a omHm m HHa-< 4 emcm m oaHN chm emcm a >H sea-< NHmem nwmcm H omaH chm o Haa-< ,emem mm.o oamH m ama-< iaaaeHacmueeem .H ooaH 2m om + mmH + momcm a HHH wearaoa-a NHmcm m amcm H oHaH m eom-< newem m.o oooH 2m msH + moNcm a HH w” eecmoaammae aaHHaa m mNHN : oHa-< «mam m.o amHm o mom-< amcm m meoN a aoasa «mam m.o OJON m mam-< wmem H oamH Nmem a eawrmam-< NHmem .emcm m oomH o qam.mam-a amem ommH m Nam-< HmHeaama meanemnm magH 2m ma + am a H .mmwmmm. . mauspopd Amwmwwv .qaoe oanmosoo mpcmpomom cam mowoom .oooasc chHmOpocQ amoux mcwwapcoUH pom woodponanmoamp amoesbmoanob Amnocmmbcoo nmbcmpomon mcwpmHH wesmwu :oHpomom .H oHomh 36 .mummca no ommna pomwwpcovwos cm Mo oocowosa ocp mopmoHUcH mesoo m 5Q omHSEhow nonpo Eonm pobmamaom .cwmpuoo kaouzfiomom boa mH namumOpOcQ Quezoa hmuux cm cm ommca pmcp mo cowmewa lease“ use bmcp mopmowpcw deEuow compmonHbcoUH ommcm m mcmzofiaom kaopmwpoeem xnma compmovv <2 acme :pomoso < mmmH-< ,emam a 00m m.o oomH H omoH - m OOmH aaoa 0: ms + em a xHx mmMu-< amss .Nmaa bHaz use so mw a so a HHH>x mmmH-< NHmcm .vmcm H.o oemH m m.o oaaH Nmem mmH + no~cm < HH>x ammH-< NHmo: .emo .vmo: H.o oaoN o .. - .. . N.o omeH m m.o ommH chm mmH + mower < H>x emceeaammne baHHaa m.o ooam o aeoH-< a .amom m OONN m H onH chm me + noNox a sx emoH-< «mad m.m omaH m amoH-< a .amsq m.m oaeH o . N.m camH o a.e OmeH m OmOH-< a .aNHmsq .amad w oweH chm oemm + mewsq a >Hx mNoH-< a .~Hmom .amo: H caaH o N omaH m aNoH-< NHmom .emoz .amo: m.H cmmH Nmam oamm + mOmom a HHHx aHoH-< Nmom .eQNUm m onH a aHoH-< Nmam .mOwum m cmsH o mHoH-< amom .momum m.o OONH m WHOH-< amam .mOwem m.m OmmH chm comm + momem a HHx .mwmmm woodpocm AmeWmV_ .QEoH oHoHUSno mbcmbomom cam moHnom A.ecoov .H aHame 37 effusion experiments were any attempts made to purify the samples. Finely ground tetraboride products were treated with distilled water and then with dilute hydrochloric acid to remove excess samarium metal, although the metal was never observed in X—ray powder photographs of final reaction products. The powdered samples were then rinsed with water several times to remove the acid, rinsed with acetone and dried at 110° C.in a drying oven. B. Effusion Experiments 1. Apparatus a. Vacuum Assembly The vacuum system and effusion assembly used in the effusion ex— periments was designed for this purpose by Dr. Harry A. Eick and Mr. Robert E. Gebelt and had been employed previously by Dr. Richard A. Kent for the measurement of the vapor pressure of thorium in equilibrium with thorium dicarbide (50). The apparatus, which is shown schematically in Figure 6, includes a backed, three stage mercury diffusion pump, Wycor condenser, a support for the effusion crucible, an optical window and a device for presenting targets to the effusate from the cell. Below the target disc holder is a magnetically operated fused silica shutter for controlling exposure time. Discs were exposed to the ef— fusion beam in succession, and, after being exposed, were ejected by means of a magnetically operated tungsten push—rod into a Pyrex re— ceiver and storage chamber. b. Effusion Cell The effusion cell was designed to meet the requirements of inertness 38 b Dewar for Liquid Nitrogen ”fl—""____,,._ Kovar Seal p Brass Bottom of Dewar Copper Magazine for Targets P‘———“.—________H———Stainless Steel Collimator Pyrex Table \ W501}. Iron Slug \\Jq Quartz Shutter B Receiver for Water Outlet 0 Exposed Targets : ° 0 o o o 4——€rucib1e . o O £2??Ctlon °_J q Quartz Table 0 .40 k Water Inlet--“" To Vacuum Pumps fi 7 \——Soft Iron Slug Optical Window i_4) 0 E;7 Prism Figure 6 (SO). Schematic diagram of vacuum system used for effusion experiments. Pyrometer 39 to hot boride mixtures and practicality of fashioning a suitable cell for effusion experiments. Zirconium diboride was chosen as the primary container for the mixed samarium borides since preliminary experiments had shown it to be effec- tively inert to rare earth borides up to temperatures of 2OOOOC. The bulk of the cell, which stood 38 mm. high, was fashioned from presintered molybdenum stock. Inside the molybdenumlase, a zirconium diboride cup was positioned; it was denied contact with the molybdenum by means of symmetrically positioned tungsten pins, three in the floor and three in the wall of the cell. The lid of the effusion cell, through which the effusion orifice had been drilled, was machined with a female taper; the base of the cell had'a male taper to match that of the lid. Both sections of the cell and the zirconium diboride cup were outgassed prior to use. The molyb— denum pieces were joined irreversibly when they were heated together for the first time. The effusion cell is represented by Figure 7. 2. Measurement of Dimensions The measurement of three linear dimensions is required for the Knud— sen method calculations: the diameter of the effusion orifice of the crucible, the distance from the orifice to the target collimator and the diameter of the collimator. All linear parameters were measured several times each; an average value for each parameter was employed in the cal— culations. Orifice diameter was measured before and after each effusion run using a microscope (Bausch and Lomb, Model SVB—73) eQuipped with a hO Figure 7. Pictorial representation of the Knudsen Effusion Cell. Lu vernier eye—piece calibrated such that one division on the vernier scale under high magnification (60X) measured 0.033 mm. The calibra— tion of the eye-piece scale was verified by sighting on a gap between measuring posts of a precision micrometer. After assembling the apparatus and evacuating it for at least half an hour so that the ground glass joints were firmly seated, the distance from the orifice to the collimator was measured with a catheto- meter (Gaertner Scientific Company, Model No. M911, Serial No. 1585a). The scale could be read directly to 0.05 mm. by means of a vernier. The position of the orifice of the effusion cell necessarily-was determined by sighting through the double glass wall of the vacuum system and cooling jacket, but the position of the collimator lip was determined by sighting through the opening made by removing the shut- ter assembly. The collimator diameter was measured with a vernier caliper which could be read to 0.00h inches. Appendix II lists tabulated values determined for the linear measurements pertaining to each effusion run. 3. Exposure Procedure The evacuation of the effusion assembly always was begun the night before an effusion run. During each effusion run, the collimator-holder assembly was cooled by the introduction of liquid nitrogen into the Dewar—type container to which the collimator assembly was attached. Before the first disc was exposed to effusate, the temperature of the cell was raised higher than the temperature desired for the exposure (except for the first run). Generally, a pressure rise was observed A2 when the cell was first heated; the cell was maintained at the higher temperature until the pressure of the system had receded to a value less than 1 x 10"5 mm. of mercury. The high pressures initially observed upon heating the effusion cell are ascribed to an outgassing process of the cell which was exposed to the air between runs. When the system pressure had decreased sufficiently, the potential applied to the induction coil was adjusted to achieve a temperature within a few degrees of that projected for the exposure. The temperature .was read at intervals of a few minutes until it appeared constant within two degrees; the shutter was then moved aside beginning the exposure of a disc. The length of exposure time was chosen to produce a manageable deposit of samarium on the target disc, insofar as could be predicted. The time of each exposure was measured using a current frequency de— pendent timer (Lab—Chron, Labline, Inc., Chicago, Ill.) which recorded ‘elapsed time to the nearest one-hundredth of a minute. The co-ordinated Operation of the timer switch and shutter on the effusion assembly was performed manually. Approximate temperatures for the individual exposures were planned in advance such that high temperatures were achieved during the middle of a series of exposures; hence lower temperatures were involved both before and after the high temperatures. This provided a check for reproducibility and a means of detection of such complications as sur— face depletion of samarium and dependence of the vapor pressure of samarium on the rate of diffusion of samarium to the surface of the sample. h3 h. Collection Efficiency; ”Bouncing" Experiments Pairs of discs, one above the other, were exposed to the effusing molecular beam of samarium. The lower disc in each pair was protected from the primary samarium molecular beam by a 0.127 mm. thick platinum disc situated below it. A small hole drilled in the lower quartz disc and a slightly smaller hole punched in the platinum disc (1.566 and 1.5h6 mm. for each platinum disc respectively) allowed some of the effusate to pass through, striking the second disc positioned directly above. It is possible that some of the "reflected” atoms would escape to the side rather than strike the lower disc. This effect would be great- .est when the cosine law for reflection was obeyed and then, because of the small distance between the two collectors, approximately l.h% would fail to strike the lower disc. It is also possible that some impinging samarium atoms would strike the upper disc and reflect directly in the opposite direction passing back through the hole in the platinum disc through which they came previously. Based on the assumptions that all samarium detected on the lower disc first had reflected from the upper disc (the primary beam would have had to penetrate the 0.127 mm. platinum) and that all the samarium which failed to "stick" to the upper disc was collected by the lower disc, an efficiency of collection was determined. Not enough individual "bouncing" experiments were performed to define a temperature dependence in the collection efficiency so an average value was used in all calcu— lations. (See Appendix III). Lil: C. Temperature Measurement Temperatures were determined by means of disappearing filament optical pyrometers (Leeds and Northrup, Serial Nos. 152h388 and 1572579) calibrated by the National Bureau of Standards. The effusion cell and many of the crucibles employed for preparative work were provided with a black-body hole (generally considered to be a small hole drilled ten times as deep as the diameter of the hole) into which the optical pyro— meter could be sighted. I Temperature readings were corrected for the transmissivity of the interposed optical window—prism combination. These corrections were determined by measuring the temperature of a particular area of the filament of a tungsten band lamp, withanriwithout the prism and window interposed. The transmissivity corrections were assumed to be constant over the temperature range involved and were calculated from l/C = 1/TQ - 1/TT where To is the observed temperature in degrees Kelvin, TT is the true temperature in degrees Kelvin and 1/C is the transmissivity correction for a window or prism. A total transmissivity correction for a system was calculated from 1/ct = 1/cp + 1/cw where l/Ct is a total transmissivity correction, the sum of the trans- missivity correction for prism and window. Thus, the true temperature was calculated from the observed temperature as in the following equation: i/TT = l/TO — 1/ct. us When the temperature of a container without a black—body hole was being determined, an emissivity constant was used to correct the appar— ent surface temperature to a black—body temperature. Since such con— tainers were used only for preparative work where the temperature measure— ment was not critical, a graph was prepared by plotting observed temper— ature versus corrected temperature obtained by applying emissivity and transmission corrections. This graph was then used to convert observed temperatures into actual temperatures. D. Quantitative Samarium Analyses 1. Preparation of Standards Standard samarium solutions were prepared from two stock solutions containing known amounts of samarium nitrate. The stock solutions were prepared from weighed amounts of samarium sesquioxide, fired to constant weight in a muffle furnace, dissolved in a small volume of con— centrated nitric acid and diluted to 250 ml. with demineralized water. Aliquots of the stock sdlutions were successively diluted to produce solutions containing very small concentrations of samarium ion as listed in Appendix IV. Lambda pipettes were used to transfer small volumes of these dilute solutions onto quartz discs like those used for the effusion experiments. The discs with small volumes of the standard solutions were warmed with an infra—red heat lamp causing evaporation of the water and deposition of very small amounts of samarium'ontthe discs. These quartz discs bearing their samarium deposits constituted the standards for the samarium analyses. be 2. Neutron Activation of Samarium Samples The discs from the effusion experiments, together with previously prepared standard discs and several blank discs, wrapped uniformly in aluminum foil, were exposed to a thermal neutron flux of at least 1012 neutrons/cm.2—sec. in the CP—5 reactor at the Argonne National Labor— atory (51). Exposure time for the discs from the first three runs was one week, for the last two runs, four days. The irradiation resulted in an (n, v) reaction of 1525m (26.7% abundance in naturally occurring samarium (52)) to i538m.which produces gamma activity of 10h Kev energy with UZlh.half—life. Fortunately, the ermal neutron cross section for this reaction is very high, 1h0 barns, compared with the other reactions of samarium isotopes not resulting in stable masses so that no interfering gamma activity is produced in the neutron—activated samples. Appendix V presents data on samarium iso- topes pertinent to neutron activation. 3. Identification of Species Present in Activated Samples The gamma spectrum of an activated sample disc was recorded using the Baird Atomic gamma ray spectrometer (Model 250) with auxiliary re— corder chart. The spectrum showed only the activity of 1538m as given by Crouthamel (53) and shown in Figure 8. In addition, the half—life of the activity calculated from the de— crease in activity with time for specific discs approximated the reported half-life of h7.l hours. — 'T V _] : . .I u 1 4 .w .‘IQ—u-vr-Jc ‘L"".l.r.zy. .m..._-,n ‘_ 2? m Q) Q c) Q. m U (A o 0 a c) M c 0H N '0 <3 O H u—a t a: :>. T3 m o u .c :3 .2 1: tr e e U) a a a 4.) s > x o s .9 L) H Q) [ ._:t :> 01-4 4..) m i H Q) a: . 'l i i 3 I I | i l 0 50 ' 100 Kev. . 150 20 250 Figure 8. Gamma-ray spectrum of a neutron irradiated samarium— bearing quartz disc. h8 h. Counting of Activated Samples The aluminum wrapper was removed from the samarium—bearing quartz discs which had been subjected to a thermal neutron flux and they were then rewrapped in ”Saran” wrap in order to confine the samarium and protect the discs from direct contact with other materials. The activities of the discs were determined in one of two differ— entiating scintillation counters (Baird Atomic amplifier-analyzer Model 250, Scalar Model 125; Hamner amplifier —analyzer Model N302, Scalar N221). A differentiating energy window of 100 Kev centered on 102 Kev. energy was used. The sets of discs were counted several times in various orders until the least active samples gradually approached background activity rendering further counting purposeless. It was hoped that, with the proper corrections for half—life of the activity and ’coincidence of detector excitation, the standard discs would show a linear relationship between the activity counted and the amount of samarium deposited on the discs. However, attempts at determining a (coincidence correction factor were never satisfactory and, ultimately, non—linear curves were prepared for each series of counting of standards and unknowns. By reading values from the curve prepared from data on the standards, the activities of the unknowns were used to obtain values for the amount of samarium present. The agreement between amounts of samarium on each disc determined by separate series of countings was not extremely good (Appendix VI). Values which were subject to the least chance of error (as judged by the appearance of various series of data) were averaged to obtain the number of moles of samarium on each unknown disc. This provided the re— quired information for use in the Knudsen effusion equation. 1:9 Part of the problem encountered in evaluating the active samples arose because of the wide range of activities exhibited in both unknowns and standards. No single standard curve could accurately cover the whole range of activity and concentration of samarium. E. Molecular Weight of Samarium Vapor Species In order to determine the molecular weight of the effusing samarium species, samarium metal was heated in a molybdenum crucible, the cover of which was pierced by a small orifice. The vapor escaping from this orifice into a vacuum was directed into the ionization chamber of the Bendix Time—of-Flight mass spectrometer. The entire charge—to—mass ratio spectrum was scanned and projected on a fluoroscope. Special at— tentiveness was directed to those areas with charge/mass ratios cor— responding to dimeric and oxide samarium species. IV. RESULTS A. Synthesis Experiments 1. Hexaborides No success was achieved in obtaining hexaborides of erbium, thulium, lutetium or scandium (see Table I). X—ray diffraction data for a typical preparation, an erbium sesquioxide—bonxicarbide reaction product, is given in Table II. These nominally failing attempts are worthy of report, however, in that similar results have been met by others (26) and that reported preparations of these hexaborides have not been substantiated well. 2. Samarium Tetraboride The first preparation of samarium tetraboride uncontaminated by hexaboride was accomplished by heating samarium and boron together in a molybdenum alloy bomb sealed with a platinum gasket which method was indicated as most promising by previous work done in this laboratory by Galloway (h8). This method tookinto atcount‘ knowledge concerning boron behavior in various containers and the tendency of samarium to vaporize from its tetraboride leaving hexaboride behind. 3. Europium Tetraboride Using an approach quite similar to that which led to the form— ation of samarium tetraboride, the preparation of europium tetraboride was attempted. However, the presence of such a phase in reaction products was never detected. 50 51 Table II. X-ray diffraction data for an erbium sesquioxide—boron carbide reaction product +7 ‘1 Vv d (8) ErB12 ErBlZ ErB4 ErB4 d (8) ErBlZ ErBlZ ErB4 Bra4 abs. .Qcaic. (hkl) §ca1c. (hkl) Ebs. 9ca1c. (hkl) gcalc. (hkl) 5.019 5.000 110 1.670* 1.673 h20 1.666 330 b.326 b.321 111 1.577 1.576 u11 u.011 b.000 001 1.539 1.538 331 3.750 3.7u2 200 1.527 1.528 A22 3.538 3.536 200 1.u90 1.l90 312 3.161 3.162 210 1.uh0 1.hu0 333/511 2.6u6 2.6l6 22o 2.6u8 201 1.33u 1.333 h31 2.u79 2.h8o 211 1.332 003 2.259 2.257 311 1.32u 1.323 tho 2.236 2.236 310 1.312 1.313 520 2.161 2.160 222 1.310 511 2.121 2.120 221 1.302 1.301 A12 2.000 1.999 002 1.280 1.280 332 1.952 1.951 311 1.265 1.265 531 1.871 1.871 loo 1.2h8 1.2l7 600 1.2u7 203 1.762 1.761 321 1.212 1.213 530 1.7h1 1.7u0 202 1.18u 1.183 620 1.71h 1.716 331 1.715 u1o 1.161 1.160 531 1.689 1.689 212 1.1h2 1.1h1 533 ”Diffuse. 52 h. Thulium Diboride Thulium diboride was prepared for the first time by arc-melting a pellet containing boron and thulium in a ratio of 2.0 (B/Tm). The preparation is not pure since a large amount of tetraboride is also formed. X-ray powder data obtained from the thulium boride reaction product are listed in Table III. Lattice parameters were calculated from the X-ray data without correction. They are a0 = 3.25, R.and Co = 3.73 R. B. Knudsen Effusion Measurements 1. Comparison of Individual Runs Considering a series of exposures of discs in succession at various temperatures without breaking vacuum as one run, it is apparent from the graph (Figure 9) showing the logarithm of samarium pressure versus reciprocal temperature (Appendix VII) that no significant difference or displacement was observed between the respective data resulting from various runs. The last effusion run employed the same effusion cell with an en- larged orifice, again as a check to assure that the pressure measured was independent of the (small) orifice size and that the evaporization coefficient was essentially unity. 2. Collection Efficiency Determination The results of the ”bouncing” experiments listed in Appendix III indicate that an average of 9h.5% of the impinging samarium atoms were retained on the target discs. 53 Table III. Observed d values for a thulium-boron reaction product with calculated d values for thulium borides Estimated Observed Calculatede (hkl) Calculatedww (hkl) Intensity Q value d values TmB2 TmB2 d values TmB4 TmB4 30 3.9t3 3.976 001 to 3.719 3.731 001 20 3.506 3.519 200 55 3.131 3.1u7 210 2 3.021 3.107 111 80 2.809 2.818 100 50 2.632 2.635 201 75 2.u61 2.u68 211 99 2.2b5 2.2h9 101 1 2.219 2.226 310 15 2.106 2.109 221 25 1.982 1.988 002 25 1.9h0 1.9l2 311 20 1.865 1.866 002 1 1.850 1.8h6 112 1 1.7l8 1.752 321 10 1.729 1.731 202 25 1.706 1.707 th 20 1.679 1.681 212 15 1.659 1 659 330 55 1.625 1.627 110 55 1.570 1.568 A11 60 1.558 1.556 102 35 1.533 1.531 331 50 1.h93 1.h91 111 1.l83 312 to 1.hll 1.u09 200 5 1.329 1.325 003 50 1.322 1.318 201 5 1.308 1.30h 511 A5 1 301 1.295 A12 30 1.280 1.27l 332 20 1.2u8 1.2hh 003 1.2l0 203 50 1.233 1.226 112 1.222 213 20 1.21b 1.207 530 10 1.179 1.173 600 35 1.163 1.156 531 no 1.1h6 1.1h9 b32 to 1.127 1.125 202 99 0 eat a0 = 3.25, 60 = 3.73 A . “a0 = 7.071, 60 = 3.997 X 5h Temperature (° K) 2,5CD 2000 I500 [.250 6 4.0 5.0 6.0 7.0 8.0 (l/T°K) x104 81 33° 3SmB4 = ZSmBG + 8m”) CR)“: Figure 9. Graphical s'czpres‘entation of Knudsen effusion data. 55 3. Calculated Values for Enthalpy and Entropy Changes (Second Law) The method of least squares was applied to the logarithm of pressure versus reciprocal temperature data to obtain the slope and intercept of the best straight line passing through the points. From the slope and intercept of the line were calculated the standard enthalpy and entropy changes for the reaction which results in the conversion of samarium tetraboride into samarium hexaboride and elemental samarium. Four points obtained during various runs were rejected after visual inspection of a preliminary graph of the data. These points were inié tjal points for the various series of exposures and showed pressures far too high to be consistent with the bulk of the data. Presumably, resid— ual oxygen-containing gases react with the effusion cell contents to produce lower samarium oxides. These volatile oxides are collected on the quartz targets adding to the amount of samarium. As the residual gas pressure subsides this effect diminishes. With the exception of those four points, all points were given equal weight in calculating the least squares equation describing the data. For none of the points accepted was the distance to the least squares line greater than twice the standard deviation. From the slope, a standard enthalpy change of 91.32 kilocalories with a standard deviation of 3.32 kilocalories was obtained. The inter— cept leads to values of 2h.62 and 1.95 calories for the standard en— tropy change and its standard deviation reSpectively. h. Calculated Values for Enthalpy Change (Third Law) By estimating the fef of the borides to be the sum of the fef's of 56 the components, and employing the fef values for samarium given by Stull and Sinke (5h), AH?98 was calculated for each pressure—temperature point in the data. In spite of the gross scatter in the values calcu- lated for the standard enthalpy change, no trend dependent upon tempera— ture was observed in the data. All calculated standard enthalpy change values (with the exception of those for the four rejected points) were combined to obtain an average vaer of 93.93 kilocalories with a standard deviation of 2.01 kilocalories. The values for the standard enthalpy calculated by the Third Law method for each point are listed in Appendix VIII. C. Determination of Molecular Weight of Effusing Species Within the limits of detection (10_7 mm. Hg) and the temperature limit for the heating source of the mass spectrometer (15OOOC), only mon— atomic samarium metal species were observed in the effusate escaping from a molybdenum cell containing metallic samarium. V. CONCLUSIONS A. Reports of Hexaborides of Erbium, Thulium, Lutetium and Scandium With the exception of a report dating from 1932 (3) by von Neuman and Stackleberg, when pure samples of rare earths or their compounds were not available, all primary reports of erbium, thulium, lutetium and scandium hexaborides have arisen in the U.S.S.R., most often in the papers of G. V. Samsonov and co—workers. These reports are disturbing in that no success in preparing these hexaborides was achieved in this laboratory. A number of approaches were tried including experiments using carbon—containing reactants with the thought that the presence of carbon might stabilize a hexaboride phase. Ultimately, it was observed that products of reactions designed to lead to a boron-to-metal ratio of six often contained a mixture of borides: the tetraboride and the dodecaboride (Table II). The details of the Russian preparative methods were not reported, but some X—ray powder crystallographic data were obtained indirectly by estimating diffraction angle values from a graphical representation of an X—ray powder photograph (13). These data proved to be subject to an interpretation different from that of the authors of the paper. In Table IV are presented the data of Neshpor and Samsonov with the inter— pretation of the researchers and the alternative interpretation of Sturgeon and Eick (55) which concludes that cubic hexaboride is absent. Other preparative attempts have resulted in the formation of mixed tetra— and dodecaborides of lutetium: Przybylska, Reddoch and Ritter (26) have obtained results analogous to those reported here when they attempted 57 58 Table IV. Alternative interpretations of X-ray diffraction data for lutetium boride. Neshpor and Samsonov(13) Sturgeon and Eick (55) - (hkl) (hkl) g (I) g (X) (ca1c.)" (hkl) mos um, (ms. Ufi4 um4 100 3.9A 3.96 001 110 210 3.1A 3.15 210 201 2.62 2.63 201 111 2.AA 2.A6 211 310 2.2A 2.23 310 200 221 2.08 2.11 221 2m 3% 193 195 3% 112 1.85 Probably Lu203 211 022 1.73 1.73 202 A10 1.71 1.71 A10 212 1.68 1.68 212 A01 1.67 1.66 330 A20 1.57 1.58 A11 331 1.53 1.53 331 220 A21 1.A8 1.A8 312 A30 1.A3 1.A1 A30 221 510 1.A1 1.39 322 5,20” 1.33 1.32 A3 1/003 310 113 1.29 1.29 A12 . 332 1.28 1.27 332 311 123 1.25 1.25 203 330 1.23 1.22 213 222 A11 1.21 1.21 530 610 1.18 1.16 531 59 to prepare lutetium and scandium hexaborides. Instead of the cubic hexaborides which they sought for nuclear magnetic resonance investiga— tions, they obtained mixtures of other borides. My conclusion is that, until more detailed and satisfactory data are presented, the reports of the preparation of the hexaborides of lutetium, thulium, erbium and scandium must be discounted. B. The Effect of Metallic Size on the Stability of the Cubic Hexaborides In 1957, Muetterties (56) proposed size limitations on the metallic radii of metals for which metal borides could be formed, apparently on an empirical basis. His lower value (1.80 A.) for hexaboride formation indicated that the heavy lanthanons (excluding ytterbium) should not form hexaborides. Such a limitation has been reported for the dodeca— borides as well (9,23,27). The preparation of cubic hexaborides for the rare earth metals be— comes progressively more difficult as the metallic radius of the metal becomes smaller. The smallest metal for which a cubic hexaboride defi— nitely has been prepared is holmium (metallic radius = 1.79 A.) and this only in very small amounts (36). It appears that a limiting minimum metallic radius is reached at holmium among the rare earths indicating that cubic hexaborides of erbium, lutetium, thulium and scandium do not exist. Furthermore, it is likely that this minimum limitation is actu- ally the result of a limiting minimum on the boron—boron distance which reaches 1.69 R. in holmium hexaboride. No compounds containing smaller boron-boron single bonds of this type have been reported. Table V contains maximum and minimum boron—boron distances observed for the various types of rare earth borides. 60 Table V. Observed boron~boron distances in those types of borides ex- hibited by the rare earths. Type 3%gi? ? Metal ao (NJ co(R) gigim ) Metal a0 (8) 00(8) MBZ 1.91 Gd 3.31 3.9A 1.71 Cr 2.969 3.066 MB4 131—131 1.77 La 7.30 A17 1.69 U 7.075 3.979 BI-A BIII 1.76 1.69 1311: -BII 1 . 80 1. 7A BII-2 BIII 1.80 1.75 BIII-2 BI 1.76 1.69 BIII-BII 1.80 1.75 , BIII~2 BIII 1.81 1.75 MB6 1.78 Ba A.268 1.69 Ho A.Q96 MBlz 1.769 Tb 7.505 1.7A6 Zr 7.AO8 61 C. The Preparation of New Rare Earth Borides Because the lattice parameters of the binary borides vary almost di— rectly in proportion to either the metallic or ionic radii of the central or heavy metal and because the size of the metal atom is often the deciding factor for stability or instability, lattice parameters reported for com- pounds which do not conform to the pattern of other members of the same stoichiometric group of compounds are either suspect or indicate that the metal involved has more than one effective metallic or ionic radius. Table VI presents the known binary borides of the rare earths together ‘with their reported lattice parameters. From the observation of such a table, it has been possible to prog— nosticate the preparation of additional rare earth borides. Such was true in the case of thulium diboride. However, such ”gaps" have rapidly been filled in the past two years, and the likelihood of preparing new binary borides is rapidbrbefiKJexhausted except in the case of the borides with very high boron contents which are not yet well characterized. D. Samarium Tetraboride Stability The qualitative fact that samarium tetraboride is unstable at high temperatures with respect to decomposition into hexaboride and excess metal now can be stated in quantitative terms. It is interesting that the large positive enthalpy for the reaction requires that, under one atmosphere of samarium vapor pressure, the temperature must be increased to about 3,5000C (actually above the reported melting point of 2,5A00C (6)) before the negative entropy can overcome the positive heat resulting in the negative free energy change required for spontaneous reactions. Table VI. Dattice parameters for known rare earth borides. 62 M32 M34 Metallic ___ ionic radius (57) a0 cO ao co d0 ao radius** Sc 1.65A5 3.1A6 3.517 0.68 Y 1.7780 3.298 3.8A3 7.111 A 017 A.113 7 500 0.88 La 1.8852 7.30 A.17 A.1A3 1.0A Ce 1.82A8 7.205 A 090 A.1A1 1.02 Pr 1.8363 7.20 A.11 A.130 1.00 Nd 1.8290 .7.219 A.102 A 126 .99 Pm Sm 1.8105 7* ? 7.17A A.070 A.133 7 0.97 Eu 1.99A A.178 0.96 mi L8w 331 39A 71ml A0m3 A308 09A Tb 1.8005 3.28 3.86 7.118 A.029 A 102 7.50A . 0.92 Dy 1.7952 3.285 3.835 7.101 A 017 . A 098 7.501 0.91 H0 1.7887 3.27 3.81 7.086 A 008 A 096 7.A92 0.89 Er 1.779h 3.28 3.79 7 071 3.997 7.A8A 0.87 Tm 1.7688 3.25A 3.732 7.05 3.99 7.A76 0.86 Yb 1.9397 7.01 A.00 A.1A7 7 A69 0.85 Lu 1.7516 3.2A6 3.70A 7.00 3.9A 7.A6A 0.8A %Said to exist (28) but no lattice parameter is reported. 39+ . . Trivalent ion. 63 This indicates that samarium tetraboride melts congruently under one atmosphere of samarium pressure. E. The Problem of Europium Tetraboride The preparation of europium tetraboride continues to elude workers in the rare earth boride area. The most rational approach to preparing such a boride is by means analogous to those used to prepare samarium tetraboride—-by confining boron and excess europium in a bomb and heat— ing at various temperatures for periods of time up to several weeks. The failure of this method seems inconsistent with the data obtained for the samarium tetraboride-hexaboride conversion. One would not expect the standard entropy for the reaction of hexaboride plus excess europium to differ greatly from the values for samarium hexaboride so that the difference in stabilities of the re— spective tetraborides of samarium and europium must be related to a difference in standard enthalpy changes. The continuing failure to prepare europium tetraboride is puzzling. VI. ERROR ANALYSIS An analysis of random error for a representative disc exposure, exposure number six, run III, in the Knudsen effusion experiments shows that the greatest error arises in the determination of the number of moles of samarium on the disc. In Table VII are listed the standard deviations for all measured parameters involved in the calculation of the logarithm of the pressure of samarium at a temperature. Table VII also shows the value of the standard deviation for each parameter di— vided by the parameter value times 100 to obtain more easily compar— able percentages. It is felt that the standard deviation calculated for the area of the effusion orifice is misleadingly large since it was calculated on the basis of the assumption that the orifice was perfectly symmetrical which in fact it was not. This means that the scatter in the values determined for the radius is not due to random error, but rather to actual variances in the diameter of the orifice dependent upon which point of the perimeter was chosen as the end of the diameter. A large systematic error in the determination of the effusion orifice area for. a single run should lead to displacement of its line on the graph de— scribing the data from the line describing data from other runs. Within the limitations of the data, no such displacement was observed. Some of the variation in observed temperature no doubt was truly random error encountered in matching apparent black—body temperature with that of the hot filament in the optical pyrometer. A standard' deviation was estimated to be eight degrees for this type of error. 6A 65 Table VII. Standard deviations of parameters measured for use in the Knudsen effusion equation. Parameter Value of Parameter Standard Deviation 100A (T) A B % so Orifice area 7.52A x 10‘3 cm. 8.70 x 10'5 1.1 Cell to colli— _3 d mator distance 9'999 Cm- 5.8 x 10 0.6 r Ezéiigator 0.9535 cm. 8.A x 10_4 0.1 Temperature 17A3O K 8 (estimated) O.A6 (Temperature)1/2 A1.75 9.6 x 10_2 0.3 t Time 3600 sec. negligible ——— 9 A Number of moles Sm 2L29 x 10‘ 6.1 x 10'10 26.6 66 There is also systematic error in the temperature of approximately the same magnitude due to the limits of the calibration of the pyrometer. HOWever, an additional problem, of indeterminate extent, was intro- duced when voltage output from the low frequency generator to the induc- tion coil used to heat the effusion crucible varied irregularly, un— controllably and unpredictably—resulting in variations of the temperature, generally downward. Nonetheless, effusion runs wherein no such fluctu— ations were detected did not show appreciably greater precision. Another complicating factor was the fact that higher than ”equilib- rium” pressure of samarium usually was observed for the first one or first few exposures in an effusion run. This may be attributable to the presence of oxygen which reacts to form a volatile samarium oxide (28) resulting in increased deposits of samarium on the target discs, an effect which diminishes as oxygen in the system is depleted. It may be attributable as well to interaction of small amounts of samarium tetraboride with the molybdenum cell since the boride had to be intro— duced into the cell through the effusion orifice itself, making it entirely possible that small amounts of the boride came into contact with the molybdenum instead of falling into the zirconium diboride cup. Thirdly, it is possible that not all elemental samarium was removed by treatment with dilute acid solution. In runs subsequent to the first, where the effusion cell was heated to high temperatures for some time before the exposure of the first disc was begun, this behavior was much less marked. That the process of heating the effusion cell to a relatively high temperature to drive off excess samarium or other volatile samarium 67 species before beginning an effusion run did not result in samarium depletion of the tetraboride surface was indicated by the appearance of the sample after completion of the effusion runs. When the effusion cell was cut open, the sample was mostly the gray tetraboride with only a portion of the surface showing the blue of the hexaboride. The sample was still loosely powdered with no evidence of sintering. The effect of varying the orifice size (i;e., no effect was ob— served in the pressures measured) indicates that the evaporation coef— ficient safely may be assumed to be unity. In calculating the values for the standard enthalpy for the reac— tion studied, seventy—three points were used to calculate the slope of the least squares equation describing the points. The standard deviation in the slope calculated on the assumption that all points were randomly distributed around a mean, true value amounted to 3.6A% of the value obtained for the slope. In the case of the intercept from which the standard entropy change is obtained, the standard deviation for the intercept amounted to 7.9% of the numerical value of the inter— cept, reflecting the lesser precision with which the intercept of the least squares equation is determined. The high error in the pressure calculated from the Knudsen rela— tionship is ascribable directly to the disappointingly large error in the assay for samarium by activation analysis. This error is not due to inadequacies of the activation process, but to limitations in the gamma—ray counting equipment available and its present state of precision in the thousands of counts per minute range. The graph relating vapor pressure of samarium over a mixture of the tetra— and hexaborides to reciprocal temperature (Fig. 9) shows agreement 68 between runs, including the last run which was conducted with a differ— ent orifice size. The values obtained from the Second and Third Law calculations agree within the limits of error. Because of the nature of high temperature chemical systems and the many difficulties and limitations encountered in high temperature chem— istry, such a large range of temperature and pressure measurements for one reaction is unusual. Some credit for this must be given to Dame Fortune since it was impossible to determine in advance what range could be studied practically. VII. FUTURE RESEARCH Because of the large cross section of 108 for thermal neutrons, the otherwise desirable neutron diffraction experiments on borides are disallowed. Therefore, the only method of determining the exact boron positions in the rare earth borides is precise single crystal X-ray dif- fraction. Using the thermodynamic data in this thesis and a measured free energy of formation of one of the samarium borides studied here, the calculation of the free energy of formation of the other would be pos— sible. Exploration of energy changes accompanying the conversion of other stoichiometry borides, not necessarily of samarium, will allow the quanti- tative description of other boride phase energy differences. Ultimately such data will lead to the delineation of phase diagrams which describe accurately rare earth boride systems. The apparent consistency of electrical conductivity and Hall voltage data with the most recent theoretical discussions of the rare earth borides does not explain the fact,that the hexaboride lattice parameters relate to the irregular metallic radii of the heavy metals while the lattice parameters of the dodecaborides and tetraborides reflect the different, regular trends visible in the radii of the triply charged metallic ions. Since both the boranes and rare earth borides have been treated successfully using the same or similar theoretical approaches, efforts should be initiated in relating these two classes of compounds chemically. 69 70 Although it still appears reasonable that the tetraboride of euro; pumishould be preparable, no pertinent suggestions concerning a new ex— perimental approach to its preparation come to mind. 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Chart of the Nuclides, 2nd ed., Bersbach and Sohn Verlag 32 Barer Strasse, MAnchen 3A, Germany 1961. Applied Gamma—Ray Spectrometry, C. E. Crouthamel, ed., Pergamon Press, New York 1960. Thermodynamic Properties of the Elements, D. R. Stull and G. C. Sinke, American Chemical Society, Advances in Chemistry Series No. 18, Washington, D. C., 1956. Sturgeon, G. D. and H. A. Eick. ”Some Aspects of the Structure and Stability of the Cubic Hexaborides of the Lanthanons," to be published. 7A 56. Muetterties, E. L. Z. Naturforsch. 12b, All (1957). 57. The Nature of the Chemical Bond, 3rd ed., L. Pauling, Cornell Uni— versity Press, Ithaca, New York, 1960. APP EN DI CBS 75 AP PENDIX I SOURCE AND PURITY Source Michigan Chemical Corp. St. Louis, Michigan Heavy Minerals Corp. A000 N. Hawthorne St. Chattanooga, Tenn. Research Chemicals Inc. Burbank, California U. S. Borax and Chemical Corp. Pacific Coast Borax Co. Division OF MATERIALS EMPLOYED 630 Shatto Place, Los Angeles, Cal. A. D. Mackay, Inc. 198 Broadway New York 38, N.Y. Carborundum Latrobe, Pa. United Carbon Products Bay City, Michigan Borolite Corp. 3115 Forbes Ave. Pittsburgh 30, Pa. Sylvania Electric Products, Inc. Chemical and Metal., Division Towanda, Pa. Climax Molybdenum Co. of Mich. Goldwater, Michigan Material Purity Dy203 99.9% LuZO3 99.9 Tb203 99.9 Y203 99.9 Gd203 99.9 Sm203 99-9 YbZO3 99.9 H0203 99.9 Er203 99.9 Eu203 99.8 Eu 99 Sm 99 Er 99 Tm 99 H0203 99-9 Gd203 99.9 SCZOS 99-9 B 99.15 B4C Unknown BN 97.0 (2.A% oxide) Graphite Better than spectroscopic ZrBz Unknown Mo (effusion cell) 99.95 Mo (bomb) > 99.9 76 APPENDIX II COMPILATION OF CORRECTED LINEAR PARAMETERS FOR INDIVIDUAL EFFUSION RUNS SO d r r2 + d2 orifice orifice-target target -—-———— area(cm2 x 103) distance (cm.) radius (cm.) F2 Run I 7.A21 10.037 0.9529 111.9 Run II 7.396 9.995 0.9532 111.0 Run Ila 7.A98 10.001 0.953A‘, 111.0 Run 111 7.52A 9.999 0.9535 110.1 Run 1v 1.1A2 10.102 0.9550 112.9 ”Bouncing" . 1.1A2 10.199 0.07828 16 970 Experiments 0.07730 l7:AlO APPENDIX III DATA CONCERNING COLLECTION EFFICIENCY FOR KNUDSEN EFFUSION TARGET DISCS First pair of target discs, exposed at 1788°K upper disc (primary target) 53.1 x 10‘10 mole Sm lower disc (secondary target) 2.38 x 10‘10 mole Sm percent Sm collected on primary disc: 95.7% Second pair of target discs, exposed at 2002°K _ upper disc (primary target) 95.5 x 10 10 mole Sm lower disc (secondary target) 7.53 x 10‘10 mole Sm percent Sm collected on primary disc: 92.7% Average percent of Sm collected on primary discs: 9A.2% 77 wme4,+Mh_~ APPENDIX IV DATA CONCERNING STANDARD SAMARIUM SOLUTIONS AND QUARTZ DISCS BEARING SAMARIUM DEPOSITS Solution A: 0.5AA50 g Sm in 250 m1., 1.2A92 x 10"2 A (5m+3) Solution B: 1.8A275 g Sm in 250 m1., A.2280 x 10'2 1_/1 (sm+3) Standard Quartz Discs Run Disc Volume Solution Number of Moles (A) Concentration of Sm (x 109) I A 100 A 1,2A9 B 10 B A22.8 C 250 Mm 312.3 D 300 B/100 126.8 E 300 A/lOO 37.A8 F 300 B/lOOO 12.68 H A00 A/1000 A.997 II + IIa A 300 A/1000 3.7A5 B 250 A/100 31.20 c 200 A/10 2A9.6 D 200 A 2,A92. E. 100 B A,228. F 200 B/100 8A.56 0 300 B/1000 12.68 III + IV A 200 B/lO 8A5.6 B 250 A/10 312.3 C 100 B/100 A2.28 D 200 A/100 2A.98 E 100 A/lOO 12.A9 F 200 B/lOOO 8.A56 o 150 B/lOOO 2 11A H 100 A/looo 1.2A9 I 10 A/lOOO 0.12A9 78 l APPENDIX V POSSIBLE (n, v) REACTIONS FOR NATURALLY OCCURRING SAMARIUM ISOTOPES Natural Cross Section Product Product Decay Mass Occurrence (Barns) Half—life Route (Mev) 1AA 3.09% 2 3A0 d K—capture 0.66 1A7 1A.97 stable 1A8 11.2A stable 1A9 13.83 A0,8OO stable 150 um ~93 a 9‘ 0.076 Y 0.02 152 26.72 1A0 A7 h e‘ 0.70, 0 6A, 0.80 v 0.10, 0.07 15A 22.71 5.5 2A m s‘ 1.65, 1.50 Y 0.11, 0.25 No active daughter species has a sufficiently short half—life to be detected in these experiments. 79 quH I oqu I waH I I I I I mHo I mHo I 0H0 I I I .I I I I w.H0m I wmm I :Nm I I wwm I own I m.mmH I amH I . me I . m.m0H o.mHH I .mmH I 00m.0. mm.H I I I m0.H I I m.0 mmo.0 mwm.0 HHm.0 mH.H I I I m.0 I I, no.0 mH.0 4:0.0 000.H NH.H I I I N.H I I mH.H ma.0 0w.0 om.m I I I I HH.0 I I mm.0 ma.m mm.o ma.0o I 0a N.Hm No I H.ma N.mm I me I m0.0H I I m.mH I I 0.m I 04.0H m.0H mm.HH ama.0 no.0 I I I ~0.H I I I I 00.0 aH.m 0.m I I I a.H I I aH.m I mm.H am.m om.m I I I mm.m I I 00.N 0.m mm.m mw.0 I I I I am.0 I I No.0 0.0 00.m om.m I I I I m.m I I mH.m a.m 00.: a0.H I I I I mm.H I I Hm.H 0m.H 04.H m0.H mw.0 I no.0 I om.0 I I 0N.H 0m.0 Ha.0 mmm.H I I I I I I I ma._ H0.H s0.H ommoo>< on m ow mm ow be on no mm m NHH I l ®H I I NH | I 0H I I mH I om.0 4H I mm.0 mH I wa.0 NH I m.m HH I I 0H m.m 0~.m m 00.0 mbq.0 w NN.H mm.0 a 3 o: o o oo.a ma.m m .o ao.m mm.H a a.m 65.0 m m.m mo.0 N A.H ma.0 H m H omHo Imomnom mcwocooo AmOH x Em Mo moHoEv m> mezmmm< "H com conowwm ommno>< 0.mmm I 0.03 I I H.0H I o.Hm 0mm I 0mm OH am 0.Hm womm 0.Hm 00.wa NS 3.0a m.HH m.mH mm m.m I :.m 0 I QIO I m.H I . N0 0.: 0.: mm m.-H I 0.00 I Hm mm I NH a.mH o.mH m I I 0 I H.H as I am moo 0.3 m.0mH I be me I mmdm I H.Hm .m m.NH H I JON I ®HN I O.mm I 0.0mH up no 0.m0 mmom H.HH O.mm mm o ...\O.-—:.TL\~ PiUNVD o . . . “\OJ N G 0101 assessmessssseaode a D Pi OJ (31h AJQDOJC)(3410JO\ o N - \8{ioic3c>w+c>c>010 o o oI4.:c3r«u3un0Jc>o oI0<3rn F1 F443—3 F4AJUN C>O P1C>C 09 4: U\ _d'PiU\ERGD'fi “Mfi O N F- OIo eIo40 9H C) 111 moHsom mcHocooo NHH USN HH mCDm COHmDMMm Aooscwpcouv H> xHszmm< 82 HJmH Nab w.H©m m.mmH owe.o HHm.o op.H mm.m ow m0.0H NH.H ma.m ommoo>< m.waH mm OmaH mHo mmm qu mm.H mH.H NH.H mmma I Cam I 4mm I he be com wNH m.m0H 0.®HH_ mp mam I mmH I I mwm.0 I 440.0 I 0m.0 I ww.0 momuom mchcooo Doom—:7 m—dmm 01000 e . o u .n 0 4| OOOHNHQOm A cluhubonuwc>unu><) r4 r~xo o-U\O\D—oo—3E\ U) HNM—fimQNQ U AoosaHpCoo H> XHQZMdmd 83 ommou>< CONN r-i\O'U\ m O\ 0\I \0 00m mom Illmmmglllllllmle \O I MON l wH I hm hm moH.am No.00 mm.mq mmm.oH m.~H mm m (\J m 00 moHnom mcwpcooo >H com aonouom AooseHoooov H> xHozmdd< APPENDIX VII LOG PRESSURE AND TEMPERATURE DATA FOR INDIVIDUAL EFFUSION EXPOSURES Run I Exposure T corrected 0 EXposure — Logarithm of emperature K Tlme (sec.) Calculated Pressure 1 1A59 3601 7_231 2 1505 3601 7,301 3 1507 3600 7,107 A 1618 3500 6.783 5 1717 3601 63,59 6 1717 1801 6.633 7 1709 1200 6.A77 8 1708 780 6.660 9 1793 120A 5.807 10 1859 1200 5.028 11 1760 1380 6 09A 12 16A9 2A00 7,099 13 15A1 2760 8.A93 1A 1A36 3600 8.398 15 1886 1200 A.652 16 1980 1230 A.238 17 201A 1260 3.016 18 2071 1200 3.6A9 8A 85 APPENDIX VII (Continued) Runs II and 11a W... 68:28:: .. sir-7:23 assesses... 1 2057 A33.2 A.068 2 1866 1268 5.258 5 1676 2A03 6.668 6 159A 3600 7.A02 .7 1522 SAOO 7.9A8 8 1595 3359 7.125 9 1309 10800 9.A06 10 1367 8AOO 9.1A8 ll 1A0A SSAB 8.795 12 1531 A620 7.770 13 1655 2700 7.276 1A 1796 1800 5,815 17 20A9 660 A.063 18 2086 600 A.063 21 1275 6000 7.8A1 22 1270 7201 7.876 23 13AA 7200 7 AA2 2A lASA 7201 6.877 25 1550 SAOO 6.A53 26 1591 5A6O 6.286 27 168 1 2700 5. 950 28 1769 2100 5.65A 29 1875 1200 5.332 30 1951 600 H.173 86 APPENDIX VII (Continued) 1 Effusion Run III. Exposure T Corrected 0 Exposure _ Logarithm emperature K~ Time (sec.) Calculated Pressure ,,_______ l 1338 SAOO 7.A90 2 1A63 5A60 7.997 3 1569 3660 7.688 b 1655 3600 7.178 5 17A5 1800 7.22A 6 17A3 3600 7,2u2 7 1865 ZAOO 5.733 8 2007 1920 A.512 9 21A? 600 3.870 10 2315 300 3.2A0 . 11 211A 900 A.0A0 I 12 1967 1320 A.833 i 13 1818 1801 A.997 1 18 1768 300 5.326 15 1760 3000 6.360 16 1708 3660 6.699 17 1571 7200 7.681 87 APPENDIX VII (Continued) Effusion Run IV. Exposure Ieiéiiiiiii oII. 51207:?) eaIéuié’EZEifii‘Zssm (2)1 1263 1AA08 7.911 (2)2 1323' 1AA00 9 0A7 (2)3 1320 10866 8.872 (2)A 1A21 7200 8.765 (2)5 1518 7200 7.785 (2)6 1622 5A00 7.127 (2)7 1716 1800 6.322 (2)8 1795 900 5.890 (2)9 1913 600 A.969 (3)0 2013 360 A.031 (3)1 2016 ‘ 180 A.218 (3)2 21A2 75 3.2A6 (3)3 2218 60 3.003 (3)A 20A8 180 3.98A (3)5 1955 600 A.75A (3)6 1912 900 5.715 (3)7 1723 1800 6.336 (3)8 1630 2700 7.899 (A)2 1789 1A700 7.158 (A)A 2003 3600 A.630 APPENDIX VIII THIRD LAW STANDARD ENTHALPY CHANGE CALCULATED AT VARIOUS TEMPERATURES Temperature 0K. 1263 1270 1275 1309 1320 1323 1338 13AA 1367 leA 1A21 1A36 1A5A 1A59 1A63 1505 1507 1518 152A 1531 15A1 1550 1569 1571 1591 159A 1595 1618 1622 1630 16A9 o Aste kcal. Temperature 0K. 1717 1717 17A3 17A5 1760 1760 1768 1769 1789 1793 1795 1796 1818 1859 1865 1866 1875 1886 1912 1913 1951 1956 1967 1980 2007 2013 201A 2015 20A9 20A9 2057 2071 2088 211A 21A2 21A? 2218 2315 o Aste kcal. 96.83 98.19 10A.50 10A.A6 87.A6 98.39 90.AA 95.58 112.98 95.65 88.86 95.86 90.12 92.05 98.28 88 (n . 1 II .1 I . ...T I. u..\.. .25 h... to... .I D. I 1.4 IAN... II?! I I IDA!» .. . :1 I L . I. I II. ..I I . _I . . , III .. ,IIn IVA)? I.I . .Il . . I [L P. Jr . .l 1188.1;n74 II . - MIST!“ HEW! C \l IllliHlJHljlflHngHHl HHIH 3 146 IIIIIIIIIIII