------------- ., JOURNAL OF RESEARCH of the National Bureau of Standards - A. Physics and Chemistry Vol. 70A, No.5, September-October 1966 Crystal Structure of BaGe [ Ge3 0 9 Jand Its Relation to Benitoite I I C. Robbins, A. Perloff, and S. Block ~ ( Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234 I (May 23, 1966) BaGe[Ge30gl is trigonal, space group P3, with lattice constants a= 11.61, c=4.74 A, and Z =3. The structure was established by three·dimensional Patterson and electron density syntheses. Three·dimensional least·squares refinement resulted in a final R value of 6.8 percent (observed data only). The previously proposed structural relationship of this compound with benitoite, BaTiSbOg, has been confirmed. The structure can be considered as composed of Ge30g rings, in which the Ge is tetrahedrally coordinated, linked through octahedrally coordinated Ge atoms to form a three·dimen· sional Ge·O network. All Ge polyhedra are linked by corner sharing. The Ba ions occupy positions in channels of the network. Key Words: Barium tetragermanate, structure, benitoite, crystal, x·ray. 1. Introduction Robbins and Levin [lJ. Their data plus the space group information are: The synthesis of three germanates of formula type MeGe4 0g (Me = Sr, Pb, Ba) was reported by Robbins a=lL61 A w= L797±0.003 and Levin [lJ .1 A comparison of indexed powder c=4.74A E= 1.783 ± 0.003 patterns suggested that the compounds were isostruc­ S.G.=P3 p (obs) = 5.1 gcm - 3 turaL This was later confirmed by Eulenberger, Z =3 p (calc) = 5.12 gcm- 3 Wittman, and Nowotny [2]. In addition, they re­ ported the synthesis of two forms of CaGe4 0g desig­ No systematic absences were observed. Preces.§.ion nated a and {3, and found the a form was isostructural films were consistent with space groups P3ml or P3mL with (Sr, Pb, Ba) Ge40g. No satisfactory structure could be derived in these Crystal chemical considerations (Robbins and Levin space groups. The possible space groups P3 or P3 [1]) suggested a structural relationship with the were then considered. The centrosymmetric choice mineral benitoite, BaTiSbOg, whose structure was could be eliminated on the basis of packing considera­ determined by Zachariasen [3J. Comparison of pat­ tions because of the short c dimension. The assump­ terns of 1:4 germanates with indexed benitoite powder tion that the space group is P3 was confirmed by the data supported this view. From these observations final structure. and a consideration of unit cell dimensions, a trial Integrating Weissenberg films of levels h k l with structure for the tetragermanates was obtained (Rob­ l = 0, 1,2,3,4 were taken with Zr-filtered MoKa radia­ bins and Levin [I]). To test the validity of the pro­ tion (A = 0.7107 A) using the multiple film technique. posed model, the structure of BaO· 4GeOz was Intensities were measured with a densitometer com­ determined. parator. Very weak reflections were estimated visually. The intensity data were obtained from a 2. Experimental Data crystal approximately rectangular in cross section with dimensions of 0.043 mm, 0.066 mm, and a length of 0.189 mm. The linear absorption coefficient for Single crystals in the form of needles elongated along molybdenum radiation is 222.41 cm -I. [00l] were obtained by slowly cooling a melt of com­ Lorentz and polarization factor corrections were position BaGe4 0g from slightly above the congruent melting point of 1392 ± 5 0c. applied. Since the main objective of the study was Unit cell dimensions, density measurements, and the determination of positional parameters, no correc­ optical data for this compound were reported by tions for absorption errors were made. The latter would be expected to affect, primarily, the thermal parameters. The data consisted of 327 observed and I Figures in brackets indicate the literature references al the end of this paper. 435 unobserved independent reflections. 385 TABLE 1. Final atomic parameters' x ajx) Y aiY) z aiz) B aiB) I )' Ba 0.3341 0.0004 0.3334 0.0005 0.0 1.0265 0.0526 I Ge(1 ) .0 .0 -.0928 0.0034 0.3509 .222 1 Ge(2) .6667 .3333 .0062 .0038 .5501 .1798 Ge(3) .3333 .6667 .1024 .0031 .2 158 .1867 Ge(4) .8 148 .0007 .8200 .0006 .4 111 .0025 .3859 .1 570 Ge(5) .6674 .0007 .5131 .0006 .5051 .0034 .1402 .0864 Ge(6) .5 180 .0006 .6719 .0007 .5929 .0025 .3680 .1275 0(1) .8459 .0032 .9286 .0035 .1193 .0075 - .4341 .4651 0(2) .5843 .0046 .4074 .0047 .2 158 .0106 1.1 598 .75 27 0(3) .7746 .0033 .6524 .0033 .3 101 .0078 - 0.1996 .5040 0(4) .5505 .0035 .5561 .0035 .6965 .0080 .0655 .5479 0 (5) .4743 .0056 .7350 .0058 .8978 .0127 2.2502 .936 1 0(6) .9264 .0038 .8428 .0036 .6430 .0082 0.0008 .5266 0 (7) .6650 .0069 .8081 .0068 .4927 .0175 3.0732 1.2087 0(8) .4059 .0043 .5880 .0041 .3274 .0091 1.0008 0.6433 0(9) .7525 .0048 .4844 .0046 .7472 .0\03 l.l328 .7087 a The standard deviations are deri ve d from th e full -matrix least-squares refinement. 3. Structure Determination unrealistic temperature factors was considered. A second least-squares refinement was made in which, Similarities in the x-ray powder patterns and unit cell alternately, scale and position parameters were varied dimensions of benitoite (BaTiSbOg) and BaO '4GeOz for 2 cycles with fix ed temperature factors and then led Robbins and Levin [1] to suggest that barium temperature factors were varied for 2 cycles with fix ed germanate probably exists as BaGeGe30g in a struc­ scale and position parameters. This was repeated tural arrangement closely related to that found for for a total of eight cycles. The result was identical benitoite by Zachariasen [3]. The large number of with the first refinement to within one standard de via­ unobserved reflections obtained in the present study tion. Therefore, only the parameters from the first was consistent with the proposed relationship provided refinement are given in this paper. Observed and the Ba and Ge atoms had x and y parameters near 113 calculate d structure factors are reported in table 2. and 2/3 and z parameters near 0 or 1/2 in the german ate Atomic scattering factors for neutral Ge and 0- 1 ...:ei~ . In benitoite Ba, Ti, and the Sia09 rings all are were taken from International Tables for X-ray ) on, or around threefold axes. The lower symmetry of Crystallography (1962). Values for Ba+2 were taken the germanate permits, at most, only one of the cor­ from Thomas and Umeda [4]. The barium and ger­ responding atoms or groups to be on a threefold axis. manium form factors were corrected for dispersion A three-dimensional Patterson function was com­ (International Tables for X-ray Crystallography, 1962). puted and peaks corresponding to Ba-Ba and Ge-Ge vectors were identified and related to the proposed model. On the basis of the trial structure and space 4. Structure Description group P3, three choices of origin were possible i.e., at the center of a Ge309 group, at a Ba atom or at an A projection of the structure of BaO-4Ge02 along octahedrally coordinated Ge atom. Using coordinates [001] is shown in figure 1. Numbering of the atoms of Ba and Ge from the model, three cycles of Fourier of the asymmetric unit is consistent with table 1. refinement were calculated for each choice of origin. The structure is made up of rings of three Ge04 Only the model with a Ge atom at the origin on a three­ tetrahedra linked together by Ge06 octahedra_ Bar­ fold axis refined satisfactorily. Using phases based on ium atoms are located in channels of the network. Ba and Ge positions from the Fourier refine ment, a Germanium atoms 1, 2, and 3 are octahedrally co­ 3-dimensional electron density map was calculated ordinated and lie on threefold axes. Germanium which yielded the oxygen coordinates. atoms 4, 5, and 6, in tetrahedral coordination, make The structure was refin ed by a full-matrix least­ up the Ge309 ring. Six rings are linked through a squares analysis of the 327 observed and 435 un­ germanium octahedron to form the germanium-oxygen observed reflections. The final conventional R value network. The two nonring oxygens of each of three based on the 327 observed independent reflections was e quivalent Ge04 tetrahedra are bonded to germanium 0.068. The total number of parameters varied was atoms above and below the ring to form Ge06 groups. 62 which included x, y, and z, an isotropic temperature Every germanium polyhedron shares all of its corners: factor for each atom and a scale factor for each level. Ge04 tetrahedra share only corners with other poly­ The final parameters from this refinement are listed in hedra with the exception of Ge (6), which shares one table 1. The temperature factors are not considered e dge with a barium polyhedron; each germanium meaningful, primarily because of absorption. The octahedron shares three edges with three different correlation matrix from this refinement indicated that barium polyhedra. many of the variables were correlated to a moderate The Ge3 09 ring, projected along [001J, is shown in degree (correlation coefficients on the order of 0.5 to figure 2. Interatomic distances, angles and standard 0.6). The possibility that this was the source of the deviations for the three germanium atoms in tetra- 386 - ~--~~---- Ge 0 o 0 FIGURE 1. [001] Projection of the BaGe [Ge30.] structure. The numberin g is that of table 1.