ABSTRACT STRUCTURAL AND PHASE INVESTIGATIONS I. CRYSTAL STRUCTURE OF LANTHANUM CARBONATE OCTAHYDRATE II. PHASE ANALYSES OF LANTHANIDE OXIDE FLUORIDES by Dennis Burton Shinn The crystal structure of lanthanum carbonate octahydrate La2(CO3)3°8H20, has been determined from an X-ray diffrac- tion study of a single crystal specimen. Four formula units are contained in an orthorhombic unit cell (a = 8.984 r 0.004, b = 9.580 r 0.004, and c = 17.00 i 0.01 g). The space group is Pccn. The final R factor is 0.061 for three-dimensional counter data collected with CuKa radia- tion (sin emax = 0.77). La2(CO3)3-8H20 crystallizes in an irregular layer structure in which the basic layer is formed by alternate rows of carbonates and metals. Two distinctive 10-coordinate metal polyhedra occur in which coordination sites are occupied both by water molecules and by bidentate and unidentate carbonates. The symmetry of these polyhedra is similar to that of a dodecahedron except that bidentate carbonates occupy two of the normal ligand sites. One fourth of the water molecules are not bound to the metals and oc- cupy holes between the layers. The average La-0(H20) bond is 2.63 R and the average La—O(C03) bond is 2.60 X, Hydro— gen bonding is apparent. Lanthanide oxide fluorides, LnOF, have been studied with high temperature X-ray powder diffraction and differ— ential thermal analysis techniques. They were found to Dennis Burton Shinn undergo reversible transitions from rhombohedral to cubic symmetry in the temperature range 495 to 608°. The enantio- tropic transition occurred with a 0.7-1.0% increase in volume. Disordering of the oxygen and fluorine atoms ap- parently occurs as temperature is increased. At the transih tion point a displacive transformation of all atoms ensues. Neodymium oxide fluoride, NdOF, was observed to decompose at 14750 to the sesquioxide and the trifluoride which volatilized. Tetragonal phases LnO1-xF1+2x’ 0.15 :,x §,0.25 and Ln = Nd, Gd, Dy and Er, were prepared by the reaction of the oxide and fluoride at 10500. Unit cell parameters obtained for these phases range from a = 3.999 R and c = 5.704 X for Nd(x = 0.25) to a = 3.907 X and c = 5.385 R for Er(x = 0.20). The tetragonal structure is a super- lattice of fluorite in which the c/a ratio deviates from J2 according to the packing of the anions. II. STRUCTURAL AND PHASE INVESTIGATIONS CRYSTAL STRUCTURE OF LANTHANUM CARBONATE OCTAHYDRADE PHASE ANALYSES OF LANTHANIDE OXIDE FLUORIDES BY Dennis Burton Shinn A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1968 6% 9 9.44-- gnao'éY ACKNOWLEDGMENT The author wishes to express his sincere thanks to Dr. Harry Eick for his encouragement and support throughout the pursuit of this work. Appreciation is extended to Dr. Alexander Tulinsky for the use of equipment and his frequent advice. The author is grateful to the E.I. duPont de Nemours Company for a duPont Teaching Fellowship. Financial as- sistance from the Department of Chemistry and the United States Atomic Energy Commission is also gratefully acknow- ledged. ii TABLE OF CONTENTS PART I. CRYSTAL STRUCTURE OF LANTHANUM CARBONATE OCTAHYDRATE Page I. INTRODUCTION . . . . . . . . . . . . . . . . . . 1 II. EXPERIMENTAL . . . . . . . . . . . . . . . . . . 10 Composition . . . . . . . . . . . . . . . . . . 10 Crystal Properties . . . . . . . . . . . . . . . 11 Unit Cell and Space Group Determination . . . . 13 Lattice Parameters . . . . . . . . . . . . . . . 15 Density and Molecules Per Unit Cell . . . . . . 15 Collection of Intensity Data . . . . . . . . . . 16 Absorption Correction . . . . . . . . . . . . . 19 Computations . . . . . . . . . . . . . . . . . . 22 III. STRUCTURE DETERMINATION . . . . . . . . . . . . 24 Patterson Syntheses and Metal Positions . . . . 24 Solution of the Light Atom Structure . . . . . . 26 Effect of Absorption on the Determination of the Structure . . . . . . . . . . . . . . . . 37 IV. DESCRIPTION OF THE STRUCTURE . . . . . . . . . . 42 Structure as a Whole . . . . . . . . . . . . . . 42 Coordination of the Metals . . . . . . . . . . . 49 Carbonate Ions . . . . . . . . . . . . . . . . . 58 Hydrogen Bonding Evidence . . . . . . . . . . . 59 Observations Concerning Previous Investigations. 60 PART II. PHASE ANALYSES OF LANTHANIDE OXIDE FLUORIDES V. INTRODUCTION . . . . . . . . . . . . . . . . . . 62 Literature . . . . . . . . . . . . . . . . . . . 62 Structures of Lanthanide Oxide Fluorides . . . . 66 Purpose of This Research . . . . . . . . . . . . 72 VI. EXPERIMENTAL . . . . . . . . . . . . . . . . . . 73 Preparations . . . . . . . . . . . . . . . . . . 73 Analytical . . . . . . . . . . . . . . . . . . . 74 X- -Ray Diffraction . . . . . . . . . . 75 High Temperature X- -Ray Diffraction . . . . . . . 75 Differential Thermal Analysis . . . . . . . . . 80 Thermal Decomposition of Neodymium Oxide Fluoride . . . . . . . . . . . . . . . . . . . 82 iii TABLE OF CONTENTS (Cont.) Page VII. RESULTS . . . . . . . . . . . . . . . . . . . 83 Preparations and Phase Analyses . . . . . . . 83 Phase Transitions . . . . . . . . . . . . . . 85 Decomposition of Neodymium Oxide Fluoride . . 95 VIII. DISCUSSION . . . . . . . . . . . . . . . . . . 97 The Phase Transition in Rhombohedral Oxide Fluorides . . . . . . . . . . . . . . . . . 97 Observations on the Tetragonal Lanthanide Oxide Fluorides . . . . . . . . . . . . . . 104 IX. SUGGESTIONS FOR FURTHER WORK . . . . . . . . . 108 REFERENCES . . . . . . . . . . . . . . . . . . 110 APPENDICES . . . . . . . . . . . . . . . . . . 114 I. Crystallographic Computer Programs . . 115 II. Diffraction Data for LnOF and Ln01_xF1+2X 120 iv Table I. II. III. IV. V. VI. VII. VIII. IX. X. XI. XII. XIII. XIV. XV. XVI. XVII. XVIII. XIX. LIST OF TABLES PrOperties of space group No. 56, Pccn . . . Positions of principal Patterson peaks . . . Positions of the metal—metal Patterson peaks. Parameters from least-squares refinement a) Atomic Coordinates b) Thermal Parameters Observed and calculated structure factors . . Positional and thermal parameter changes due to absorption . . . . Interatomic distances . Bond angles Corresponding reflections in LnOF phases . . Reported LnOF structural data Analytical results . . Structural data for tetragonal LnO 1-XF1+2X ° High Temperature X-ray diffraction data for LnOF NdOF high temperature structural data . . . Differential X—Ray X-Ray X-Ray X—Ray X-Ray X—Ray X—Ray powder powder powder powder powder powder powder thermal analysis diffraction diffraction diffraction diffraction diffraction diffraction diffraction data data data data data data data results . . . . for for for for for for for Nd0.73F1.54 Nd0.85F1.3 Gd0.72F1.5 DYO.77F1.46 Er0.85F1.3 E10.80F1.4 Page 14 25 27 34 35 36 41 46 47 7O 71 76 86 88 89 92 121 122 123 124 125 126 LaOF and NdOF 127 LIST OF TABLES (Cont.) Page XXIII. X—Ray powder diffraction data for SmOF and EuOF 128 XXIV. X-Ray powder diffraction data for GdOF and TbOF 129 XXV. X-Ray powder diffraction data for DyOF and YOF 130 XXVI. X-Ray powder diffraction data for HoOF and ErOF 131 vi 10. 11. 12. LIST OF FIGURES Crystal of La2(C03)3-8H20 . . . . . . . . . Crystals of La2(C03)3-8H20 . . . . . . . . Representation of space group Pccn . . . . Stereosc0pic illustration of La2(CO3)3-8H20 unit cell . . . . . . . . . . . . . . . Stereoscopic illustration of La2(C03)3°8H20 half cell . . . . . . . . . . . . . . . Stereoscopic illustration of La2(C03)3°8H20 half cell . . . . . . . . . . . . . . . Stereoscopic illustrations of lanthanum coordination . . . . . . . . . . . . . . (a) Dodecahedraon, D2d (b) Dodecahedral derivative, sz . . . . . . . . . . . . Lanthanide oxide fluoride structures . . . Schematics of X—ray diffraction patterns of Er-O-F phases . . . . . . . . . . . . Thermal expansion of NdOF . . . . . . . . DTA curves for selected Gd—O-F stoichiometries vii Page 12 12 14 43 44 44 45 54 67 84 90 94 I . INTRODUCTION Lanthanide carbonates have found limited application to date. One practical application is their use as start- ing materials for the preparation of water-soluble lanthan- ide complexesl. The possibility of using the relative solubilities as a method of lanthanide separation has also been investigatedz. However, the carbonates have been studied frequently. Various methods of preparation, stoi- chiometries, thermal behavior, spectroscopy, X-ray dif— fraction and other miscellaneous properties have been re- ported. Unfortunately many of the results and their interpretations have been inconsistent, due in part to hydrolysis encountered in the preparation of pure materials in the pH range, 4.0-5.5, at which formation takes place. An equally important difficulty in the interpretation of results is the lack of knowledge of the various lanthanide carbonate crystal structures. In order to demonstrate the inconsistencies of the re- ported results some of the pertinent recent investigations will be reviewed. This review is not exhaustive; a more complete survey may be found in reference 3. Lanthanide carbonates were once commonly prepared by carbonation of the hydroxide either with carbon dioxide or by addition of alkali carbonate to a solution of the metal salt saturated with C02. Unfortunately the products were often contaminated by alkali metals. Recently methods which 1 2 eliminate this problem have been developed. The most pop- ular technique involves the hot hydrolysis of the lanthanide trichloroacetates first described by Salutsky and Quill‘. The reaction is: 2Ln(C2C1302)3 + (3+X)H20 —> 3002 + 6CHC13 + Ln2(c03)3-x_H20 (1) The stoichiometries of products obtained by this reaction vary from report to report. For lanthanum, neodymium and samarium, Salutsky and Quill reported X_2:5.5, 2.5 and 3.0 respectively. However, Charles5 suggesUai X_= 8 for lan- thanum and 2 for neodymium to holmium. Head and Holley6 reported the preparation of the carbonates of lanthanum to gadolinium under a pressure of C02. With 200-300 psi the normal carbonates, Ln2(C03)3'XH20, were obtained where X_2:8 for La-Nd and 2-3 for Sm-Gd. With lower pressures a Nd2(CO3)3-2H20 was also obtained and at a C02 pressure of 1000 psi a La2(CO3)3-6.4H20 was found. In a later report7 they found X_2:2 for terbium to ytterbium, and 5 for lutetium. Carbonate to metal ratios were less than 1.5 for preparations carried out in air. Stroudph3 reportedHB or 4» waters for terbium, gadolinium and yttrium normal car- bonates and 3—5 "water ‘for the dysprosium to lutetium oxydicarbonates, Ln20(CO3)2'Xfi20, all prepared in air. Sastry, EE.E$:8 have compared the products resulting from the older techniques with the trichloroacetate hydrolysis. In the latter technique the effect of using COz-water or plain distilled water for washing was examined. Either 3 normal carbonate octahydrates or oxydicarbonate dihydrates were formed for praseodymium and neodymium depending on the method. Among the other methods of preparation is the re- action of warm, 45-600, solutions of metal acetates with C02 at 900 psi reported by Head9. By this method the nor- mal carbonates of La, Ce, Pr, Tb and Y were obtained with X_2:8 for La—Pr and 2-3 for Y and Tb. To summarize, the reported stoichiometries may be divided into at least three general groups; Ln2(CO3)3°XH20 for La-Nd where X_= 6-8 but usually 8, Ln2(C03)3°XH20 for Nd-Lu where X_= 2—6 but usu- ally 2, and Ln20(CO3)2'XH20 for Pr—Lu when the preparations are carried out with a limited source of C02. Nearly every investigator who has prepared a normal lanthanide carbonate has also studied its thermal decomposi— tion. The reports of these investigations are in general agreement on two points: the first stage of decomposition is dehydration to the anhydrous carbonate and the second is decomposition with loss of carbon dioxide to form the lan- thanide oxide. The existence and nature of any intermediate phases are matters of some disagreement. Consider the de— hydration stage first. In thermogravimetric analyses(TGA) of La2(CO3)3-8H20 Charles5 observed inflections correspond- ing to the 6-, 3- and 2- hydrates. Pannetier, 2E._l-1° Obserwxlno intermediates for this compound by TGA; however, in a differential thermal analysis (DTA) two endothermic peaks were observed which corresponded to dehydration. An X-ray powder diffraction photograph of material heated through 4 the first transition indicated it to be identical to the octa- hydrate whereas X-ray powder diffraction patterns of the com- pletely anhydrous material were different. These authors be- lieved the first DTA peak was due to adsorbed water, however, the peak seems too well defined for this type of reaction. Sastry, 35 31.8 claimed no inflections, corresponding to the formation of intermediate hydrates, occurred in the TGA curves of Pr2(CO3)3-8H20 and Nd2(C03)3°8H20 in air or C02. However, obvious inflections corresponding to the hexa—, di- and mono-hydrate are observable in their reported praseodymium TGA curves. Head and Holley6 found no evidence of intermedi- ate hydrates in the cases of La, Ce or Pr but did Observe Nd2(CO3)3-2H20. Caro11 has also observed this Nd phase. Reports of intermediate phases occurring in the de- composition of the anhydrous carbonates are somewhat more consistent. Charles reported inflections in TGA curves cor- responding to the dioxycarbonate, Ln202C03, for La-Gd which were undetectable for Tb-Ho. Head and Holley6:7 also found the same approximate phase in thermal analyses of La, Pr-Yb carbonates under C02 atmospheres. Another intermediate containing less carbonate was observed in the decompositions of the carbonates of Nd-Gd. The dioxycarbonate phase has also been reported by Sastry, 33 al.8 for the Nd case and by Pannetier, et__l,1° in their DTA and TGA studies of La(CO3)3°8H20. Strouth3 observed oxydicarbonates and di- oxycarbonates in the DTA of Y, Gd and Tb carbonates. Caro11 observed the dioxycarbonate of Nd. In summary, from the 5 thermal decomposition of Ln2(C03)3-XH20, evidence of inter- mediate hydrates is mixed and whereas Ln202C03 is generally found in the decomposition other phases have also been ob— served. The infrared Spectra of the lanthanide carbonates have been reported3I5I8I11'12 but not interpreted in complete de- tail. Charles5 commented that the Spectra of Ln2(CO3)3'2H20, Ln = Nd-Ho, differ significantly from that of Ln=La. He assigned absorptions at 3400 and 1650 cm-1 to bound water molecules and stated that other observed absorptions may be due to coordinated water and various vibrational modes of the carbonate ions. Sastry, et 31.8 noted that two CO stretching and two in-plane CO3 deformation bands are pres— ent in the spectra of the Pr, Nd and Tb carbonate hydrates and oxydicarbonate hydrates. They pointed out that such Split- ting occurs in basic carbonates and in compounds where the carbonate ion is a bidentate or unidentate ligand. They suggested the C—0 stretch splitting is similar to that of unidentate carbonates, but did not make an assertion of its existence. Caro11 has attempted a more detailed analysis of the infrared spectra of the various carbonate phases. He believed the CO3 vibrational spectrum in Ln2(CO3)3-8H20 is nearly identical to that in cobalt carbonate complexes such as [Co(NH3)5C03]Br.13 This observation would indicate CO3 is a unidentate ligand bonded to the lanthanide ion. Sur- prisingly, he postulated octahedral coordination of the metals by four water molecules, a unidentate carbonate and 6 another carbonate bonded to two metals. Caro found the spectrum of Ln2(C03)3°2H20 more complex than that of the cnufiwdrate and postulated the carbonates are in two types of sites. In summary, the interpretations of the infrared spectra of the normal carbonates are either vague or of doubtful value. Further analyses would seem to require crystal structure information. Other spectroscopic studies have been made of the lan- thanide carbonates. Barnes and Pincott14 examined the elec- tron transfer spectra of Ln2(CO3)3-3H20 and other salts, where Ln=La, Sm, Eu, and Yb. Lanthanum shows no electron transfer bands and was used to check against false assign- ment. The spectra were observed to be similar to those of other oxyanion salts of the lanthanides. Brasseur15 has postulated on the relative orientation of the carbonate ions in various carbonates from the optical properties of the crystals. For (La, Di, Ce)2(CO3)3'8H20 he concluded that all the carbonates had parallel orienta- tions on the basis of a comparison of calculated and observed indices of refraction. No structure of any lanthanide carbonate phase has been determined by Single crystal X-ray diffraction. With one exception10 the X-ray powder diffraction photographs of Ln2(CO3)3'XH20 have been indexed by analogy to the unit cell observed in naturally occurring lanthanite, (La, Ce)2(CO3)3- 8H20. The studies of lanthanite crystals are summarized in "Dana's System of Mineralogy"16. From optical crystallography 7 these crystals were determined to have orthorhombic symmetry, dipyramidal —2/m 2/m 2/m. The parameters a = 9.50, b = 17.1 and c-- 9.003 were obtained by an unreported method. The unit cell contains four formula units but the space group was not determined. Sastry, gt al.3xepmfied similar lattice parameters from powder data for Ln2(CO3)3'8H20 of Pr and Nd. Caro11 reports analogous results for Pr except that the b parameter is about one half the previous value. On this basis Strouth3 indexed X-ray powder diffraction patterns of Ln2(CO3)3°XH20 of Tb, Gd and Y where X_is 3, 4 and 3 re- spectively. However, only the first 9—12 lines of relatively complex powder patterns were indexed and the hkfl values ob- tained are somewhat curious in that many common low index lines were not observed. Pannetier, gt £1.10 indexed La2(CO3)3°8H20 on the basis of an orthorhombic unit cell in which a = 8.56, b = 5.78 and c = 8.89X and suggested a P2221 space group from powder data. Although they gave no data, Head and Holley6t713pdded on the basis of X-ray powder dif— fraction that the Ln2(CO3)3‘8H20 for La-Nd are isomorphous but different from the lower hydrates of Nd-Yb and Y which are also isomorphous. Lu2(CO3)3'5H20 appeared to have a third structure. The powder pattern of lanthanum dioxycar- l.10 as hexagonal, bonate has been indexed by Pannetier, gt a = 7.76 and c = 9.47 R. In summary the compounds of the general formula Ln2(CO3)3°8H20 appear to crystallize with orthorhombic symmetry similar to that observed in lanthanite; for which the structure is unknown, and the lower hydrates 8 and the oxycarbonates have different but also unknown struc- tures. The intent of the preceding historical survey was to indicate the need for the determination of lanthanide car- bonate structures. A complete structure analysis of the various carbonates should allow the interpretation of the following experimental observations. 1. The normal carbonates, Ln2(C03)3'XH20, appear to be classified into at least two different groups on the basis of stoichiometry. Within each group a modest range of water content is possible without changing the general structure, at least as observed by powder X~ray diffraction. The observed stoichiometries are undoubtedly a reflection of the trend in metal ion size and the ability of the metals to accommodate ligands of various sizes. It is to be expected that the lighter lanthanides will have the maximum coordina— tion numbers for a specific ligand. The observed change in stoichiometries from Ln2(CO3)3°8H20 for La-Nd to Ln2(C03)3' (2-3)H20 may result from one of two structural differences: a. The coordination number of the metal is high 9-12, for the lighter members and is less for the heavier (and smaller) metal ions. This decrease in coordination number might be ac- complished by removing water molecules from the coordination sphere, decreasing the water content. 9 b) The coordination number may remain unchanged if the effective size of the ligands is decreased. This could occur if a carbonate were to act as a bidentate or tridentate ligand replacing two or more water molecules in the coordina- tion sphere of the metal. 2. In the thermal decomposition of Ln2(C03)3'8H20 the evidence for the presence of intermediate hydrates is contra- dictory. In one instance at least X—ray powder diffraction photographs of a suspected intermediate were identical to those of the octahydrate. Knowledge of the way the water molecules are bound in the crystal should explain these ob- servations. The course of decomposition should also be ex- plicable on the basis of structural changes. 3. The infrared spectra of the carbonates are very complex. Without knowledge of the nature of the bonding of the carbonate to the metals and the coordination of the metals there appears to be little hope of prOperly inter- preting absorption spectra. In View of the indicated usefulness of a structural examination of the lanthanide carbonates it was fortunate that Ln2(CO3)3.XH20 crystals of La, Pr and Nd were available in this laboratory. In this study the structure of La2(C03)3-8H20 has been determined by single crystal X-ray diffraction. The results of this structural determination should aid in the interpretation of lanthanide carbonate chemistry. II. EXPERIMENTAL Crystals of lanthanum carbonate hydrate, La2(C03)3'XH20 and Pr2(CO3)3-§H20 were obtained from Prof. L. L. Quill of this department. They had been prepared according to equation (1) by slow hydrolysis of lanthanide trichloroacetate solu- tions at room temperature. Crystallization of the precipi- tated carbonates had been allowed to continue undisturbed for several years. The crystals, still in the reaction media when they were obtained for this investigation, were filtered, washed repeatedly first with distilled water and finally with acetone. Those specimens which were to be used for X-ray diffraction intensity measurements were coated quickly with Canada balsam in an effort to minimize possible dehydration. Other crystals were air-dried 1-2 hours, and then stored in capped vials. Composition Lanthanum carbonate hydrate was analyzed for carbon and hydrogen by Spang Microanalytical Laboratory, Ann Arbor, Michigan., Metal content was determined by ignition of air- dried samples in platinum boats at approximately 900°. Anal, Calculated for La2(CO3)3-8H20: La, 46.15; C, 5.98; H, 2.69. Found: La, 46.32i0.10; C, 6.0:0.1; H, 2.7:0.1. Errors listed are the standard deviation of four metal determina- tions and the probable error of duplicate carbon and hydro- gen analyses. 10 11 The observed analytical results support the formation of the octahydrate reported5'5'9'10 and not the hexahydrate4. The apparent high lanthanum content may suggest a small im- purity of another lanthanide. Ignition of a sample ex- posed to the atmosphere for approximately two weeks indi- cated an increase in the lanthanum content to 46.49%. If the experimental increase in metal percentage is assumed to result from a decrease in the water content of La2(C03)3'8H20, the stoichiometry is La2(CO3)3-7.9H20. Thus although the stoichiometry will be referred to as octahy- drate, the water content in individual samples may vary below this value. Crystal Properties Crystals of La2(C03)3°8H20 and Pr2(CO3)3°8H20 were ex- amined with a Spencer AO polarizing microscope and with a Bausch and Lomb Dynazoom metallograph to aid in the selec- tion of an orientation for structure analysis. ‘As Figures 1 and 2 indicate, the lanthanum crystals were observed to be colorless and transparent. Although the large faces appear rectangular, the face angles are 86.0i0.5o and 94.0:0.5°. Observation of these crystals under crossed polarizers indi- cated extinction directions coincident with the diagonals of the large face and with the face normal. These direc- tions correspond to the observed crystallographic axes a, b and c. Cleavage was observed to be micaceous along (001). Attempts to cleave along planes normal to (001) led to com- plete disintegration of the crystal. 12 FIQUIJ 1. Crystal of La2(C03)3'8H20. Figure 2. Crystals of La2(CO3)3'8H20. 13 Unit Cell and Space Group Determination Preliminary Weissenberg photographs established the orthorhombic symmetry. Precession photographs of the hkO and Okz levels confirmed this. Weissenberg photographs were made with a Charles Supper Co. camera mounted on a North American Philips X—ray generator. Exposures, using copper radiation (45 kilovolts and 20 milliamperes) with a nickel filter, were taken for two crystal orientations. Exposure times varied from 8 to 72 hours. Reflections were present for the following conditions. hOO, OkO, 002 only when h, k, z = 2n Okfl, hOE only when 2 = 2n hkO only when h + k = 2n hkfi with no regular extinctions. These conditions are satisfied unambiguously by space group P21/c 21/c 2/n (No. 56) which will be referred to as Pccn. In addition to the above restrictions it was noted that hkz reflections with z = 2n + 1 were in general very weak or absent. Ignoring the weak reflections would lead to as- signment of the space group Pmmn (No. 59). Weissenberg photographs of Pr2(CO3)3-8HZO indicated it to be isomorphous with the lanthanum compound. The conditions governing pos- sible reflections and coordinates of equivalent positions for the general and special position sets of Pccn are found in Table I. Schematics of the symmetry of the space group are illustrated in Figure 3. 14 Table I. Properties of space group No. 56, (Pccn). Posi- Point Co-ordinates of Conditions for tions Symmetry Equivalent Positions Non—extinction 8e 1 i(x,y,z; 1/2-x,1/2—y,z; th: no cond. __ Okfi, hofl: E =2n 1/2+x,y,1/2-z; hkO: h+k = 2n _ hoo,0ko,00p,: x,1/2+y,1/2—z) (h,k,£ = 2n) 4d 2 i(1/4,3/4,z; 1/4,3/4,1/2+z) as for Se, plus 4c 2 :(1/4,1/4,z; 1/4,1/4,1/2+z) hkfl: 2 = 2n 4b 1’ 0,0,1/2; 1/2,1/2,1/2; as for Be, plus 0,1/2,0; 1/2,0,0 th: h+k, k+£, (h+£) = 2n HI 4a 0,0,0; 1/2,1/2,0; 0,1/2,1/2; 1/2,0,1/2 ? 4' fl. 7" ? i l i l. f........n...u...1 ........... . ....... i .1 4 4—; .——> 4 i I I I 3 i : 0 o o : I o 0 o 0 o : o o o AIH F... I! )— ., w J 4 Figure 3. Representation of Space group Pccn. 15 Lattice Parameters Lattice parameters of lanthanum carbonate octahydrate were determined from calibrated X—ray powder diffraction data. The crystals were ground, mixed with potassium bro- mide powder (Baker Analyzed Reagent, 99.4% KBr) and applied to a glass plate in a thin layer using Canada balsam as binder. Diffraction patterns were obtained for this sample with a Siemens diffractometer mounted on a Siemens Crystal- loflex IV X—ray generator using copper radiation (35 kilo- volts and 20 milliamperes), nickel filter, proportional counter and one-eithth degree per minute scan. The result- ing diffraction patterns were calibrated by comparing the observed positions of potassium bromide peaks with those calculated on the basis of a KBr lattice parameter,17 a - 6.5966 8. In the 20 range utilized, 0-650, the maximum correction was 0.010. The carbonate lattice parameters were calculated from twenty—one reflections which could be indexed unambiguously using a least squares program written by Vogel and Kempterla. The refined parameters, expressed on the basis of space group Pccn, are: a = 8.984 r 0.004 R, b = 9.580 t 0.004 R, and c = 17.00 i 0.01 R. For the space group Pmmn, c = 8.50 i 0.005 8. Density and Molecules Per Unit Cell The density of La2(CO3)3-8H20 was derived by the pycno- metric method Mdifll water as a medium. At 260 a value 2.72 i 0.01 g/cm3 was obtained. Based on the lattice 16 parameters observed for space group Pccn and a stoichiometry La2(CO3)3-8H20, this density corresponds to four molecules per unit cell. Under these conditions the theoretical density is 2.73 g/cm3. Collection of Intensity Data Two sets of intensity data were collected with copper radiation (la: 1.5418 A) on separate crystals using film and counter techniques, respectively. The preliminary set of data was obtained on a crystal with (001) face dimensions 0.167 mm x 0.150 mm and thickness 0.055 mm. The crystal was mounted on a glass fiber and aligned with the b—axis as the axis of rotation. X-Ray alignment was accomplished with oscillation photographs of the zero-layer line. Equi—inclination Weissenberg photos were taken of the hKE levels, K = 0"6. Intensities were collected by the multiple film technique. Film packs, com- posed of three or four sheets of Ilford Industrial type G X—ray film, were exposed for 60 hours at 40 kilovolts and 20 milliamperes, Intensities were estimated visually by com- parison with a calibrated intensity strip, prepared using the (202) reflection of the crystal under investigation. The intensities of each layer were then correlated and scaled to those of the most heavily eXposed film in the pack. On the average the inter-film correlation factor was about 2.6. The values for each reflection were averaged and scaled linearly according to the time of exposure. A total of 705 non—equivalent reflections were measured. 17 The set of intensities used in the final refinement of parameters was measured with a General Electric XRD—5 gonio- stat equipped with scintillation counter. A crystal of ap- proximate dimensions 0.160 x 0.152 x 0.110 mm, Figure 1, was mounted on a glass fiber. The b-axis of the crystal was aligned parallel, visually and by X—ray, with the goniometer ¢-axis. X-Ray alignment was accomplished at a 2° take-off angle by maximizing intensity of the (040) re- flection. At X = 90.0° the two arcs of the goniometer, set parallel to the X—ray beam, were adjusted to produce maximum equal intensities at ¢ 3 0° and 180° and ¢ = 90° and 270° The value of 29 was also maximized. The 0 settings corre— sponding to (hOO) and (002) reflections were determined by maximizing 0 and 29 at X = 0° for the (400) and (008) re- flections. The values of 29 of the (hOO), (OkO), and (003) reflections, h, k, E = 4, 6 and 8 were measured carefully. From these values the following lattice parameters were calculated: a = 8.976 R, b = 9.563 R, c = 17.00 2. These parameters were used for the generation of x, ¢ and 29 values for other reflections. The quality of the crystal was examined both as an aid in the selection of the best quadrant for data collection and as insurance that integrated intensities would be ob— tained. At X = 0° the (400), (Zoo), (008) and (0033') re- flection intensities were counted versus 0 at 0.04° inter- vals. At X - 90° the (040) reflection intensity was meas— ured as a function of m at 0.04° intervals. Four scans were 18 made with the direct beam normal to [100], [100], [001] and [001]. The eight scans obtained were plotted and the quad— rant to be used in data collection was chosen on the basis of the symmetry and narrow peak width of the plots. The settings of x, T and 29(0.: 29.: 100°) were gen- erated using a program written by J. Gvildys, Argonne National Laboratory. Intensities of 749 independent reflections were measured with stationary—crystal, stationary—counter tech- nique. These measurements were made with a 4° take-off angle. The X, ¢ and 29 values were set and the reflection was counted for 10 seconds with a nickel filter. The back- ground was measured by replacing the Ni filter with a balanced Co filter and counting for 10 seconds. In principle the absorption of the Co and Ni filters matches at all wave- lengths other than those which lie between the two absorp- tion edges (1.608 R for Co and 1.488 R for Ni). If intensity measurements are made prOperly with each filter, the in- tensity difference between the two measurements results only from radiation whose wave length is within the narrow band between the absorption edges. In the case in question, this is principally CuKC1 radiation. Therefore the difference in count was recorded as the intensity of the reflection. In- tensities of 116 reflections were recorded as zero, of these 108 had 2 = 2n + 1. Similarly 94 of 125 reflections with intensities less than 2 had 2 = 2n + 1. The maximum intens- ity observed was 1547 cps for (002). Only 5 reflections with E = 2n + 1 produced intensities of greater than 30 cps 19 whereas for 29 reflections with z = 2n the count was above 300 cps. During collection of the data the alignment of the crystal was Checked periodically by measuring the intensi— ties of the (040), (060), (400), (600) and (008) reflec— tions. These intensities were checked ten times during the data collection procedure, and no significant deviations were observed during the period of data collection; 13 hours of exposure at 40 kilovolts and 40 milliamperes over a 100 hour period. Absorption Correction The linear absorption coefficient, 0, for La2(CO3)3-8H20 is 444 cm-1. This value was Calculated from tabulated mass absorption coefficients and the experimental density. The crystals employed in the collection of intensity data were relatively large. In the case of the crystal used on the goniostat it was estimated that the path length of dif— fracted radiation through the crystal could differ as much as 0.004 cm for the two reflections. Use of this differ— ence in conjunction with the intensity-absorption equation indicates that corrections as high as 5X would be required to put all intensities on the same relative scale. An ap- proximate method for absorption correction was not used for two reasons: 1) the complicated external form of the crystal and 2) the magnitude of the corrections involved. Thus, the FORTRAN absorption correction program written by Coppens, 20 Leiserowitz and Rabinovich19 was used to effect the correc- tions. The program is a modification of one written by Busing and Levy2°. The calculation involves evaluation by the method of Gauss of the integral: correction = fl/V exp[-u(ri + rd)]dv, where V = crystal volume and ri and rd are the path lengths of incident and diffracted radia- tion, respectively. In COppens, Leiserowitz and Rabino- viCh's program an axial system dependent on both diffraction geometry and crystal orientation is established within the crystal. The volume of the crystal is determined and a grid of sampling points is constructed within it using distances measured from an internal origin to the crystal boundary planes. The incident and diffracted radiation path lengths between the crystal faces and each sampling point axe then calculated for every reflection of interest. An absorption factor is calculated for each sampling point and the total absorption is computed as a weighted average over all sampling points. The diffractometric intensities were corrected using the following data: a) orientation - b-axis coincident with ¢—axis b) number Gaussian points - 1440 (12, 12, 10 along a, b, C) c) number boundary planes - 8. 21 (hkz) of distance from estimated boundary chosen origin possible error plane (cm) (cm) 001) .0058 .0003 001) .0058 .0003 010) .0080 .0002 010) .0088 .0002 .110) {0076 .0002 lip) .0076 .0002 110) 10079 .0002 110) .0079 .0002 d) Linear absorption coefficient, u = 444 cm-1 The correction factors varied fromzamadmum value of 64.1, for (002), to a minimum value of 12.0, for (1 4.15). In general the correction factor decreased in a zone of reflections as the Miller indices increased. Based on a limiting stoichiometry La2(CO3)3°7.5H20 and a Correspond- ing density, d = 2.75 g/cm3, the uncertainty in the ab— 1 sorption coefficient was estimated as 11 cm- For the limiting value of u = 456 cm—1 it was found that relative intensities differed from those calculated with u = 444 cm—1, by less than 3%. On the other hand, the effect on the ab- sorption coefficient resulting from an uncertainty in the crystal dimensions is more significant. For instance, an alteration of the dimensions of the {001} faces by -0.0003 cm and the other faces by +0.0002 cm introduced relative intensity differences of as much as 8%. In addition, a number of less prominent crystal faces (e.g. (112)) were not included in the description of the crystal on the as- sumption that the effect of their inclusion should be small. The validity of the absorption correction calculation was verified by comparison of experimentally determined and 22 and calculated absorption effects on (OkO) reflections. Intensities of reflections measured at X - 90°, (OkO) re- flections, have a ¢-dependence which is a function of ab— sorption only. Over a 90° range in ¢, absorption decreased the intensity of the (040) and (080) reflections by factors of 0.51 and 0.47 respectively. The corresponding factors derived from the correction program were 0.47 and 0.45. However, even though the effect of absorption has been re- duced significantly it still introduces a great limitation on the final results. Computations Calculations were performed on a CDC 3600 computer equipped with 64K memory. The programs for the least-squares calculation of lattice parameters, for generation of dif- fractometer settings, and for absorption correction have been mentioned previously. The programs used for intensity data reduction, Fourier functions, and distance and angle calculations were obtained from A. H. Zalkin who wrote them. The first of these programs is described in Appendix I. The full matrix least—squares program is a version of the Sparks, Gantzell and Trueblood program (ACA no. 317) as modified by Zalkin. This program is also described in Appendix I. The function minimized was 2W(|Fo| - |FC|)2 where W is the weighting and IFJ and )Fcl are respectively observed and calculated structure factors. Scattering fac- + tors used were those computed by Cromer and Waber21 for La3 23 and carbon and that computed by Tokonami22 for 02-, the scattering factor for La3+ was corrected for anomalous dispersion in the final stages of least-squares refinement. The corrections, used, Af'= —2.10 and Af" - 8.90, were those given by Cromer23. The stereo drawings of the structure were made using a CDC 6600 digital computer and a cathode ray plotter with a program written by A. C. Larson. III . STRUCTURE DETERMINATION Patterson Syntheses and Metal Positions A three-dimensional Patterson function was calculated from film intensity data which had been corrected for Lorentz, polarization and velocity effects, but not for absorption. The positions and relative peak heights of the larger Pat- terson peaks observed are given in Table II. The correspond- ing peaks obtained from absorption corrected diffractometric data are also found in the table. The locations of the eight lanthanum atoms in the unit cell were determined in the following manner. According to the notation of Table I, the possible lanthanum positions include: 8 La in Wyckoff set Be, or 4 La in set 4a, 4b, 4c, or 4d and 4 additional La in a non—identical set 4a, 4b, 4c, or 4d. Use of the eight-fold positions was eliminated as incompatible with the Patterson results. Furthermore the low intensity of reflections for which 2 = 2n + 1 indicated that the metals were situated in one of the combinations of four-fold sets 4c—4c, 4d-4d, or 4c-4d. In these sets the only variable parameter is 2. Analysis of the Patter- son excluded the placement of all the lanthanum atoms in either of the sets 4C or 4d. Such a situation would result in the appearance of nine Patterson peaks along [OOz]--only a peak at 0, 0, 1/2 is observed. Therefore four lanthanum atoms must be in each of the sets 4c and 4d: 24 25 Table II. Positions and heights of principal Patterson peaks x y 2 Relative* Relative* Height Height 0.00 0.00 0.000 999 999 0.00 0.00 0.500 935 926 0.00 0.50 0.465 450 483 0.00 0.50 0.535 450 483 0.00 0.50 0.965 425 460 0.00 0.50 0.035 425 460 0.50 0.00 0.465 422 458 0.50 0.50 0.000 422 439 0.50 0.00 0.965 418 462 0.50 0.00 0.035 418 462 0.50 0.50 0.500 413 443 0.50 0.50 0.425 206 270 0.50 0.50 0.575 206 270 0.50 0.50 0.930 198 268 0.50 0.50 0.070 198 268 0.06 0.25 0.500 41 26 0.00 0.00 0.250 41 108 0.00 0.00 0.750 41 108 0.02 0.00 0.935 - 154 0.02 0.00 0.435 — 142 0.12 0.00 0.985 — 138 0.12 0.00 0.485 - 136 0.48 0.50 0.630 — 120 0.48 0.50 0.130 - 112 0.50 0.50 0.375 - 110 0.06 0.25 0.000 34 23 0.22 0.25 0.000 28 26 0.50 0.00 0.870 25 95 0.50 0.00 0.130 25 95 0.22 0.25 0.500 25 24 0.02 0.50 0.395 — 108 0.48 0.00 0.100 — 107 0.50 0.50 0.875 - 103 0.02 0.50 0.895 - 102 0.02 0.50 0.360 15 101 0.48 0.00 0.600 - 101 * From diffractometer data corrected for absorption. ** From film data uncorrected for absorption. 26 4c |+ (1/4,1/4,z) H- (1/4,1/4,1/2 + 2) H- 4d (1/4,3/4,z'), r (1/4,3/4,1/2 + 2') In order to determine the z-parameters in the two sets all the inter-atom vectors were calculated and the number of identical vectors summed. These data are tabulated in Table III. A comparison with the observed Patterson peaks disclosed two possible solutions: Solution 1: z = 0.000, 2' 0.033 0.250, 2' 0.283. Solution 2: 2 Originally only solution 1 was recognized. This oversight severely delayed the final solution of the structure. The full sets of coordinates for the two solutions are: Solution 1: La(1 at +(1/4, 1/4, 0) ,:(1/4,1/4,1/2) and Solution 2: La(1 ) La(2) at +(1/4, 3/4, 0. 033) ,+(1/4, 3/4, 0. 533). ) at t+(1/4,1/4,1/4), r(1/4,1/4,3/4) and )a m( t+(1/4,3/4,0.283), i(1/4,3/4,0.783). Solution of the Light Atom Structure The heavy atom method was used to solve the light atom structure. In this method it is assumed that the atoms with predominant scattering factors, the lanthanum atoms in this case, will determine the phase of most structure fac- tors. These phases may then be used to give a Fourier syn- thesis which is a close approximation of the actual structure. In the case of La2(C03)3°8H20 the structure factor of a particular reflection may be written as: 27 Table III. Positions of the metal — metal Patterson peaks Peak Positions— Peak Positions— Relative Relative Unknown za Wts Known z c Wts Peak Peak Parameters Parameters Heights Heights 0,0,0 8 0,0,0 8 999 ' 999 0,0,1/2 8 0,0,1/2 8 926 935 O,1/2,i(z — z') 4 0,1/2,rv 4 460 425 1/2,0,i(z + z') 4 1/2,0,iv 4 462 418 0,1/2,1/2i(z — z') 4 0,1/2,1/2,iv 4 483 450 1/2,0,1/2i(z + z') 4 1/2,0,1/2iv 4 458 422 1/2,1/2,i22 2 1/2,1/2,0 4 439 422 1/2,1/2,1/2i22 2 1/2,1/2,1/2 4 443 413 1/2,1/2,i22' 2 1/2,1/2i2v 2 268 198 1/2,1/2,1/2:22' 2 1/2,1/2,1/2,i2v 2 270 206 aOne metal in each equivalent position of the Wyckoff sets 4c and 4d. bWeights equal the number of identical interatom vectors. Cv = z - z' = 0.033. d From film data. eFrom diffractometer data. 28 8 F(hk£) - 2 f exp[2v1 (tha + kyLa + 22 La 1.16)] + i fn exp[27r1(hxn + kyn + Ezn)] where fLa and fn are the scattering factors of lanthanum and the light atoms respectively and x, y, and Zgare the fractional coordinates of the respective atoms in the unit cell. Since fiLa is much greater than any fn’ the magni- tude of the first term will be much greater than that of the second for values of hkz in which E = 2n, but the first term will vanish for values of hkfi in which E = 2n + 1 because of the special positions of the metals. Lipson and Cochran24 point out that if the scattering fac- tor of the heavy atom is too large the Fourier Synthesis will tend to show only this atom and the lighter atom posi— tions will be very inaccurate. The best results are obtained . 2 _ 1f ZfLa-Zf 2 , , 2 = n n' But for La2(C03)3 H20. 2fLa 6498 and g f: - 1196, excluding hydrogens and assuming the appropri— ate atomic number for f. Thus the light atoms should not be located very accurately by Fourier techniques. However, the method was used and approximate light atom parameters obtained by Fourier synthesis were refined by least-squares analysis. Such a Fourier-least—squares procedure of re- finement permits “faster locatiOn. of atoms than that ob— tained by a Fourier technique alone. The solution of the light atom structure commenced using the film data uncorrected for absorption. The metal posi- tions, solution 1 above, the isotropic thermal parameters 229 and over-all scale factor were refined by least—squares. All data were included with unit weighting. The refinement yielded R = 0.264 (R=ZW| [Fol — IFCH/Z wlrol) and thermal parameters which were non-positive, approximately -0.5. It was surmised that the negative thermal parameters were due to the effect of absorption. Subsequently the same re- sult was observed when refinement of diffractometeric data was initiated. Justification for the use of the nega- tive thermal parameters in refinement will be discussed further in a later section. 'An electron density difference function, (l/V) 3&2 (|F0| - [FC)) exp—2vi(hx + ky + fiz), was calculated usifig only fl = 2n data. Because the metal structure has Pmmn symmetry the difference Fourier showed duplicate images mirrored across the xz and yz planes con— taining the metal atoms. To locate the light atoms various peaks in the Fourier were selected as trial atoms and the behavior of their thermal parameters was tested in least— squares calculations. In this manner a 4-fold carbonate, symmetric about the 2-fold axis, was located near La(2). After several more cycles of least—squares refinement three 8-fold water molecules displaying orientations similar to those of the carbonate were recognized. At this point R was still 0.21 and all but one thermal parameter was still negative. An 8-fold carbonate and an 8—fold water remained to be located. The principal peaks remaining in the differ- ence Fourier were of two types; near the xy plane of the metals or along the 2—fold axis. The positions of the 30 latter peaks, which were the largest, were physically unreal --that is they were superimposed over what would be normally considered the volume of the metal atoms. Attempts to re- fine atoms assigned to the other peaks near the metal xy planes met with some success, reducing R to 0.19. However, the problem of atom overlap was encountered again. That this overlap resulted from the Choice of lanthanum atom positions will be discussed later. In the belief that part of the difficulties encountered resulted from imprecise data, attempts to solve the structure from film data were discontinued. The solution of the structure was then.attempted with diffractometer data uncorrected for absorption. After lanthanum atoms had been assigned and refined in the man- ner described previously, the value of R was 0.28 when all hkz data were included and the thermal parameters were ap- proximately —2.0R% Use of only E =1h1data produced R = 0.18. Employment of the techniques described earlier yielded a 4—fold carbonate and three 8-fold waters in the previously obtained positions (R = 0.19 for all data). The difference function again indicated the presence of atoms, apparently carbonate groupings, near the metal xy plane in seemingly unreal positions. At this time the importance of the al- ternative solution of metal positions was recognized. With the original Choice of metal positions the carbonate group- ings were located at an inversion center. Since the carbon- ate has no center of symmetry, duplicate overlapping groups 31 were required to fulfill the symmetry condition. Use of the metal position, z = 0.250 and z' = 0.283, and subse- quent shift of 2 parameters of established atoms by +0.250 removed the overlap of carbonate groups. The process of atom location was continued producing the essentially cor- rect placement of all but an 8—fold water and an R value of 0.16. Before the complete structure had been solved the pro- gram for absorption correction became available. This correction was applied and the resulting data were entered in the least-squares refinement of the previously obtained parameters. After location of all atoms, except hydrogen, R was reduced to 0.08 and the isotropic thermal parameters had shifted to positive values. In an effort to improve the fit by deleting the less precise intensity data the 125 reflections with intensities of less than 2 cps and 10 reflections in which the background intensity was greater than the peak intensity were given zero weight in the least—squares calculation. This procedure eliminated possible adverse effects of a large proportion (20%) of low reliability data. Subsequently, zero weight was assigned to 8 of the 29 most intense reflections in which the observed structure factors were significantly lower than the calculated values. Although extinction may have caused this discrepancy a direct relationship was not observed between intensity and the deviation. An alterna- tive cause of the deviation may be inadequate absorption 32 correction. In any event, exclusion of these latter reflec- tions produced a measurable effect on the thermal parameters of some of the light atoms even though the positional para- meters were not shifted significantly. All other observed data were given unit weight. An anomalous dispersion cor- rection to the scattering factor of lanthanum was included in succeeding calculations. After several least-squares cycles using isotropic thermal parameters R was reduced to 0.063. If no data were deleted and unit weighting was assigned the R would have been 0.076. The thermal para- meters were allowed to refine anisotropically using Bij = 4bij /a* a* where a3 is the ith reciprocal cell length 1 3 l and the temperature correction is of the form: exp(-b11h2-b22k2-h3322—2b12hk-2b13h2—2b23kg). Using a technique described by Levy25 the symmetry relations among coefficients were evaluated. For the two lanthanum atoms, one carbon atom and one oxygen atom, all of which were located on the 2—fold axis, 813 atiBza = 0. When re- finement was initiated it was found that several of the light atom coefficients changed non—positive definite, although the aqueous oxygens and metal parameters refined satisfac- torily. This difficulty is due to the overall inaccuracies associated with the light atom structure--even the light atoms which refined properly had very large standard devia- tions. The principal causes of this inaccuracy are the dom- inance of the metal contribution to most observed reflections 33 and the low reliability of that data to which it does not contribute. In addition specific absorption effects may still be present in the data. As a result of the difficulty described above only the anisotropic coefficients of metal and aqueous oxygens were refined. The final R factor was 0.061 in contrast to the 0.063 value obtained with isotropic thermal parameters. The shift of any parameter in the last cycle of refinement was less than 0.1% of its standard de— viation. Final coordinates and their standard deviations are listed in Table IVa, thermal parameters and their deviations are found in Table IVb and the observed and calculated struc- ture factors are given in Table V. Water molecules are designated by Aq, the 4-fold carbonate by C(1)-0(1)—0(2) and the 8—fold carbonate by C(2)-0(3-5). The standard deviations in the positional parameters of the light atoms range from 0.019 to 0.038 A, while those of the thermal parameters are in some cases actually greater than of the anisotropic coefficients. It was noted that the thermal parameters of 0(2) and Aq(4) were abnormally large, isotropic B = 5.9 and 6.1 £2 , respectively. For 0(2) this parameter indicates only a large vibrational amplitude for a non-coordinating oxygen. However for Aq(4), the non—coordinating aqueous oxygen in the structure, all possible sites may not be occupied. Recall the discussion of stoichiometry, that the water con- tent may be less than eight per formula. The assumption 34 Table IV. Parameters from least-squares refinement a. Atomic coordinates Atom x y z La(l 0.250 0.250 0.2500 La(2 0.250 0.750 0.2829(1) Aq(1 0.310(2)* 0.385(2) 0.117(1) Aq(2 0.113(2) 0.323(2) 0.380(1) Aq(3 0.121(2) 0.649(3) 0.409(1) Aq 0.382(4) 0.393(4) 0.492(2) 0.250 0.750 0.110(3) 0.320(2) 0.660(2) 0.148(1) 0.250 0.750 0.034(3) 0.456(3) 0.497(3) 0.282(2) 0.019(2) 0.384(2) 0.208(1) 0.018(2) 0.618(2) 0.240(1) 0.317(2) 0.492(2) 0.296(1) * Standard deviations in parenthe51s. 35 mm m0 muHss CH mumpmfimumm HH¢_ .hm H0\ Tfimv * .x. 3m ** .mflmmnucmumm CH mCOHumH>mp Cumpcmum * Av.oVH.H Amvo Ah.ovm.H Acvo Av.ovh.H Amvo Am.ovc.o Amvo Ho.Hvo.h Amvo Ac.ovm.H AHVo Ao.ovm.m AHvo As.Hvo.H- Ao.Hvs.m Am.va.o Am av 18.3Vm oH Am.va.h Avvos Ao.Hve.o Am.ovm.o AH.Hvo.o Am So Ah. gv AH.HVh.H Havoc Am.ovo.ou Ho.ovo.H- .Ao.ovm.on AH. va.H m AH. 2V. Ao.va.H Havoc Am.ovH.o As.ovm.o Am.ovo.o Ao.th.H Ao Hymn H Ao.ovm.o AHvoe on on ASH. ovoo. a- AHH.onv.o AHH.oVHS.o AoH. ovcc. o Advoq on on AoH.oV©o.o AHH.ovmc.o AHH.ovmm.o AoH. ovum. o AHVmH mum «Hm «Hm mam «um *mAHHm Ho mv muwumewumm Hmsumze .Q .ucmfimsflwmn mmumsvmlummma Eon mumumfimnmm . >H OHQMB Observed and calculated structure factors. Table V. II“ Lyapm "‘me ”(Lulu MILPm'CA I! L'“?“ NILMVCM. I II Craven. 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Difference density maps were calculated using both iso- tropically and anisotropically refined data. In all cases the largest residual peaks were associated with the metals. The approximate numbers of electrons associated with these peaks were estimated using the height of lanthanum peaks in a Fourier of F(calculated) to scale the relative heights. The largest peak heights corresponded to one to two electrons. All other peaks in the difference function were about one electron or less. Some of these residual peaks were identi- fied later as probable hydrogen peaks. Attempts to refine H atom parameters by the method of least-squares were com- pleted with very limited success. The most reasonable results will be discussed in a later section. Effect of Absorption on the Determination of the Structure It was mentioned previously that least—squares refine— ment using film data uncorrected for absorption produced negative thermal parameters. This effect was found to be even more pronounced using diffractometric data similarly uncorrected. At that time we postulated the phenomenon re- sulted from absorption, as the effect would be more marked for the larger crystal used in the diffractometric work. The first attempts to correct for absorption using the program of COppens e£_§l,19 did not eliminate the negative parameters since an undetected error occurred when the 38 program was reproduced. To support the conjecture of large absorption effects a Wilson plot of ln(|Fo|2/§ ofi) versus sin2 6 was constructed. The term [5312 is the average value of the observed structure factor for a sin2 9 interval and 0fi is the atomic scattering factor of atomj_. The slope of a Wilson plot equals -2B/7\2 where B is an overall temperature coefficient. The arithmetic average (2 |F0|2)/n was evaluated including both observed and ab- sgnt reflections in five equal intervals of sin2 6 between 0.05 and 0.55. Boundary points were assigned half weight. 2 . . . . . The lFol were diffractometric intenSities corrected for Lorentz and polarization effects. The quantity E 0fi , excluding H atoms, was determined for the median value in each 29 interval. From the slope of the Wilson plot a physically impossible value, B :—1.2X% was obtained. To prove that this negative temperature coefficient resulted from absorption rather than some other physical factor, in— tensities were collected using molybdenum radiation (AK - 0.7107 R). The linear absorption coefficient for La2(CO3)3-8H20 is only 22 cm.1 with this radiation in con- trast to the value of 444 cm"1 for copper radiation. In— tensities were obtained for the (0kg) level, with the Weissenberg multiple film method, on a crystal of approxi- mate dimensions; 0.18 x 0.18 x 0.10 mm. After intensities had been corrected for Lorentz and polarization effects, a Wilson plot was prepared. From this slope the value B = 2.082 ‘Was calculated. This positive value obtained with weakly 39 absorbed molybdenum radiation seemed to verify that absorp- tion caused the negative coefficients. An average B, B3 was calculated from the final refined isotropic parameters by weighting each individual B according to the number of electrons in that atom. The result, B = 1.7 82 , substan- tiated further the original postulate. The effect of absorption on crystal structure refine- ment has been discussed in two recent papers. Werner26 noted that failure to correct for absorption in BiOF approxi- mately doubled the R value and altered thermal parameters significantly. However, positional parameters were not changed substantially, but their standard deviations increased. Srivastava and Lingafelter27 made a study of the influence of absorption on a variety of parameters. They found that thermal parameters decrease to negative values with increas— ing size of regular parallelopiped crystals. They stated that this effect should be anticipated since the amount of absorption is related to the crystal volume and the ob— served structure factors will show the slope of the absorp- tion correction line. In the case of large crystals they observed for B changes much larger than the corresponding standard deviation. Changes in positional parameters were generally within the standard deviations and the R values were higher. My observations regarding the effects of absorption are in agreement with those discussed above. Not only did .R decrease dramatically during refinement when the data 40 were corrected for absorption but the thermal parameters changed from non-positive, definite, to positive. To ob- tain an estimate of the effect of absorption on positional parameters a least—squares refinement was performed using uncorrected data. All data (633 reflections) were given unit weighting and refinement continued until all parameter shifts were less than 0.3% of the standard deviation. The resulting parameters were compared with those refined similarly with absorption corrected data. The positional and thermal parameter differences are listed in Table VI. Twenty—three of the positional parameter changes are less than the corresponding standard deviations and none is greater than 2 sigma of the corrected data. The largest change is 0.04 R. Surprisingly, the increase in R was small, less than 0.01. This discussion may be concluded by observing that even with serious absorption errors the La2(CO3)3'8H20 structure could be solved with some accuracy. To do this, however, negative thermal parameters had to be refined. Such a procedure, of course, has little general applicability if facilities are available to eliminate or correct for absorption. 41 Table VI. Positional and thermal parameter changes due absorption. Ax(x10*4) Ay(x10*4) Az(x10+4) La(l) (0) (0) (0) La(2) (0) (0) — 2 C(1) (0) (0) -14 0(2) (0) (0) +23 .4 0(1) +6 -45 o .1 C(2) -32 — 4 + 8 .3 0(3) +23 +39 + 8 .8 0(4) + 4 -32 + 1 .0 0(5) -11 + 1 - 8 .2 Aq(l) — 8 + 1 + 8 .0 Aq(2) -48 + 6 — 8 .0 Aq(3) —44 +11 + 6 .8 Aq(4) +19 +69 +12 .4 IV. DESCRIPTION OF THE STRUCTURE Structure as a Whole Stereoscopic illustrations of the complete and partial structure, which may be viewed in 3-D with a standard stero- scope, are shown in Figures 4—7. The letter designations for the atoms used in the illustrations are given in Figure 4. Interatomic distances and angles are listed in Tables VII and VIII. As is evident in Figures 4—6, La2(CO3)3-8H20 crystallizes in a layer structure. The primary components of the layers are alternating rows of metals and 8-fold carbon- ates parallel to the x-axis. The carbonates, designated by C, N, O and P in the illustrations, are situated so that each oxygen is bonded to two metals. Every carbonate oc- cupies a total of six coordination sites on the four neigh— boring metals in the layer. Similarly each metal is bonded to four carbonates to produce an irregular La-C03 layer. The carbonates are tilted 170 out of the x-y plane with one bond, C-P, nearly parallel to the x—axis. In adjoining rows of carbonates the C—P bonds have opposite orientations. One oxygen—oxygen distance, 0(3)-O(4) = 2.72 8, between adjacent carbonates is smaller that that normally expected for non-bonded oxygens. This short distance may imply that the negative charge on each oxygen is distributed to two metals and one carbon thereby reducing the effective oxygen size. The four remaining coordination sites of the 42 43 1 :v:‘ ' ’ /;z: ’ o ' ‘ ' o I‘I H W ‘ ‘ U“ u If“; U -' U. Qt“ N ' '9 mm m; 0*. w. 0 5w "' J‘ in)“ .%€0¢N ‘ H’fl: mgpt" x” “x ‘b y y g u ”o x x ”09 " “x . ‘ V0 v "‘ u *‘mfi%3#gfl~o I MnfiE. 4‘00 WJH o M ‘ WdyOW ‘ m 00' ' ' u 00 v w x .1 x x I: X i x I Figure 4. Stereosc0pic illustration of La(CO3)3-8H20 unit cell. Atom Identification for Figures 4-8. L — La(l) c — C(1) or C(2) J-La(2) D-o(2) ' U-Aq(1) M-O(1) V-Aq(2) N—o(3) w - Aq(3) o - 0(4) X - Aq(4) P - 0(5) 44 ‘- -II-I I. .c ulna-O I. -¢’.. ~ - ""‘.' - «on... - Unfit--0 - - - .uoa——- a- n . hu—IuI——_—~ an... n--.-‘-~V— I... ~— -«-~.-«.- IO-..'O~ Figure 5. Stereoscopic illustration of La2(CO3)3-8H20 half cell. .. ul-l - -COo - -0.- .z.-. - nu’o - u-- u._ - - c. mmo 0’ u u.- a :‘.-.‘l-.- ---l‘~ — ‘ ~‘--- ‘~ ‘._ .- - - — —flum>fiumo Hmnpwnmompoa so 6 mo 3 3 .Qouomamowvoo Am .w musmflm bNQ «D 55 of the plane angles is 531° versus 540° for an ideal penta- gonal plane. The individual angles range from 103 to 107°. For the La(2) coordination all five atoms are within 0.13 R of the average plane and the sum of plane angles is 538°, with individual angles ranging from 100 to 117°. The pentagonal pyramid model seems to fit the La(2) coordination somewhat better than that of La(l), that is, the pentagons are closer to being planar. In the case of La(2) the principal dis- tortion of the pentagonal plane is the out of the plane bend of Aq(3) which is opposite the shared edge. The five angles within the pentagonal plane of La(2) are unequal largely because of the shortness of the shared bidentate edge, 2.14 R, compared to the average length of 3.10 R of the other edges. Thus the angles associated with the shared edge are increased with respect to the others which are de- creased. The polyhedral arrangement just described also may be derived from the pentagonal bipyramid. Using the numbering rules given by Muetterties and Wright32, in which 1 and 7 designate apical positions, the 4, 6 and 5 sites are split into two sites each by occupation by two bidentate carbon- ates and two waters respectively. The presence of a bicapped square antiprism is diffi- cult to detect in La2(CO3)3°8H20. Definitely no 4-fold in- version axis is coincident with the crystallographic two- fold axis. However, distorted polyhedra which approach the necessary symmetry requirements can be discerned. For 56 La(l) the "square faces" consist of Aq(1)—O(5)—Aq(2)-O(3) with 0(4) at the caps. The four atoms in the "square face" are within 0.26 R of the average plane and the face angles are 97, 80, 99 and 79° for a total of 355°. The 0(4)-La(l)— O(4) angle is 173°, with La(1)-O(4) making about an 84° angle with the plane. In the analogous La(2) polyhedron, Aq(3), 0(4), 0(1) and 0(3) form the "square" and 0(5) are at the apices. All the atoms of the "square" fall within 0.21 X of the average plane. The O(5)-La(2)-O(5) angle is 169° and the La(2)—O(5) line makes about a 74° angle with the average plane. The sum of the "square" angles, however, is 379° indicative of a more highly distorted bicapped square antiprism arrangement about La(2)than La(l). The greater distortion for La(2) might be expected since two of the equ- atorial sites have a short separation due to bidentate co- ordination by the 4-fold carbonate. One feature of the bicapped square antiprism model which corresponds to the experimental geometry is that the cap sites should be more distant from the metal than the others. In the La2(C03)3'8H20 the oxygens in these sites are 0.1 to 0.2 2 further from the metals than the other ligands. A useful model for the coordination polyhedra in La2(C03)3°8H20 may be derived from the dodecahedron. Using the numbering rules suggested by Muetterties and Wright as shown in Figure 8a, sites 5 and 6 are occupied by bidentate carbonates which split each site, Figure 8b. The splitting of the sites alone lowers the model symmetry to sz- The 57 polyhedra symmetries are actually lower in the lanthanum carbonate structure since the orientation of the carbonates as well as that of the other ligands prohibits the presence of mirror planes, thereby further reducing the symmetry to C2. An ideal dodecahedron may be visualized as two inter- penetrating orthogonal trapezoids. In the present cases the trapezoids are neither quite planar nor orthogonal. The planes of the two trapezoids about each metal were calcu- lated by the least-squares technique using the appropriate carbon coordinates as the positions of substituted bidentates. The standard deviations of these planes are 0.04 and 0.27 X for the two La(l) planes and 0.16 and 0.01 R for those of La(2). The angles between the planes are 86 and 87° re- spectively for the La(l) and La(2) coordinations. Normally a dodecahedron is described by two angles 6A and 9B as is indicated in Figure 8a. The predicted values of 9A and 8B for a hard sphere dodecahedral model are about 37° and 70° respectively. On the basis of energy considerations, Hoard and Silverton4° calculated values of 35.2 and 73.50. The corresponding angles in the present case compare favor- ably with these values if only the angles involving uni- dentate ligands are considered. In the La(2) polyhedra 6A is 35° and 6B is 73°. For La(l) the corresponding angles are 33°or 32° and 74°. Thus the polyhedra in question, al- though distorted from C2V, approximate the symmetry of the suggested dodecahedral derivative model. 58 Which of the models just described is most appropriate for this structure? An examination of the various structural models indicates the ease with which they may be intercon- verted without significantly changing individual atom environ- ments. The bicapped square antiprism and dodecahedron modifications are in fact special cases of the model based on the pentagonal pyramid. In the bicapped square anti- prism the two opposite edges containing the 2-fold axis are oriented about 60° apart and in the dodecahedron the angle is 90°. The model from the pentagonal pyramid permits any angle between 0 and 90°. The observed angles are 87° for the La(2) case and 83° for the La(l) case. On this basis the best description of the polyhedra is probably as dodeca- hedral models distorted slightly towards a bicapped square antiprismatic arrangement. However, such a description should be regarded only as a conceptual tool since the poly- hedra are of low symmetry. Carbonate Ions The geometries obtained for the two carbonate ions in- dicate they are somewhat distorted. The 4-fold carbonate is planar due to symmetry requirements but one bond length is apparently longer than the others, 1.30 i 0.06 8 versus 1.25 i 0.038. The bond, to the terminal uncoordinated oxygen, has an unusually large thermal parameter. This bond is expected to be shorter than those to coordinated oxygens. For example,in the nitrate ions of the species 59 41 the terminal Ce2M93(N03)12'24H20 35 and Th(N03)4'5H20 oxygens have the shortest bond lengths and large thermal parameters. Because of the high standard deviation of these lengths, further conjecture seems unwarranted. In the case of the 8-fold carbonate the atoms are planar within experi- mental error and the bond lengths are approximately equal, 1.28 R. The C—O distances reported in other carbonate structures range from 1.23 R in Na2C03'2H20 42 to 1.31 R in NaZCa2(CO3)3 43, however, the often-cited value for calcite is 1.294 2.44 The O-C-O angles do not equal 120°, and only for the 4—fold carbonate is deviation from 120° within the limits of experimental error. Interestingly, the angles are less than 120° if both oxygens are coordinated to the same metal and greater if they are not. Hydrogen Bonding Evidence The distances observed for many of the O-O bonds in— volving water molecules strongly suggest the existence of hydrogen bonds. In the final electron density difference map several residual peaks appeared in positions appropriate for bonding hydrogens. The attempts to refine some of these parameters met with only limited success. The most reason- able results were obtained for hydrogens located between the terminal carbonate oxygen, 0(2), and the water molecules, Aq(3). But even here the calculated parameters were some— what improbable. Unfortunately the location of the hydrogen atoms will require more accurate data. 6O Observations Concerning Previous Investigations Knowledge of the La2(CO3)3'8HZO structure allows inter- pretation of some of the reported results of the lanthanide carbonate systems reviewed in the introduction. The lighter lanthanide carbonates should normally occur as octahydrates isomorphous to this lanthanum compound. Preliminary work indicates this is true for the praseodymium analogue. However, two of the water molecules are so loosely bound that stoichiometries as low as the hexahydrate will be ob- served occasionally4r6. The hexahydrate should be observed in thermal decomposition of octahydrate as a stable inter- mediate although it has not always been reported. Observa- tions of dihydrates in thermal studies suggest they too are structurally similar to the octahydrate. The infra-red data reported for Ln2(CO3)3°8H20 should be interpretable from the structure. The spectral assignments of the car— bonate ions may be complicated since carbonate oxygens are involved in both bidentate and unidentate bonding and also are hydrogen bonded to water molecules. The symmetry of the ion is sz for the 4—fold carbonate and Cs for the 8~fold ion, although the site symmetries are lower, C2 and C1 respectively. These symmetries will cause splitting of the fundamental frequencies corresponding to the free ion. More accurate atomic parameters are required for a quanti— tative analysis of the carbonate ion spectra. The expected assignment of spectral bands to water molecules bound to 61 the metals have been reported.2 Although the structures of the dihydrate and anhydrous carbonate cannot be predicted it is possible that the basic layer structure observed in the lanthanum compound also would be found in these cases. It is also probable that the metal coordination numbers in these structures are either less than ten or that they re— main the same by substitution of carbonate oxygens for water molecules in the coordination sphere. Neodymium seems to represent the borderline in stability between the octahydrate and dihydrate. The structure determination of crystals of Nd2(CO3)3°§HZO should be of great interest. V. INTRODUCTION Lanthanide oxide fluorides are often encountered as contaminants in investigations of the metal trifluorides. The stoichiometric phases, LnOF, have been studied most fre— quently, but the number of reported investigations is still small-—about twelve. Undoubtedly the sparsity of data re- ported for these oxide fluorides results from the variabil- ity of the anion composition. This variability, which is extensive in some instances, makes the attainment of ac- curate property data difficult. The significance of this variability problem appears evident in the lack of agree— ment of reported structural parameters and even structural types for nominally identical stoichiometries. Literature Klemm and Klein45 studied the phases in the lanthanum- oxygen—fluorine system using Xeray powder diffraction. They prepared a series of samples of the composition LaO1-XF1+2x’ —0.5 §.x.: 1.0 by heating appropriate mixtures of LaF3 and Lagos at 900° in vacuum. In the region 0.0 i x.: 0.5 they observed an apparently face—centered cubic phase of the CaF2 type. Samples with a value of x > 0.5 contained both the cubic phase and LaFa. For x ::-0.02 the authors observed another phase, which they thought to be tetragonal. Both this phase and La203 coexisted for x < —0.02. Zachariasen46 62 63 has made the most prominent contribution to lanthanide oxide fluoride crystal chemistry. Employing X-ray powder diffrac- tion techniques he investigated the hydrolysis products of lanthanum and yttrium fluoride as a function of their molecu- lar weight. In both of these systems he observed a rhombo- hedral phase for the stoichiometric LnOF. This was appar- ently the same phase identified as tetragonal by Klemm and Klein. For lower fluoride content, x < 0.0, both the rhombo— hedral oxide fluoride and the oxide were present. In the composition range 0.0 i X.: 0.3 a tetragonal phase was ob- served. The dimensions of this unit cell increased with in- creasing fluorine content. For higher fluoride content, x > 0.3, the tetragonal phase and the trifluoride were pres- ent. Both the rhombohedral and tetragonal structures are superstructures derived from fluorite. The superstructures result from ordering of the oxygen and fluorine atoms into special sites. These structures will be discussed in detail in the next section. Zachariasen also studied the tetragonal PuOF and cubic AcOF phases. In the cubic phase it was as- sumed that the oxygen and fluorine atoms were statistically distributed over the 8—fold anion sites. Zachariasen postulated that the disordered cubic phase should exist at high temperature for all lanthanide oxide fluorides. However, his attempts to prepare cubic samples of LaOF and YOF by quenching were unsuccessful, although the intensity of the superstructure lines was decreased. At approximately the time of Zachariasen's publication other somewhat contradictory reports appeared. Hund47v48 64 studied the yttrium—oxygen-fluorine system. He obServed a tetragonal phase by cooling approximately stoichiometric mixtures of Y203 and YF3 slowly from 900°. However, when samples with a slight fluoride excess were quenched from 1200° the product diffraction patterns were typical of a fluorite structure. Disordering of oxygen and fluorine atoms was postulated for the cubic phase. Mazza and Iandelli49 reported the possible formation of solid solutions between oxide fluorides and fluorides. The increase of fluoride content increased the lattice parameters of the cubic cells for PrOF, NdOF and SmOF. These workers also reported reflec— tion spectra of these and related phases. Zalkin and Temple- ton5° reported a cubic HoOF phase formed in attempt to pre- pare NaHoF4. This report must be regarded with some doubt since the product was a mixture of two phases. More recent investigations of the lanthanide oxide fluorides, are in agreement with Zachariasen's results. Templeton and Dauben51 found the pyrohydrolysis product of TbF4 to be rhombohedral TbOF. Popov and Knudsen52 prepared the rhombohedral LnOF, Ln = lanthanum to terbium, by the pyrohydrolysis of the corresponding trifluorides. In the cases of PrOF, CeOF, and TbOF the hydrolysis was carried out with moist hydrogen. The authors noted the oxide fluorides are soluble only in hot sulfuric or perchloric acids. Rhombohedral lattice parameters for these prepara- tions were given in a later report53. Vorres and Riviello54 prepared rhombohedral LaOF and YOF by heating the sesquioxide pl 1“ J; h) 1 v ‘ LA. 9| l A»; \-c Pl. (I) I); 65 and trifluoride at 1000°. They prepared isomorphous phases of Y, Dy, Er, Tm, Yb and Lu by hydrolysis of the trifluorides at 500°. These authors also observed tetragonal phases on the exterior of pellets used in the preparation of LiLnF4 for Ln = europium to ytterbium. Batsanova and co-workers55:56 have prepared the stoichiometric oxide fluorides (La, Pr, Nd, Sm, Gd, Dy, Ho, Er, and Yb). Two methods of preparation were used; hydrolysis of the trifluoride at 800—9000 and reaction of Ln203 and LnF3 at 1000-1100°. All preparations were rhombohedral except LaOF and NdOF prepared by the second method which were cubic. The authors reported densi- ties, refractive indices and infrared spectra for many of these phases and rhombohedral lattice parameters of the Dy to Yb phases. The recent report of the crystal structure of scandium oxide fluoride by Holmberg57 is also of interest. ScOF crystallizes in a monoclinic Space group isotypic with that of monoclinic ZrOz. Each scandium is surrounded by four oxygen and three fluorine atoms. The structure analysis confirmed that the oxygen and fluorine atoms are situated in specific sites. In contrast Kutek58 has prepared a cubic SCOF by a slightly different method. Apparently the oxygen and fluorine atoms were disordered in this fluorite-type phase. 66 Structures of the Lanthanide Oxide Fluorides Three crystal structure modifications have been observed for the lanthanide oxide fluorides; rhombohedral, tetragonal, and cubic. Each of these structures may be related to that of fluorite, Can. In the fluorite structure, Figure 9a, each metal is at the center of eight anions situated at the corners of a cube and each anion has a tetrahedron of metal ions about it. The resulting symmetry is cubic, space group Fm3m, with four molecules per unit cell. It is common to place the metals at 000 plus F.C.(face-centered translations) and the anions at i(%j%-%J plus F.C. Alternatively, by choosing a different origin the anions are placed at 000 and é-é-é-plus F.C. and the metals at %-%-%-plus F.C. The radius ratio requirement for fluorite type structures is r(M)/r(X) 2.0.73. The fluorite structure occurs only with relatively large metal ions. The ionic radii of the lan- thanides51 range from 1.061 R for La3+ to 0.848 R for Lu3+. Assuming an anion radius of 1.38 R in the oxide fluorides, a radius ratio range of 0.77 to 0.61 is calculated for the trivalent lanthanides. Thus not all the lanthanide oxide fluorides should be stable with an undistorted fluorite lattice. In the cubic lanthanide oxide fluorides, in which the cations occupy the normal metal sites in fluorite, one of two possible anion arrangements may exist. The first of these possibilities is that the oxygen and fluorine atoms ,__ .\ 9:4 (C) Figure 9. Lanthanide oxide fluoride structures. (a) Fluorite structure. (b) Ordering of oxygen and fluorine in rhombohedral LnOF. (c) and (d) Disordered cubic and ordered tetragonal LnOF structures. 68 are distributed statistically in the 8-fold sites of Space group Fm3m. The second is that the oxygen atoms occupy one of the 4-fold sets of space group F43m (i333 % i-i-plus F.C.) and the fluorine atoms the other 4—fold set. Such a structure would consist of alternate layers of oxygen and fluorine atoms parallel to (111). The possibility of an ordered cubic structure has hardly been considered in the literature. These two possible cubic structures would be indistinguishable by normal X-ray diffraction techniques because of the similar magnitude of the oxide and fluoride ion scattering factors in comparison with those of the lan- thanides. The cubic fluorite structure may be referred to a rhombohedral unit cell. The transformation matrix is: 1 1 1 :9: :9: 1 1 2' 1 2 1 1 — -— 1 2 2 This places the endpoints of the rhombohedral translations at the most distant face-centers of a cubic cell. The rhombohedral lattice parameter, ar, equals~f175 aC and the angle a is 33.56°. In the bimolecular rhombohedral unit cell observed by Zachariasen and others for LnOF, a varies between 33.0 and 33.2°. This variation suggests a small distortion from the cubic cell. The atoms all occupy the special positions of space group R3m, i(xxx). For LaOF; x(La) = 0.242, X(F) = 0.122 and x(0) = 0.370. For perfect 69 cubic symmetry these values would be 0.250, 0.125 and 0.375 respectively. Zachariasen's distinction between oxygen and fluorine atom sites was based on symmetry and size considera- tions. As is shown in Figure 9b the ordering of oxygen and fluorine atoms permits 3—fold symmetry about only one body diagonal of the original cube. The anions are arranged in alternating pairs of layers, —F—F-O-O—F—F-, normal to this 3-fold axis. The cubic fluorite lattice may also be referred to a bimolecular tetragonal unit cell. The transformation matrix i5: 1 1 ”‘2‘ 2" 0 1 1 2 2 ° 0 0 1 As is indicated in Figures 4c and 4d the tetragonal lattice f2 = —§-a and c = a or J2at. parameters would be a c t c t In approximately stoichiometric LaOF, Zachariasen observed c/a = 1.43 rather than 1.414. In this structure, assigned to space group P4/nmm, the fluorine atoms are at 000 and 1 1 -§-§ 0, the metal atoms at éOz and 0%?‘ and the oxygen atoms at 00%- and %‘%’%u The value of z is 0.222 rather than 0.25. In this case the slight distortion from cubic symmetry results from the ordering of the oxygen and fluorine atoms into alternate layers normal to the 4-fold axis. 70 The fluorine-rich tetragonal phases must accomodate more than four anions per unit cell. This excess probably is located at the interstitial sites éOz and 0&3, 2;: 0.75. For LaO_7F1,5,IL4 0 and 0.6 F occupy the oxygen posi— tions and 0.6 F are in the intersitial sites. Zachariasen noted that the intensity of the superstructure lines decreased in diffraction patterns of tetragonal samples as fluoride content increased. From this observation he concluded that z for the metal positions increased with increasing fluoride content. No consideration in the literature has been given to a cation vacancy structure. The tetragonal and rhombohedral structures represent superlattices of the fluorite structure. The corresponding reflections listed in Table IX indicate the manner of split- ting due to superstructure. Table IX. Corresponding reflections in LnOF phases Cubic Tetragonal Rhombohedral 111 101 110, 222 200 110, 002 211 220 200, 112 101, 332 311 103, 211 200, 321, 433 222 202 220, 444 400 220, 004 422 331 301, 213 211, 442 554 420 310, 222 319” 543 422 312, 204 211, 431, 655 In Table X the structural data reported for cubic rhombohedral lanthanide oxide fluorides are tabulated. The rhombohedral parameters listed for the cubic phases were 71 Table X. Reported LnOF structural data a) Rhombohedral Ln3+ Radius1 ar2 0 V/Molc3 Ref. 8 8 deg. 23 La 1.061 7.132 33.01 47.87 46 La 1.061 7.111 33.12 47.75 54 Pr 1.013 7.016 32.99 45.66 53 Nd 0.995 6.953 33.04 44.43 53 Sm 0.964 6.865 33.07 42.85 53 Eu 0.950 6.827 33.05 42.09 53 Gd 0.938 6.800 33.05 41.57 53 Tb 0.923 6.758 33.02 40.74 53 Tb 0.923 6.751 33.09 40.80 51 Dy 0.908 6.716 33.07 40.12 54 Dy 0.908 6.685 33.10 39.39 56 HO 0.894 6.647 33.15 39.06 54 HO 0.894 6.637 33.16 38.67 56 Y 0.89 6.697 33.20 40.08 46 Er 0.881 6.628 33.14 38.73 54 Er 0.881 6.625 33.21 38.77 56 Yb 0.858 6.545 33.30 37.87 56 b) Cubic Ln3+ Radius1 aC ar4 V/Molc3 Ref. 8 R R X3 La 1.061 5.756 7.050 47.68 45 Ce 1.034 5.703 6.984 46.33 53 PI 1.013 5.644 6.912 44.95 49 Nd 0.995 5.595 6.852 43.79 49 Sm 0.964 5.519 6.759 42.03 49 HO 0.894 5.523 , 6.764 42.12 50 Y 0.89 5.363 6.568 38.56 47 1Ln3+ radii (2) reported by Templeton and Dauben51, value for Y3+ estimated from relevant Ln203 and LnF3 crystal data. 2Reported errors range from 0.001 R to 0.005 8. 3Volume per molecule LnOF. 4ar =nJ1.5 aC — for a rhombohedral cell with a = 33.56°. 72 derived for a cell with a = 33.560 and ar = J1.5 ac. Also listed are the Ln3+ crystal radii and the calculated volume per molecule of LnOF. It is interesting to note that para— meters observed for nominally identical phases often differ. In general the parameters decrease regularly with the size of the metal ion but the values listed for rhombohedral YOF seem too large on the basis of the given ion radius. Most of the molecular volumes of the cubic phases are less than those of the corresponding rhombohedral phases, as much as 3.7% in the case of YOF. Purpose of this Research The primary purpose of this research was to investigate phase transitions of lanthanide oxide fluorides at high temperatures. It was intended that the study would be con— fined principally to the rhombohedral phases, which report- edly exist only for the stoichiometric LnOF. Data such as transition temperatures were to be correlated to the crys- tal chemical properties of these systems. Subsequently it was found desirable to make representa- tive surveys of: the phases existing for various LnOl_xF1+2X stoichiometries, the effect of composition changes on the transitions and the nature of the decomposition of LnOF at high temperatures. These investigations provided much definitive data but also exposed several paths for future research. VI. EXPERIMENTAL Preparations Lanthanide trifluorides were prepared by conversion of commercial oxide specimens with ammonium fluoride accord- ing to the following equation: ano3 + 6NH4F > 2LnF3 + BHZOT + 6NH3T Mixtures of 99.9% Ln203 (Michigan Chemical Company) and a 50% excess of reagent NH4F (J.T. Baker Chemical Company) were heated in platinum boats. The reaction was accomh plished in a Vycor tube situated in a horizontal tube fur- nace. A flow of dried inert gas was maintained through the reaction vessel. The temperature was initially elevated slowly to 150-2000 during a 3-4 hour period, then increased to 350-500° where it was maintained for 2-4 hours before being cooled to room temperature. The completeness of the con- version was established by the increase in weight of the lanthanide phase as well as by X-ray powder diffraction identification of the products. In most preparations, normally 4-6 grams of the trifluoride, the weight increases deviated less than 1% from the theoretical values after a single treatment. On occasion further heating with addi- tional ammonium fluoride was required to produce the desired product. 73 74 Preparations of the lanthanide oxide fluorides, LnOF, were attempted by two techniques. In the first method the trifluorides of lanthanum, terbium and ytterbium were hy- drolyzed in air at approximately 850, 500 and 9000 respec- tively. In the second technique equimolar mixtures of the sesquioxide and trifluoride, thoroughly mixed and compacted in platinum boats, were heated in an inert gas atmosphere. In a typical preparation the temperature was increased from 25° to about 10500 during a 3 hour period, maintained there 4-5 hours, gradually kwered to 500-600° in 2-3 hours and then to room temperature. The rhombohedral oxide fluor- ides of La, Nd, Sm-Gd, Dy-Er and Y were prepared by this technique. Identification of these phases was by comparison of the X-ray powder diffraction data to values found in the literature. The observed data are given in Tables XXII to XXUJin Appendix II. Weight loss during heating was invari— ably less than 0.5% for samples which varied from 2—10 grams. Phases of the general stoichiometries LnOi-xF1+2x’ Ln = Nd, Gd, Dy and Er, were prepared from the sesquioxide and trifluoride in a manner identical to that described above. Eight gadolinium preparations (—0.1 2.x :.0.5), six neodymium and erbium preparations (—0.1 i.x :,0.4) and a dysprosium phase (x 2325) were prepared. Analytical Two methods were employed for metal analysis: direct ignition to the oxide at approximately 850° or dissolution 75 in hot sulfuric acid, precipitation of the oxalate and subsequent ignition to the oxide. Precision and undoubtedly accuracy were best with the former method. Both oxygen and fluorine contents were determined by neutron activation at the Dow Chemical Company, Midland, Michigan. The stoichiometries of the tetragonal phases were deduced from the metal and fluorine contents. Results of analyses are given in Table XI. X-Ray Diffraction X-Ray powder diffraction data were obtained by two techniques, both employing copper radiation. Most routine phase analyses were accomplished from Debye-Scherrer photo- graphs prepared with 114.59 mm Norelco cameras. Data ob- tained on a Siemens diffractometer from samples mounted on glass plates were used for more accurate results and for the calculation of lattice parameters. Platinum powder (99.98% pure, J. Bishop and Co. Platinum Works) for which a = 3.9231 259 was mixed with these samples. Lattice parameters were calculated using Vogel and Kempter's least- squares program.18 High Temperature X—Ray Diffraction High temperature X-ray diffraction data were obtained with a Materials Research Corporation high-vacuum diffrac- tometer attachment,6° model X86-G, mounted on a Siemens diffractometer. In this unit the sample was situated on a 76 Table XI. Analytical results a) Metal Analyses in LnOl_xF1+2X Ln x Ln(calcd) Ln(found) #Samples La «0 79.86 80.2 : 0.3 2* Nd «0 80.43 80.45: 0.1 2 Nd «0 80.43 80.5 : 0.3 2* Sm ~0 81.13 81.13: 0.1 3 Eu ~0 81.28 81.08: 0.1 2 Gd «0 81.79 81.79: 0.1 3 Tb ~0 81.98 81.4 : 0.3 2* Dy ~0 82.22 82.7 : 0.3 2* Ho r~0 82.49 82.9 : 0.1 2 Er ~0 82.69 82.54: 0.1 2 Y ~0 71.67 71.69: 0.1 4 Nd 0.27 : 0.02 77.9 78.2 i 0.3 2* Gd 0.28 : 0.02 79.3 79.1 : 0.3 2* Dy 0.23 : 0.02 80.2 79.5 : 0.3 2* Er 0.20 : 0.02 80.9 80.82: 0.1 2 *Determined by oxalate precipitation. Probable errors based on variance found in all analyses. b) Oxygen and Fluorine Analyses in LnOi-xF1+2x O O F F Ln X (calcd) (found) (calcd) (found) F/Ln Nd 0.02i0.02 8.7 6.7i0.6 11.1 11.1i0.3 1.05:0.04 Nd 0.27:0.02 6.3 7.8i0.7 15.8 15.9i0.3 1.54i0.04 Gd 0.28i0.02 5.8 5.8t0.5 14.9 14.9i0.3 1.56i0.04 Dy 0.23i0.02 6.1 5.7i0.5 13.7 13.6i0.3 1.46i0.04 Er 0.20i0.02 6.2 5.2i0.5 13.0 12.9:0.3 1.41:0.04 77 metal ribbon resistance heater. Flat heaters of 5 mil plat- inum-40% rhodium or 5 mil platinum were used. Samples were ground to a fine powder in dry nfheptane and a few drops of this slurry were placed on the heater. The samples covered an area approximately 5 x 8 mm and were 0.1-0.4 mm thick. The heaters with mounted samples were connected to the electrical leads in the normal position for a horizontal diffractometer, 123. sample surface is in a vertical position. Temperature measurement proved to be a difficulty. The thermocouples provided by the manufacturer acted as a heat sink, caused the heater temperature to be lower at the point of attachment than at other areas. Also these thermocouples junctioned within the diffractometer attachment near the sample. Consequently the reference temperature was unknown and increased with heater temperature. Finally the tempera— ture of the sample surface was lower than the heater tempera- ture. The thermal gradient was particularly large, for specimens of the rhombohedral oxide fluoride--as much as 100° at a surface temperature of 500°. The cause of the gradient was due to either poor sample-heater contact or to the low thermal conductivity of the samples. Temperature measurements required in this study were generally below the range of Optical pyrometry. To circumvent the diffi- culties mentioned above, temperature measurements were made by internal calibration. Platinum powder was mixed with the samples and the temperature was determined from its 78 lattice parameter expansion using the data tabulated by Campbellsl. The lattice parameter of platinum was calcu- lated from the position of the (311) reflection after the sample had been aligned at temperature, as described below. The reflection was scanned , 1/8 degree per minute, two or three times and its 29 position determined reproducibly to : 0.01°. Assuming zero alignment error this precision corresponded to a temperature uncertainty of :10° and the probable error may have been :20°. The accuracy of the measurements was confirmed by temperatures observed in thermal analyses, described in a later section. Most high temperature eXperiments were run under vacuum conditions. A two inch oil diffusion pump was con- nected to the diffractometer attachment gig two pieces of 9.5 mm bore Tygon—R vacuum tubing through two 6.4 mm diameter vacuum ports. Pressures measured in the vacuum main by an ionization gauge were generally 4-8 x 10—6 torr. However, small leaks occasionally present in the attachment raised the observed pressure to the 10.5 torr range. Undoubtedly the pressure was considerably higher within the camera be— cause of the slow pumping Speed through the small ports. In fact, at relatively low temperatures (900-1100°) hydrol- ysis of the lanthanide oxide fluorides was observed. The vacuum ports should be enlarged as the manufacturer has modified later models of the attachment. Sample alignment was accomplished with controls for translation (sample horizontal displacement), azimuth rotation 79 and inclination rotation. In the initial alignment at room temperature these three controls were adjusted to produce maximum intensity for the platinum (111) reflection at 39.79° (26). The most critical of the alignment controls was the translation adjustment. Fine adjustments of this control were made using the Kal peak of the platinum (311) reflec- tion which occurs at 81.260. The diffractometer itself had to be realigned if the values listed for (111) and (311) were not attainable simultaneously at room temperature. At high temperatures sample alignment was accomplished by adjusting the translation so that the (111) and (311) plat- inum reflection positions corresponded to identical lattice parameters. Unit cell measurements are much more sensitive to sample displacement at low than at high 29 values. Thus the parameter derived from the (311) reflection was used to adjust the (111) position. Repeated measurement-adjustment cycles produced the desired internal consistency, : 0.01°(29). Diffraction patterns were obtained over the temperature range 25-1000° for most of the rhombohedral LnOF phases prepared. Initially scans were made for 26 = 25—50° to find the phases present at a given temperature. With two phases present the fraction of each was estimated from the peak height of its most intense reflection relative to the height obtained with the corresponding pure phase. Lattice para- meters of the high temperature phases were obtained in several instances. Attempts were made to quench observed high temperature modifications. 80 To obtain information regarding the nature of the phase transitions the thermal expansion of neodymium oxide fluoride, NdOF, was determined between 25 and 900°. Because of the poor quality of the diffraction lines at higher angles, the 29—range 25-60° was generally examined, although some experi- ments were run to 120°. The rhombohedral-hexagonal lattice parameters were obtained by hand-fitting the five most in- tense isolated reflections. Cubic parameters were obtained by averaging all the observed diffraction data. The effect of temperature on the structures of ses was ls exa ' ed. LnOl_XF1+2X pha a 0 min Differential Thermal Analysis Differential thermal analysis (DTA) was used to deter- mine transition temperatures in rhombohedral oxide fluorides, to study the effect of composition on the temperatures of these transitions and to discover any phase transitions in Ln01_xF1+2X, x > 0.0. A simple DTA apparatus was constructed. The sample holder was fabricated from 25 mm diameter 310 stainless steel rod. Two symmetrical 7.9 mm diameter, 12.2 mm deep, sample wells were drilled in the rod toikmbmmodate sample and refer- ence materials. These wells were lined with 5 mil platinum foil. One of the sesquioxides was used in each analysis as the inert reference. Both it and the sample were packed firmly in the appropriate well. A press—fit stainless steel cap covered the wells. The sample holder was enclosed in a 81 Vycor tube situated in a resistance tube furnace (type MK-70, Hevi—Duty Heating Equipment Company) and a dry inert gas was passed through the tube. A 36-gauge Iron—Constantan thermocouple enclosed in Inconel shields (Continental Sens- ing Company) was placed in each sample well through holes in the cap. The differential temperature was recorded on a Sargent Model SR recorder (1.0 millivolts full scale) while sample temperature was measured periodically with a Honey— well Model 2720 potentiometer. The sample temperature was calibrated at 99.4° with boiling water and at 583° with K250452. The observed temperatures were 100.40 and 589°. A correction of -1° per 100° was assumed over the tempera— ture range of interest. Sample temperatures were read to : 0.5°. However, a probable error of : 2.0° seems more appropriate for temperatures obtained from DTA Since these were obtained manually while the sample temperature was changing. Heating rates between 1 and 3° per min. over the temperature range of interest were obtained by manual operation of a rheostat. In each run the differential temperature was measured in at least one heating and cooling cycle. The maximum temperature was in general less than 725°. However, in one run a temperature of 840° was at- tained and in another 1075°. Pt-Pt-10%Rh thermocouples were used in the latter experiment. The temperatures of any observed transitions were obtained from plots of the differential temperature(mv) versus sample temperature. 82 Thermal Decomposition of Neodymium Oxide Fluoride A sample of NdO F , x 310.05, was heated under 1-x 1+2x high vacuum (less than 10-6 torr) in an out-gassed open tantalum crucible. The weighed sample was heated 52 hours at approximately 1475°, 38 hours at approximately 1600° and 10 hours at 1475° to constant weight. Evolved products which had condensed on the glass chamber and final residual product were examined by X-ray powder diffraction. VII . RESULTS Preparations and Phase Analyses Rhombohedral oxide fluorides Specimens of La, Nd, and Sm-Er were prepared, however, X—ray diffraction and metal analyses indicated the presence of a slight excess of oxide in the DyOF and HoOF preparations. Several attempts to pre- pare rhombohedral YbOF were unsuccessful, yielding diffrac- tion patterns with many unidentified reflections. Four phases were identified by X-ray diffraction in the systems LnOl_XF1+2X, where x = -0.1 to +0.5 and Ln = Nd, Gd, and Er. Schematic illustrations of the X-ray re- sults for ErOl_XF1+2X are shown in Figure 10. For x 2:-0.1, Ln203 and rhombohedral LnOF were present and at x 230.0 only the rhombohedral phase was observed. AS the fluoride content was increased, x > 0.0, a tetragonal phase appeared together with the rhombohedral phase. The limits of the two phase region varied somewhat in the three systems studied. For the neodymium and erbium systems the tetragonal phase was in evidence for x 2:0.05 and was the dominant phase at x 2:0.10. In these systems, only the tetragonal phase was apparent for x 2:0.15. In the gadolinium system the strongest reflection of the rhombohedral phase was still preSent at x 2:0.20. The tetragonal phase existed with variable composition, x 230.15 to 0.25, for Nd and Er. The variations in stoichiometry were accompanied by changes 83 84 Er—O-F phases. ErF3 l 1' 1 IIMIIM. Ero.6F1.8 1 L 1 1 ll 1.. I -11. 11. [ll Er0,75F1.8 11 I I] 1L1 Er0.83F1.34 3:- L J [I ILJ I0 I ErO.9F1.2 I“ l ”11 1114 ErOF J l . [L 11 Er01_1F,8 I, - M. u... Er203 L . l l ., l .1- 4 3 Interplanar spacing, "d", in K Figure 10. Schematics of X-ray diffraction patterns of 85 in the lattice parameters. However for Gd the region of stability appeared to be much smaller, x 2:0.25. No change in the tetragonal reflection positions was perceptible in any gadolinium diffraction patterns in which the phase was a component. Table XII lists the structural data for tetragonal Ln01_xF1+2X phases prepared in this study as well as those reported by Zachariasen. Diffraction data for the previously unreported phases are listed in Tables XVI to XXI in Appendix II. As the data in Tables XX and XXI indicate, diffraction patterns of the erbium phases con— tained several lines which could not be indexed. For x greater than 0.25 the diffraction patterns exhibited lines of the trifluoride as well as those of the tetragonal oxide fluoride. The assignment of phases for the compositions LnO F is qualitatively supported by the thermal analy- l-X 1+2X sis results reported in the next section. Phase Transitions The existence of a rhombohedral to cubic structural transition was confirmed for the lanthanide oxide fluorides, LnOF. The transitions were observed for the Nd, Sm, Eu, Dy, Ho and Y phases using high temperature X-ray diffraction. Both the face-centered cubic and rhombohedral phases were perceptibly present over a 30° range about the transition temperature. It seems probable that the temperature gradi— ent present in the sample accounted for part of this range. The temperature, determined by the platinum reflections, was 86 Table XII. Structural data for tetragonal LnO F l-X 1+2X Metal x a(g) C(R) c/a V/Molc(R3 La* 0.0 4.083(1)** 5.825(1) 1.427(1) 48.55( La* 0.3 4.098(2) 5.840(4) 1.425(2) 49 04( Nd ~0.15 3.999(2) 5.704(3) 1.426(2) 45.61( Nd 0.27 4.014(3) 5.720(4) 1 425(2) 46.08( Gd 0.28 3.977(1) 5.528(1) 1.390(1) 43.72( Dy 0.23 3.933(1) 5.451(1) 1 386(1) 42.16( y* 0.0 3.910(5) 5.43 (1) 1.389(4) 41.5 ( Y* 0.3 3.930(5) 5.46 (1) 1.389(4) 42.2 ( Er ~0.15 3.893(1) 5.400(2) 1.387(1) 40.92( Er 0.20 3.907(1) 5.385(1) 1.378(1) 41.10( *- Parameters as given by Zachariasen ** Standard deviation in last digit given in parentheses. 87 a mean value representative of the diffracting portion of the sample. At an observed mean temperature just below the transition temperature part of the sample will be above the transition-i,§,, will produce the high temperature diffrac- tion pattern. Analogously, above the transition tempera- ture some of the sample will still exhibit a rhombohedral structure. Therefore the transition temperature is the temperature at which both phases are present in equal quanti- ties. When samples were allowed to equilibrate for a few minutes no hysteresis effect was observed within the limits of error in temperature measurement. However at least partial quenching of the cubic phase was possible in the cases of neodymium, samarium and europium oxide fluorides. Attempts to quench other phases were unsuccessful. Some of the transition temperature and lattice parameter data obtained for the transitions were in error due to initial difficulties with temperature measurement. Transition temperatures and cubic lattice parameters considered re— producible are given in Tables XIII a and b. Data for the thermal expansion of NdOF lattice parameters are given in Tables XIV a and b. It should be noted that d for the rhombohedral structure is constant within ex— perimental error below the transition temperature. A plot of the NdOF volume per molecule versus temperature is il- lustrated in Figure 11. By linear extrapolation of the two volume-temperature lines to the transition temperature the 88 Table XIII. High temperature X-ray diffraction data for LnOF a) Transition Temperature Ln in LnOF T(20% cubic) T(50% cubic) T(80% cubic) Nd 504 : 10° 519 : 10° 534 : 10° Eu ___ ___ <535 Gd 588 597 616 Dy (558) (573) (588) H0 579 593 607 b) Cubic Lattice Parameters Sample Temperature a(g) NdOF(quenched) 25 : 10° 5.631 : .003 NdOF 648 5.685 i .001 SmOF 539 5.606 i .002 EuOF(quenched) 25 5.535 : .002 EuOF 539 5.573 i .002 GdOF 617 5.554 i .005 DyOF 627 5.487 : .005 HoOF 620 5.466 t .002 89 Table XIV. NdOF high temperature structural data a) Rhombohedral * Run T* ar*(g) a V/Molc*(83) Ref. 25 250 6.953 33.040 44.43 A1 25 6.949 33.06 44.43 D1 25 6.950 33.07 44.48 D3-H 152 6.963 33.05 44.66 A9-C 215 6.975 33.00 44.75 D4-H 215 6.976 33.00 44.82 A2-H 237 6.973 33.03 44.84 AO-C 265 6.983 33.03 44.92 D6-H 315 6.983 33.02 44.98 A7-C 366 6.993 32.98 45.06 D7-H 398 6.994 33.00 45.15 A3-H 418 6.997 32.98 45.18 A6-C 450 6.992 33.06 45.26 A5-C 480 6.992 33.07 45.29 *Probable errors for T, ar, 0 and V/Molc are 15°, 0.004 R, 0.030, and 0.04 83. b) Cubic Run T* ac(g) ar(R)** V/molc(Ra) D13-C 15° 5.631(3 * 6.897 44.63 7)* D14—H 96 5.637 1 6.904 44.77 2 D15-H 258 5.647(2 6.916 45.02 4) 81 -H 529 5.675 2) 6.950 45.70(4 B12—C 549 5.678 1 6.954 45.76 2 D16-H 559 5.675 1) 6.950 45.70 2 B8 -c 569 5.678 2) 6.954 45.76 4 D2 -H 569 5.678 1 6.954 45.76 2) B7 —c 579 5.681 1) 6.958 45.84 2 B11-C 579 5.681_1 6.958 45.84(3) D17-H ’588 5.679(2 6.955 45.80 4) B2 -H 608 5.682 1 6.959 45.85 2 89 -H 618 5.683 2 6.960 45.89 4) D10-H 638 5.686 3) 6.963 45.96 7 86 -c 648 5.685 1 6.962 45.93 2; 01 —H 648 5.685 1 6.962 45.93 2 85 -c 668 5.688 1 6.966 46.01 2 B10—H 697 5.690 1 6.969 46.06 2 Dll-H 697 5.688 3 6.966 46.01 7 B4 -c 726 5.691 1 6.970 46.08 2 B13-H 736 5.693 1 6.972 46.12 2 83 —H 756 5.692 1 6.971 46.10 2 02 —H 786 5.696 1 6.976 46.18 2 B14-H 878 5.703 1 6.984 46.36 2 * Probable error in T is 15°, standard deviations for a and - c V/Molc in parentheses. *‘X- ar =~J1.5 aC for rhombohedral cell with a = 35.560. Volume per Molecule, 83 90 0 Increasing Temperature _ t Decreasing Temperature 710 0/1’ b' 46.0 _ f 0 Cu 1c O (y? 0 l/ o _ T/ 48 0 .31};)3 45.5 L __ #5 o o / 1. 45.0 — Rhombohedral o / o o o 44.5 _ / n 1 L L 0 200 400 600 800 Temperature, °C Figure 11. Thermal expansion of NdOF 91 volume change for the transition was estimated to be 0.31 83. The change represents a small but Significantly larger volume in the cubic structure. This is in marked contrast to the Comparative results in the literature, Table X, which indicate the rhombohedral structure has the larger molecular volume. Also observed in the present study were the volumes per formula unit for rhombohedral HoOF at 25° and 571° (respec— tively 39.06 and 40.31 83) and for cubic HoOF at 6200 (40.83 23). Assuming a linear extrapolation of the rhombo- hedral data to 620° a volume difference of 0.41 83 is calcu- lated. The molecular volume of cubic EuOF quenched to 25° is 0.30 83 greater than the analogous rhombohedral value. From these results a volume increase in the rhombohedral to cubic transitions of all the lanthanides is expected. Differential thermal analyses confirmed the existence of the rhombohedral—cubic phase transitions in lanthanide oxide fluroides. The transitions observed for all LnOF preparations during both heating and cooling cycles are listed in Table XV. The temperatures at which the reaction commenced in heating and cooling cycles, T2 and T3, gener- ally agreed within 5° and the temperatures of the peak maxima, Ti and T5, agreed to within 15°. However, the median values of reaction commencement and peak maxima, Tged and Tmed’ agreed to within 2° or less and these were assumed to be the transition temperatures. The differences in T° and T' in heating and cooling cycles suggest hysteresis. In- deed, the evidence of hysteresis effects in the oxide fluoride 92 Table XV. Differential thermal analysis results Stoich—* Heat- 3 Cool— iometry * ing 0 , ing 0 . o . Rate T1 T1 Rate T2 T2 med Tmed o/min ° 01min 0 ° 0 0 K2804 2 582.5 584 2.0 583.5 582 583 583 LaOF 3.0 495 501 2.0 495 490 495 494 NdOl.1F.8 3.0 525 533 2.0 528 519 526 526 NdOF 1) 3.0 526 535 2.0 507 500 517 518 NdOF 2) 2.5 530 535 2.0 507 497 517 516 NdOF 3) 3.0 528 534 2.0 520 514 524 524 NdO.93F1.14 3.0 522 533 2.0 - (516) - 524 Ndo,8581,3 2.0 - — — - — - - SmOF 5.0 527 535 3.0 521 515 524 525 EuOF 2.0 513 518 2.0 513 509 513 513 GdOl.1F.8 3.0 602 610 2.0 606 602 604 606 GdOF 3.0 611 615 3.0 606 595 608 605 GdO.9F1.2 3.0 612 617 2.5 605 599 608 608 GdO.8F1.4 3.0 — - - — - - - TbOF 2.0 549 556 2.0 554 545 552 550 DyOF 2.0 560 563 1.5 557 552 558 558 YOF 2.5 569 578 2.0 570 567 570 572 HoOF 3.0 588 594 2.5 590 582 589 588 Er01.1F.8 3.0 588 593 3.0 585 579 586 586 ErOF 2.0 591 597 1.0 592 588 592 592 8r0.981.2 3.0 595 604 2.0 599 594 597 599 EIO.B5F1.3 3.0 - — — - — - - *- The probable error in temperature measurements is 2°. T3 and T2 are the temperatures at which the reaction commenced and Ti, T5 are the temperatures corresponding to the DTA peak in the heating and cooling cycles respectively. ** StOichiometries for LnO1—xF1+2x’ x > 0.0,are approx1mate. 93 transition data is greater than that in the reversible transi— tion data in K2S04 also presented in Table XV. However, with the exceptions of the Nd and Sm cases the hysteresis effects are less than 10°. In general the transition temper- atures are observed to increase from 495° for LaOF to 592° for ErOF. A noticeable exception to this trend is the 606° transition temperature for GdOF. It was considered possible that the transition temperature varied Significantly as a function of composition. The results listed in Table XV for LnOl_XF1+2X suggest that compOSition does affect the transition temperature. However, over the range -0.1 :.x 2 0.1 the change is small, about 10°, and would not account for the relatively high transition temperature of GdOF. Figure 12 illustrates the DTA results for GdO1-XF1+2x which are typical. Notice that hysteresis increases with increas- ing fluoride content. The magnitude of the DTA peak also decreases as the proportion of rhombohedral phase decreases. Samples containing very little or no rhombohedral phase produce no DTA peaks in the temperature range examined. These analyses support the earlier conclusions based upon X-ray phase analysis. The tetragonal phases, LnO , were examined for 1-xF1+2x a possible phase transition using both differential thermal analysis and high temperature X-ray diffraction. No endo- thermic DTA peaks were found in the temperature range studied for GdO,3F1.4 below 725°, for NdO_85F1.30 below 820° or for ErO.85F1.30 below 1050°. In the latter two samples an I. IL]. .I WISH- N'S.‘ 7 94 Gd01.1F0.8 \\ heating _ cooling 1 J l 4 l - l ' I ' r heating _ 7 >0 — -a 'O . :;-— cooling 8 1 H " 1 = g : I To 21: heating _ Gd00.9F1.2 - cooling 1 1 l 1 1 r- l f | I [ "' GdOo . 8F]. .4 heat' L ing % 44 l __ : 1 500 600 700 Figure 12. Temperature, °C DTA curves for selected Gd-O-F stoichiometries. 95 exothermic trend which was observed above 800° was assumed to result from hydrolysis of the sample. Above 10500 a sharp endothermic increase occurred for the ErO.85F1.3 case. This increase continued until heating was stopped at about 1075°. This endotherm probably resulted from Sintering. Sintering was observed in all Ln01_XF1+2X preparations (1050°) for x greater than 0.1. Examination of the tetra- gonal phases by high temperature X-ray diffraction was ham— pered by hydrolysis of the samples above 800°. No sharp structural transition was observed below 1000°. Superstruc- ture lines remained until the sample hydrolyzed to LnOF which was observed as a cubic phase at high temperature but reverted to the rhombohedral phase on cooling. However, changes in intensities of the tetragonal phases which were observed in these experiments could not be correlated with certainty to the hydrolysis reaction. A complete thermal analysis of the tetragonal phases will require further ex~ perimentation. Decomposition of Neodymium Oxide Fluoride In the thermal decomposition of neodymium oxide fluoride a dirty white product evolved which was examined by X-ray diffraction. The diffraction pattern was diffuse but was unmistakeably NdF3. The residue from the decomposition was a sintered mass of black-violet crystals. This dark crys- talline mass became a lighter blue~gray when powdered. X-ray 96 diffraction of the residue indicated only A-Ndzog. A 39% weight loss was observed in the decomposition. Assuming the following reaction: 3NdOF > Nd203 + NdF3T. the calculated weight loss is 37.4%. However, fluorine analysis of the starting material indicated the stoichiometry was NdO F , x = 0.05. For this composition the calcu- 1-x 1+2x lated weight loss is 39.2% VI II . DISCUSSION The Phase Transition in Rhombohedral Oxide Fluorides The transition of rhombohedral lanthanide fluorides to cubic symmetry at high temperature has been observed as predicted by Zachariasen. It would be desirable to describe the nature of these transitions structurally and thermo- dynamically. Such a description*woukirequire an exact structural knowledge of the rhombohedral and cubic phases. The ordered anion structure as given by Zachariasen for the rhombohedral phase appears well established,even though it was determined from powder data and the Special anion posi- tions were deduced from symmetry and size arguments. Zachariasen considered the cubic phase to have the CaF2 structure with a disordered anion arrangement. Little con- sideration has been given to a possible ordered cubic struc- ture based on space group F43m. Since the two alternatives would be indistinguishable a choice must be made on some other basis. If the disordered configuration has nearly the same internal energy as the ordered cubic structure, then the disordered structure should become increasingly stable with increasing temperature because of entropy-free energy arguments. That is, the disordered structure will be favored at high temperatures. Since transition from the ordered rhombohedral structure to another ordered struc- ture would require complex anion migrations through inter- mediate configurations which are disordered, a transition 97 98 to the disordered structure will be assumed in the following discussion. It will describe the general classification of phase transitions and will attempt to define the nature of the transitions in lanthanide oxide fluorides. Polymorphism is the phenomenon of a chemical substance which crystallizes in more than one structure (called poly- morphs or polymorphic modifications). Two types of polymor- phic transitions may be differentiated. Enantiotropic transi- tions are reversible: when the substance is heated it trans— forms to the structure stable at high temperature but reverts to the original form on cooling. Monotr0pic transitions proceed in only one direction from a state metastable over the entire temperature range at a given pressure to a stable state. The transitions in LnOF are enantiotropic. Solid state transitions may be classified in a number of ways. In a thermodynamic sense transitions may be of first-, second—, or higher order. A first-order transition is one for which there is a discontinuous change in energy and in all physical prOperties. These transitions are governed by the Gibbs phase rule. First—order transitions include normal polymorphic transformations and phase changes, such as melting, with which are associated a latent heat, a volume change and an entropy change. Transitions of the second order involve a discontinuity in the first derivative of the energy, 133:: specific heat, but not in the energy, volume or entropy. Both ferromagnetic and order-disorder transitions in alloys are typical second order transitions, 99 often called 1 points. AnOther characteristic of A points is that the transition is Spread over a large temperature interval up to the A point where it ceases sharply. Classification of the rhombohedral-cubic transitions in the oxide—fluorides on a thermodynamic basis is not clear- cut. If order-disorder of anions is accepted then a second- order transition is predicted. However, the transitions in question: appear to have volume changes of less than 1%, occur over a modest temperature range, are somewhat sluggish since the high temperature form may be quenched sometimes, and exhibit a relatively sharp thermal effect suggestive of a latent heat. These characteristics are not general for second-order transitions, but are not unknown. The alloy AuCu3 undergoes a second-order transition involving disorder- ing of the atoms. This transition has a latent heat, ex— hibits a 0.35% volume change which appears discontinuous, and orders so sluggishly that the disordered phase may be quenched. This is an example of an order-disorder trans- formation in which the order decreases gradually up to the critical temperature, but then the still partially-ordered phase rearranges quite abruptly with an associated latent heat. Thus the transitions of the lanthanide oxide fluorides are very similar to a known order-disorder transition. It may be questionable whether these transitions are strictly second-order or represent a superposition of first— and second—order processes. Such a possibility seems more likely with the oxide fluoride than with binary alloys. The oxygen and fluorine atoms could be disordering below the transition 100 without changing the metal structure. At the transition point the metal structure undergoes a distortional trans- formation which is probably first-order. Superimposed on this transition is the completion of the typically second- order process of anion disordering. Buerger63 has classified structural transitions on the basis of kinetics and the change of bonding and structure in the following manner. The change in internal energy during a polymorphic transition is essentially the change in bonding energy. The energy absorbed in a transformation during heating implies a reduction of net bonding. This reduction may occur by a decrease in interaction between first—nearest neighbors, second-nearest neighbors, or both. The kinetics of the transitions depend on the bonds disa turbed and the intermediate configuration. Thus Buerger's classification of transformations are: I Transformations of first coordination Dilational (rapid) Reconstructive (sluggish) II Transformations of secondary coordination Displacive (rapid) Reconstructive (sluggish) III Transformations of disorder Rotational (rapid) Substitutional (sluggish) IV Transformation of bond type (usually sluggish) 101 How does the LnOF rhombohedral-cubic transtion fit into this categorization? If the conclusions of the preceding thermodynamic discussion are accepted the transformation Should be considered as two superimposed processes, anion order-disorder and structural reorganization. Consider these processes with respect to the changes in first coordination of the metal. Four fluorine and four oxygen atoms are the nearest neighbors of the metals in both low and high tempera- ture structures. At low temperature atoms of one type are ordered on one side of the coordination sphere and at dif- ferent distances from the metal than the other anions. At high temperature the anions are disordered and at equal distances from the metal. The change in first coordination requires the breaking and making of bonds(a reconstruction process) and perhaps the transformation should be considered under that category. However, this change for LnOF is more appropriately classed as a transformation of disorder which is substitutional. For either category the transform- ation is expected to be sluggish. The disorder transforma- tion will be discussed later in this section. In both the high and low temperature modifications eight other metal atoms are the next nearest neighbors. The low temperature secondary coordination is a rhombohedral distortion of the high temperature arrangement. No breaking of bonds is required in the transformation between these arrangements and so the change should be regarded as dis- placive. Such transitions are usually rapid. Buerger 102 indicated a number of prOperties for this type of transforma- tion. The high temperature form is always more open and thus has a larger molecular volume. It also has a larger heat capacity and entrOpy since the atoms in the open form are held in position with less force and are more capable of absorbing thermal energy. The low temperature form will have a lower symmetry and will in fact be a subgroup of the high temperature form. (The structures are sometimes re- ferred to as derivative and basic structures.) AS a con- sequence of this latter property the down-temperature modi- fications invariably produce twins. A transition of this type may occur in ScOF for which only twinned single crystals were obtained.57 Disorder transformations are very similar to displacive ones and their speeds may vary from sluggish to rapid. In the substitutional disorder transformation of B' and B" among fixed A atoms the B' and B" become statistically equi- valent. Again the symmetry of the low temperature phase is a subgroup of that of the high temperature one. Generally the volume is greater for the high temperature form due to the juxtaposition of identical atoms with an increase in repulsive energy. The ordering transformation is often sluggish because of the low probability that atoms will inter— change locations to produce the ordered configuration rather than another disordered configuration. I have suggested for the rhombohedral-cubic LnOF transi— tions the substitutional disorder and displacive secondary 103 coordination categories of Buerger's classification. Which more appropriately describes the transitions? Undoubtedly each applies to some degree. Both predict a larger volume and higher symmetry for the high temperature phase, as ob- served. With respect to speed of transitions the displacive transformation should be very fast while order-disorder is slower, particularly in the ordering process. The present transitions are relatively fast but some are sluggish enough to permit quenching of the disordered phase. In this latter respect the ordering of the anions must be the predominant criterion. Thus I conclude that both of the categories are useful for the description of these transitions. The transition temperatures for the rhombohedral-cubic transitions increase in general with increasing atomic num- ber, GdOF being a noticeable exception. The temperature trend should be related to the type of transition, If dis- order is the important factor, migration of the ions to new sites should be considered. The fact that anions apparently occupy the large interstitial sites in tetragonal LnOl_XF1+2X suggests that they can migrate through these holes. The ability of anions to diffuse should determine the tempera- ture of the transition. It is reasonable to expect that the electrostatic attraction of the cation for the anion is an important energy consideration in this process, since it {prevents the anion from leaving its site. In addition, the repulsive effect of the three anions which the migrating anion must pass also retards migration. As the atomic number 104 increases and cell size decreases the anions become more tightly packed. Qualitatively this decreases the hole Size between anions making passage of the migrating ion more dif- ficult. In other words, the repulsive force increases with increasing Z. Both the attractive and repulsive forces which are hindrances to anion migration increase with de- creasing cation size. Thus the temperature of transition is expected to increase also. Unfortunately no explanation can be offered for the anomalous value obtained for gadolin- ium oxide fluoride. Observations on the Tetragonal Phases, LnO F 1-X 1+2X The tetragonal LnOl_XF1+2x has been observed in this study as a single component only for values of x greater than 0.1. This observation is contrary to previously re- ported results in which the pure phase was also observed for x = 0.0 to 0.1. The structural data presented in Table XII for LnOl_xF1+2X have some interesting aspects. Immedi- ately obvious is the change of cell volume with atomic number. Of greater interest is the variation of the c/a ratio which has two distinct value ranges, about 1.43 for lanthanum and neodymium and 1.39 for gadolinium to erbium. Recall that the ratio is expected to be 1.414 for the tetra- gonal cell derived from the fluorite arrangement. How can this variation be explained on the basis of the tetragonal structure given by Zachariasen? In his structure the oxygen and fluorine atoms are ordered in layers 105 normal to the c-axis. Because the oxygen atoms are effectively larger than fluorine atoms it might be expected that the alternating oxygen and fluorine layers would pack more tightly than oxygens within the layer. That is, c/a should be less than 1.414 8. However, this argument assumes anion-anion contact along both the[LUM and[001]directions. The condition in fluorite structures for this anion contact is that the cation to anion radius ratio be less than about 0.73. Above this value the cation will be in contact with the eight surrounding anions preventing complete anion con- tact. Using the cation radii given by Templeton and Dauben51 and an anion radius equal 1.38 8, calculated radius ratios are 0.769, 0.721, 0.680 and 0.638 respectively for La, Nd, Gd and Er. On this basis complete anion-anion contact is expected only for lanthanides smaller than neodymium. For the oxyfluorides Gd through Er, anion contact must be the determining factor since anion—anion distances are less than 2.81 and 2.77 2 along [110] and [001], reSpectively. For this condition the argument has been made above that the c/a ratio should be less than 1.414, which is as observed. In the case of the phases of La through Nd, anion contact is effective only in the oxygen layer, and the larger lanthanide ion separates the oxygen from the fluorine layers. In the lanthanum phase the anion-anion distances along [110], the distance of closest approach, are 2.90 8, while along [001] they are 2.92 X, To summarize, because of the nature of the layered structure, as cation size decreases, shrinkage is less within the oxygen layer than between 106 the alternate oxygen and fluorine layers. Thus the c/a ratio changes markedly as 2 increases. The addition of excess fluoride ions, half of which go into interstitial sites and half of which replace oxygens, Should have little effect on packing. Only a slight change in the c/a ratio is observed except in the case of erbium. Recall, however, that the diffraction patterns of the erbium phases contained extra lines. A calculation of the size of the interstitial holes in LnOi-xF1+2x was made using the distances between symmetrically opposite anions. For the lanthanum case this value is 4.85 R and for erbium 4.74 2, Assuming that this distance is equal to four anion radii, then the average radius is about 1.2 X, This is much smaller than the normal fluoride and oxide radii and the assumption of anions in the inter- stitial Sites would appear doubtful. However, it has been established that in solid solutions of YF3 in CaF2 (up to 55 mole per cent) anions are in the interstices and cation vacancies are insignificant64. The size of these inter- stitial holes is of the same order of magnitude as those found in LnO F Apparently the anions are consider- 1-x 1+2x' ably distorted in both cases. In LnO F the stability 1—x 1+2x of the tetragonal phase is expected to decrease with increas- ing atomic number because of the decreasing size of the interstice. No tetragonal-cubic transition was observed in the 'temperature range of this study. Although a transition may 107 take place at higher temperatures, it is somewhat surprising that none was observed below 800°. The ions are mobile at these temperatures making disordering very likely. Perhaps a tetragonal—cubic transition is not favored because of a required decrease in volume. The molecular volume for tetragonal LaOF reported by Zachariasen?‘6 was 48.55 £3 and that for cubic LaOF45 was 47.68 83. Although not impossible such a transition with volume decrease seems improbable, particularly for a disordering process. For molecular volumes in general it is very curious that the values de- duced from the literature for cubic oxide fluorides are less than the corresponding rhombohedral volumes. In this study the opposite has been observed. Either the reports of cubic parameters are in error or they represent an ordered structure, such as F43m, which could have a smaller volume. IX. SUGGESTIONS FOR FURTHER WORK Knowledge of the La2(C03)3'8H20 crystal stru2ture serves as an aid in interpretation of lanthanide carbonate chemistry. However, a complete understanding of these carbonate systems will not be possible until all the related structures are known. The structures of both a Ln2(CO3)3-2H20 phase and Lu2(CO3)3’5H20 should be determined if suitable single crys- tals can be prepared. The coordination number of the metal of these phases would be of great interest in light of the unusual coordination polyhedra in the lanthanum compound. Obviously the structure of the available Nd2(CO3)3'XH20 crys- tals should be studied. Hopefully these crystals would exemplify the dihydrate. The possibility of obtaining single crystals of the anhydrous carbonates or oxycarbonates seems improbable. However, knowledge of their structures is required for complete interpretation of the interrelation- ships in the lanthanide carbonate systems. The lanthanide-oxide—fluoride systems offer a number of interesting projects for further research. A neutron dif- fraction study of the rhombohedral and cubic LnOF phases should allow the verification of the anion positions presumed in the present work. An investigation of the high tempera- ture decomposition of the rhombohedral phases by mass Spectrometry would be profitable. The tetragonal LnOl_XF1+2x phases offer several projects of interest. It is probable that complex crystal structures exist in some of these phases 108 109 and perhaps single crystal structure determinations could be Undertaken. The possibility of transitions in these phases at high temperature also should be investigated more completely. Finally a study of the probable phase transi- tion in ScOF would be very instructive with respect to the examination of order-disorder processes. 10. 11. 12. 13. 14. 15. 16. 17. REFERENCES T. Moeller and E. P. Horwitz, J. Inorg. Nucl. Chem., 12, 49 (1959). L. Gordon, R. A. Brandt, L. L. Quill and M. Salutsky, Anal. Chem., 23” 1811 (1951). Sr. M. Clarus Strouth, "Thermal Decomposition of Yttrium, Scandium, and Heavy Lanthanon Oxalates and Carbonates," Thesis, Michigan State University, 1962. M. L. Salutsky and L. L. Quill, J. Am. Chem. Soc., 12, 3306 (1950). R. G. Charles, J. Inorg. Nucl. Chem., 21” 1489 (1965). E. L. Head and C. E. Holley, Jr., “Rare Earth Research III," Gordon and Breach, New York, 1964, p. 51. E. L. 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Soc., 61, 1544 (1939). R. Wang, R. Bodnar and H. Steinfink, Inorg. Chem., 5” 1468 (1966). A. Zalkin, J. D. Forrester and D. H. Templeton, J. Chem. Phys.,.§2, 2881 (1963). I. Jelenic, D. Grdenic and A. Bezjak, Acta Cryst., 11” 758 (1964). E. L. Muetterties, J. Am. Chem. Soc., 88, 305 (1966). I. I. Chernyaev, V. A. Golovnya and A. K. Molodkin, J. Inorg. Chem. (U.S.S.R.), 3, 100 (1958). 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. ‘F 112 M. C. Steele, Austral. J. Chem., 19, 367 (1957). J. L. Hoard and J. V. Silverton, Inorg. Chem., 2“ 235 (1963). T. Ueki, A. Zalkin and D. H. Templeton, Acta Cryst., 29, 836 (1966). C. J. Brown, ibid., 2, 167 (1949). F. E. Wickman, Arkiv Mineral. Geol., 1, 95 (1949). R. L. Sass, R. Vidale and J. Donahue, Acta Cryst., 19, 567 (1957). W. Klemm and H. A. Klein, Z. Anorg. Allgem. Chem., 248, 167 (1941). W. H. Zachariasen, Acta Cryst., 4, 231 (1951). F. Hund, Z. Anorg. Allgem. Chem., 265, 62 (1951). F. Hund, ibid., 273, 312 (1953). L. Mazza and A. Iandelli, Atti accad. ligure sci. e lettere, Z” 44(1951); C. A., 41” 4194 (1953). A. Zalkin and D. H. Templeton, J. Am. Chem. Soc., 15, 2453 (1953). D. H. Templeton and C. H. Dauben, ibid., 16, 5237 (1954). A. I. Popov and G. E. Knudsen, ibid., p 3921. N. C. Baenziger, J. R. Holden, G. E. Knudsen and A. I. POpOV, ibid., p 4734. K. S. Vorres and R. Riviello in "Rare Earth Research IV," Gordon and Breach, New York, 1964, p. 521. L. R. Batsanova and G. N.~Kustova, Russ. J. Inorg. Chem. (Eng. Transl.), 9, 181 (1964). N. V. Podberezskaya, L. R. Batsanova and L. S. Egorova, J. Struct. Chem., (U.S.S.R.)(Engl. Transl.), 6, 815 (1965). B. Holmberg, Acta Chem. Scand., 20, 1082 (1966). . Kutek, Russ. J. Inorg. Chem. (Eng. Transl.), 9, 1499 (1964). H. E. Swanson and E. Tatge, Nat. Bur. Std. (U.S.), Circ. 539, Vol. I, p. 31. 60. 61. 62. 63. 64. 65. 66. 67. 113 D. K. Smith, Norelco Reptr., 19” 19 (1963). W. J. Campbell, U.S. Bur. Mines, Inform. circ., 8107. (1962). A. J. Majumdar and R. Roy, J. Phys. Chem., 69, 1684 (1965). M. J. Buerger, "Crystallographic Aspects of Phase Transformations," in “Phase Transformations in Solids," R. Smoluchowski, J. E. Mayer and W. A. Weyl, Eds., John Wiley and Sons, New York, 1951, p. 183. J. M. Short and R. Roy, J. Phys. Chem., 61, 1860 (1963). H. Lipson and W. Cochran, "The Determination of Crystal Structures," Vol. III in "The Crystalline State," L. Bragg, Ed., Cornell University Press, Ithaca, New York, 1966, p. 340. J. S. Rollett, Ed., "Computing Methods in Crystal- lography," Pergamon Press, Oxford, (1965). R. A. Sparks, R. J. Prosen, F. H. Kruse and K. N. True- blood, Acta Cryst., g, 350 (1956). APPENDICES 114 APPENDIX I Crystallographic Computer Programs A. A. Zalkin's Incor Program This program reduces raw intensities for input to the fourier or least—squares programs. Input parameters define the system under study. Goniostat or Weissenberg data are corrected for Lorentz and polarization or Lorentz, polari- zation and velocity effects respectively, after the compu- tation of sin2 6 and sin G/A for each reflection from reciprocal lattice relations. The reciprocal of the Lorentz- polarization factor is calculated from, l/LP = 2 sin 6 cos 6/(1 + cos2 26) and the velocity correction from 1/2 V = (1 — (bk/2a sin 6)2] /(sin 6) where a is the axis and h the corresponding index. Pro— visions are also available to scale the data and correct for Ka and Kg splitting in spectrometric data. The abso- 1 2 lute value of the structure factor, F, is calculated as the square root of the corrected intensity, [F]2 B. Zalkin's Least-Squares Program The method of least-squares is used to minimize with respect to atomic position, temperature parameters and over- all scale factor the function: 115 116 R = 2 wh(]F0|h — l/K [Fclh)2 = z wh (dei)2 h h where h is the index hkfi, wh is the weight of the obser— vation, IFOIh is the observed structure factor, chlh the theoretical structure factor and 1/K is the scale factor. Discussions of the method appear in references 65-67. It may be shown that the 5 linear weighted observational equations of the form; .55. 13' "848 laijpj = 737i 91' which relate the m parameters pj to the observation gi, and wi is the weight, may be reduced to m normal equations of the form; It is common to express the observational and normal equa- tions in matrix form as A 2.: g_ and A?A_g_= A? g_ respec— tively where the matrix A?A_is symmetric and positive. The solution of the normal equations minimizes the (g.- A_§)T (§_- A_P), the sum of squares of residuals. The structure factor chlh depends on parameters non- linearly. However, if an approximation of the parameters is known, linear observational equations may be formed of the type, m d(|F I /K) c h - jglaJw. dp Apj -;Jwi (|F0|h - 1/K|Fc|h) j 117 where Apj are the corrections to the parameters and may be T represented by A_P_= B, The normal equations are A A_§ 3 A?B_where element (ATA)jj. is Z w leclh leclh h d . d ., h p: p] and element (ATB)j is leclh pi % wh(K|Folh — IFclh) Solution to the normal equations for the corrections gives improved values for the parameters. -More than one iteration is usually necessary since the initial observational equa— tions are approximate. The standard deviations of the parameters are given by where ij is jth diagonal element of the matrix (A?A)-1 and A1 is (KIFOIh - [FC|h)i. 118 A general flow chart for Zalkin's Least-Squares routine is given below. Initial input< 1) Input FOh (2) Start Next Cycle No ) No (3) Calculate and a chlh lecl/dpj(4) Form and accumulate all products (leCl/dpj)(d|FC|/dpj')(5) Has last reflection been calc.? Yes Solve normal equations Add all shifts to parameters and replace previous parameters Has last cycle been calc.? I Yes Calculate standard deviations 119 (1) Initial input data: Includes unit cell parameters, atomic scattering factors, equivalent positions of space group and parameters of atoms to be refined. (2) IFOIh; h,k,£, (Fol, l/w, and sin 9/1. H "513 m m H : 2' 2 . (3) chlh JA£ + Bh where A cos 2? (h ri) h and m B = 2 f. e 1 sin 2? (h'ri) Where Ti : h2(b11) i + k2(b22) + 32(b33)i + 2hk(b12) + i i 2h£(b13)i + 2k£(b23)i or 3 Bsin2 6/12, m = total number of atoms per unit cell, ri = position of atom i, f. = l scattering factor of atom i. (4) leCIh/d(1/K) = Wchlh dAh B dB le | /d = w Ah + h h c h pi chlh dpi TFCIEV dpi the (NPAR + 1) term = w(|Fo| - 1/KIFCI) = w(del) (5) Terms of normal equations. S A(II JJ) = Z (Deriv). (Deriv)., i=1 3 3 form lower triangular matrix of order (NPAR + 1) _ 2 A(1 1) Z wlFC] NPAR + 1)(NPAR + 2) 2 A[( ] = E w del: l APPENDIX II X-Ray Powder Diffraction Data 120 121 Table XVI. X-Ray powder diffraction data for NdO.73F1.54_ No hkz d ca1cd* d obs 1/10 1 001 5.720 —— — 2 101 3.286 3.283 100 3 002 2.860 2.858 20 4 110 2.838 2.835 35 5 111 2.543 2.545 1 6 102 2.322 2.328 7 7 - -- 2.228 1 8 112 2.015 2.012 66 9 200 2.007 1.998 15 10 003 1.907 1.904 1 11 201 1.894 —- - 12 103 1.722 1.717 24 13 211 1.713 1.709 13 14 202 1.643 1.645 5 15 — -- 1.636 5 16 113 1.583 1.582 2 17 212 1.520 1.520 2 18 004 1.430 1.429 2 19 220 1.419 1.417 5 20 203 1.382 1.382 1 21 221 1.377 —- - 22 104 1.347 1.346 2 23 213 1.307 1.307 7 24 301 1.303 1.304 9 25 - -- 1.296 2 26 114 1.277 1.276 3 27 222 1.271 1.270 4 28 310 1.269 1.266 1 29 311 1.239 -- - 30 302 1.212 -- — 31 204 1.165 1.164 2 32 312 1.160 1.161 7 33 005 1.144 -- - 34 223 1.138 1.137 1 35 214 1.119 1.118 2 36 320 1.113 1.113 1 37 105 1.100 38 303 1.095} 1'098 2 39 321 1.093 1.093 3 *a 4.014 R and c = 5.720 R. 122 '** Table XVII. X-Ray powder diffraction data for NdO.85F1.3 No. hkg d calcd* d obs I/Io 1 001 5.704 -- - 2 101 3.275 3.270 100 3 002 2.852 2.848 13 4 110 2.828 2.824 22 5 111 2.534 2.529 2 6 102 2.322 2.320 5 7 112 2.008 2.005 41 8 200 2.000 1.996 18 9 003 1.901 1.899 2 10 201 1.887 1.886 1 11 103 1.717 1.717 13 12 211 1.707 1.705 24 13 202 1.637 1.635 5 14 113 1.578 1.577 2 15 212 1.515 1.513 2 16 004 1.426 1.425 1 17 220 1.414 1.412 4 18 203 1.378 1.377 2 19 221 1.373 -- - 20 104 1.343 1.342 2 21 213 1.303 1.302 6 22 301 1.298 1.296 4 23 114 1.273 1.272 1 24 222 1.267 1.266 3 25 310 1.265 1.262 3 26 311 1.235 -— - 27 302 1.208 -- - 28 204 1.161 1.160 2 29 312 1.156 1.156 5 30 005 1.141 -- — 31 223 1.135 -— - 32 214 1.115 1.115 2 33 321 1.089 1.088 5 * a = 3.999 R and c = 5.704 R, ** Stoichiometry approximate. 123 Table XVIII. X-Ray diffraction powder diffraction data for Gd0.72F1.58 No hkfl d calcd* d obs I/Io 1 001 5.528 5.529 5 2 - —- 3.900 1 3 101 3.228 3.228 100 4 110 2.812 2.810 25 5 002 2.764 2.764 - 6 111 2.506 2.512 1 7 102 2.270 2.269 12 8 200 1.988 1.987 21 9 112 1.971 1.972 37 10 201 1.871 1.870 4 11 003 1.843 1.843 2 12 - -- 1.769 1 13 211 1.693 1.693 20 14 103 1.672 1.672 14 15 202 1.614 1.613 7 16 113 1.541 1.542 5 17 212 1.496 1.496 2 18 220 1.406 1.406 2 19 004 1.382 1.382 3 20 221 1.363 —- — 21 203 1.352 1.352 1 22 104 1.305 1.305 2 23 301 1.289 1.209 2 24 213 1.280 1.280 4 25 310 1.258 1.257 2 26 222 1.253 1.253 1 27 114 1.240 1.240 1 28 311 1.226 -- — 29 302 1.195 1.196 1 30 312 1.145 1.146 5 31 204 1.135 1.135 2 32 223 1.118 -— - 33 005 1.106 —— - 34 320 1.103 —— - 35 214 1.091 1.091 4 *a = 3.977 R and c = 5.528 R. 124 Table XIX. X-Ray powder diffraction data for DyO‘77F1.46 No hkz d calcd* d obs I/Io 1 001 5.451 -- - 2 101 3.190 3.191 100 3 110 2.781 2.782 27 4 002 2.726 2.727 9 5 111 2.477 2.479 1 6 102 2.240 2.242 13 7 200 1.966 1.967 20 8 112 1.947 1.948 32 9 201 1.850 1.851 2 003 1.817 1.818 5 211 1.674 1.675 24 103 1.650 1.650 13 202 1.595 1.595 8 113 1.521 1.522 5 212 1.478 1.479 4 220 1.391 1.391 4 004 1.363 1.364 1 221 1.347 1.348 1 203 1.335 1.335 1 104 1.288 1.288 5 301 1.275 1.275 4 213 1.264 1.265 7 310 1.244 1.245 2 222 1.239 -- - 114 1.224 1.226 1 311 1.213 -- - 302 1.181 -— - 312 1.132 1.132 6 204 1.120 1.120 2 *a = 3.933 R and c 5.451 R. 1.11. ‘1‘ III I Ill-’1‘]. I. 11 125 ** Table XX. *X—Ray powder diffraction data for ErO.85F1 5 No hkz d ca1cd* d obs 1/10 1 001 5.400 5.405 5 2 — -- 3.834 2 3 101 3.158 3.161 100 4 110 2.753 2.753 26 5 002 2.700 2.701 9 6 111 2.453 2.454 1 7 102 2.219 2.218 13 8 - -- 2.180 1 9 200 1.947 1.950 19 10 112 1.928 1.928 27 11 201 1.831 1.832 2 12 003 1.800 1.800 2 13 - 1.787 1 14 - 1.734 2 15 211 1.657 1.657 22 16 103 1.634 1.634 10 17 202 1.580 1.579 7 18 113 1.507 1.506 7 19 212 1.468 1.463 1 20 220 1.377 1.375 2 21 004 1.350 1.349 1 22 221 1.334 1.336 1 23 203 1.322 1.322 2 24 104 1.276 1.276 3 25 301 1.262 1.262 4 26 213 1.251 1.251 3 27 f 310 1.231 1.230 2 28 222 1.226 1.225 2 29 114 1.212 1.212 1 30 ‘ 311 1.200 -- — 31 302 1.170 1.170 1 32 312 1.120 1.120 3 33 204 1.109 1.110 1 34 223 1.093 -- - 35 005 1.080 36 320 1.080} 1°°8° 1 37 214 1.067 1.067 3 38 321 1.059 1.060 2 “X— a = 3.893 R and c = 5.400 R. ** Stochiometry approximate. 126 Table XXI. X-Ray powder diffraction data for ErO.80F1.40 No hkfl d calcd* d obs 1/10 1 001 5.385 5.385 8 2 - -- 3.818 2 3 - -- 3.754 1 4 101 3.162 3.163 100 5 110 2.762 2.764 22 6 002 2.692 2.694 15 7 - -- 2.515 1 8 111 2.458 2.461 1 9 - -- 2.360 1 10 102 2.217 2.218 13 11 - -- 2.161 1 12 200 1.953 1.954 18 13 112 1.928 1.928 30 14 201 1.836 1.838 1 15 003 1.795 1.795 3 16 - -- 1.775 2 17 - -- 1.737 2 18 211 1.662 1.662 20 19 103 1.631 1.631 12 20 202 1.581 1.581 7 21 - -- 1.519 1 22 113 1.505 1.504 5 23 212 1.466 1.466 1 24 - -- 1.423 1 25 220 1.381 1.382 5 26 004 1.346 1.346 1 27 221 1.338 1.340 2 28 203 1.322 1.322 2 29 104 1.273 1.273 3 30 301 1.266 1.265 2 31 213 1.252 1.252 3 32 310 1.235 1.235 1 33 222 1.229 1.230 2 34 114 1.210 1.210 1 35 311 1.204 -- - 36 302 1.172 -- - 37 312 1.123 1.123 2 38 204 1.108 1.109 1 39 223 1.095 -- - 40 005 1.077 -- - 41 214 1.066 1.067 2 42 321 1.062 1.063 2 *a = 3.907 R and c = 5.385 R. 127 Table XXII. X-Ray powder diffraction data for LaOF and NdOF L aOF NdOF hkz d ca1cd* d obs I/Io d caicdH d obs 1/10 111 6.737 -- - 6.567 -- — 100 3.456 -- — 3.373 -- - 222 3.368 3.365 34 3.283 3.274 36 110 3.314 3.316 100 3.234 4.234 100 211 2.882 2.883 34 2.811 2.810 36 221 2.650 2.650 3 2.584 2.583 3 333 2.246 2.246 2 2.189 2.187 3 322 2.229 2.230 4 2.174 2.174 4 332 2.050 2.051 37 1.999 1.997 32 101' 2.026 2.026 38 1.976 1.978 35 210 1.940 1.941 1 1.893 -- — 43E_ 1'751 1.751 13 1'7°8 1.706 11 111 1.748 1.705 321 1.736 1.735 27 1.693 1.694 26 200 1.728 1.730 20 1.686 1.689 25 444 1.684 1.684 1 1.641 1.642 2 220 1.657 1.657 6 1.617 1.618 6 443 1.628 1.628 2 1.587 1.587 2 311 1.609 -- - 1.570 -- - 432 1.504 1.505 3 1.467 1.466 3 331 1.499 1.501 3 1.462 422 1.441 1.441 6 1.405 1.405 8 544 1.421 1.423 1 1.386 1.386 555 1.347 1.349 1 1.313 1.313 1 554 1.335 1.334 2 1.302 1.301 2 433 1'325 1.324 4 1'292 1.291 2 201 1.323 1.291 211' 1.315 1.315 9 1.283 1.284 a = 7.132 R and a = 33.010. **a = 6.953 R and a = 33.040. 128 Table XXIII. X-Ray powder diffraction data for SmOF and EuOF SmOF EuOF hk£ d ca1cd* d obs I/Io d caicd** d obs 1/10 111 6.483 -- - 6.450 —- — 100 3.334 -— - 3.312 -— - 222 3.242 3.247 31 3.225 3.228 32 110 3.196 3.201 100 3.176 3.182 100 211 2.777 2.782 40 2.761 2.764 35 221 2.553 2.556 3 2.538 2.538 4 333 2.161 2.163 3 2.150 2.151 4 322 2.147 2.151 5 2.135 2.136 6 332 1.974 1.976 31 1.963 1.964 35 101 1.954 1.956 38 1.941 1.943 39 210 1.870 1.872 1 1.859 1.861 1 433_ 1.686 1.685 12 1.677 1.677 12 111 1.685 1.675 1.675 7 321 1.673 1.674 25 1.663 1.665 26 200 1.667 1.668 21 1.656 1.659 21 444 1.621 1.623 1 1.612 1.613 1 220 1.598 1.599 6 1.588 1.589 6 443 1.567 1.568 2 1.559 1.559 4 311 1.551 1.551 1 1.542 1.543 2 432 1.449 1.451 2 1.441 1.441 4 331 1.445 1.446 2 1.436 1.435 1 422 1.389 1.386 10 1.380 1.381 7 544 1.368 1.369 1 1.361 1.362 2 555 1.297 -- — 1.290 1.290 1 554 1.285 1.286 2 1.278 1.279 4 442 1.276 1.281 2 1.268 1.268 2 201 1.276. 1.268 1.268 2 211 1.268 1'272 6 1.260 1.260 7 a a: 6.827 R and a 6.865 R and a = 33.070. = 33.05°. 129 Table XXIV. X-Ray powder diffraction data for GdOF and TbOF GdOF TbOF hk£ d calcd* d obs I/Io d calcd** d obs I/Io 111 6.420 -— — 6.383 -— - 100 3.299 -- - 3.276 -- - 222 3.212 3.210 34 3.192 3.188 31 110 3.163 3.161 100 3.141 3.142 100 211 2.749 2.748 39 2.731 2.731 34 221 2.528 2.527 4 2.511 2.510 2 333 2.141 2.140 3 2.128 2.126 2 322 2.126 2.126 3 2.112 2.113 2 332 1.955 1.954 46 1.943 1.943 31 101 1.933 1.934 37 1.920 1.921 34 210 1.810 1.850 1 1.838 1.841 1 433_ 1.670 1.671 6 1.659 1.658 10 111 1.668 1.669 12 1.656 321 1.656 1.656 24 1.645 1.645 22 200 1.649 1.649 21 1.638 1.640 20 444 1.606 1.604 1 1.596 1.593 1 220 1.581 1.581 6 1.570 1.572 5 443 1.552 1.551 3 1.542 1.542 2 311 1.535 -- - 1.525 -— - 432 1.435 1.435 4 1.425 1.426 3 331 1.430 1.431 3 1.421 1.422 2 422 1.375 1.375 7 1.365 1.366 8 544 1.355 1.355 1 1.347 1.347 3 555 1.285 1.286 1 1.277 -- - 554 1.273 1.273 3 1.265 1.266 2 442 1.264 1.265 3 1.255 1.256 2 201 1.263 1.261 1 1.254 -- - 211 1.255 1.255 9 1.246 1.248 7 *a = 6.800 R and a = 33.05°. **a = 6.758 R and a = 33.020. 130 Table XXV. X-Ray powder diffraction data for DyOF and YOF DyOF YOF hkz d caicd* d obs 1/10 d caicd** d obs 1/10 111 6.343 — - 6.323 —- — 100 3.261 - - 3.265 -— - 222 3.172 3.166 33 3.162 3.148 25 110 3.126 3.125 100 3.129 3.110 68 211 2.717 2.718 39 2.717 2.701 15 221 2.498 2.496 5 2.496 2.482 2 333 2.114 2.120 6 2.108 2.100 2 322 2.101 2.100 11 2.098 2.088 4 332 1.932 1.931 51 1.929 1.918 25 101 1.911 1.911 52 1.914 1.900 28 210 1.830 —- - 1.832 -- — 433 1.650 1.651 13 1.646 1.638 7 111 1.649 1.646 11 1.651 321 1.637 1.636 42 1.637 1.622 15 200 1.631 1.631 36 1.632 1.621 14 444 1.586 1.583 4 1.581 1.574 1 220 1.563 1.564 13 1.564 1.555 3 443 1.533 1.532 8 1.530 1.523 1 311 1.518 - - 1.519 -- - 432 1.418 1.418 8 1.417 1.408 2 331 1.414 1.412 4 1.414 -- - 422 1.359 1.358 16 1.358 1.356 5 544 1.339 1.338 4 1.336 1.330 1 555 1.269 1.271 2 1.265 1.260 1 554 1.257 1.258 2 1.254 -- - 442 1.249 1.250 10 1.248 201' 1.248 1.248 6 1.250 1'249 1 211' 1.240 1.240 8 1.242 1.241 1 *a = 6.716 R and a = 33.07°. Ha = 6.697 R and a = 33.200. 131 Table XXVI.’ X-Ray powder diffraction data for HoOF and ErOF HoOF ErOF hkz d caicd* d obs I/IO d caicd** d obs 1/10 111 6.278 -- — 6.258 -- - 100 3.234 -- - 3.224 -- — 222 3.139 3.148 34 3.129 3.139 35 110 3.100 3.108 100 3.091 3.097 100 211 2.693 2.704 32 2.685 2.691 36 221 2.475 2.485 3 2.467 2.481 3 333 2.093 2.090 6 2.086 2.094 3 322 2.081 2.075 2.080 5 332 1.913 1.920 32 1.907 1.912 32 101 1.895 1.901 38 1.890 1.893 36 210 1.814 1.820 1 1.809 1.814 1 111 1.635 1.630 433 1.634 1.640 9 1.629 1.633 10 321 1.622 1.626 22 1.618 1.620 23 200 1.617 1.622 20 1.612 1.612 21 444 1.570 1.576 1 1.565 1.570 1 220 1.550 1.555 5 1.545 1.548 5 443 1.518 1.525 1 1.513 1.517 2 311 1.505 -- - 1.500 1.503 1 432 1.405 1.409 2 1.400 1.404 3 331 1.401 —- - 1.397 1.401 2 422 1.346 1.351 7 1.342 1.346 7 544 1.326 1.332 2 1.321 1.325 2 555 1.256 -- - 1.252 1.255 1 554 1.245 1.250 1 1.241 1.244 2 201 1.238 1.234 442 1.237 1'243 2 1.234 1°236 3 211 1.230 1.235 6 1.226 1.228 6 6.647 8 and a 6.628 R and a 33.15°. 33.14°. .— ,,_,—_- _ ATE UNIVERSITY L 93 03103 924 RAlRIES 5 "11(1)