Werner H. Baur

Computer simulation of crystal structures applied to the solution of the superstructure of cubic silicondiphosphate

Abstract The superstructure of cubic SiP2O7 has a volume 27 times as large as the substructure of this compound. Because conventional methods failed in solving the superstructure, computer simulation of the structure was applied. Computer simulation depends on the accurate prediction of individual interatomic distances in a structure and on an appropriate weighting scheme. The predicted distances are treated as observations in a distance least-squares refinement, in which the positional coordinates of the atoms are varied until the calculated distances conform to the predicted values. Cubic SiP2O7 (a = 22.418A, space group Pa3, Z = 108, Dx = 3.22) has 50 atoms in the asymmetric unit. The initial R-value for the simulated structure was 0.18, which dropped to 0.061 after three cycles of least squares refinement using Fobsd = 1382. In the substructure, all Pue5f8Oue5f8P angles in the diphosphate groups are straight because of symmetry requirements, and the angles Pue5f8Oue5f8Si are 164°. In the superstructure, the average angle Pue5f8Oue5f8P is 150°; the average Pue5f8Oue5f8Si angle is 149°. The tendency to decrease these angles may be responsible for the formation of the superstructure. However, two diphosphate groups retain, even in the superstructure, the 180° configuration. Such a feature is usually only observed in high temperature polymorphs and is explainable as a positional disorder of bent P2O7 groups, or by the assumption of a highly anisotropic motion of the bridging oxygen atom. The silicon atoms in cubic SiP2O7 are octahedrally coordinated, as they are in the two monoclinic polymorphs of SiP2O7. However, the three modifications are topologically distinct from each other as can be proved by considering the three-dimensional nets on which the three structures are based.

The crystal structure of Li3.75Si0.75P0.25O4 and ionic conductivity in tetrahedral structures

The crystal structure of Li4−xSi1−xPxO4 (x = 0.25), a member of the solid solution series between Li4SiO4 and Li3PO4, was determined by X-ray diffraction and refined to an R = 0.038 for 478Fobs. The space group is P121m1 and the cell constants are a = 5.1157(6), b = 6.1162(9), c = 5.3088(8) A and β = 90.40(1)°. It is isostructural with disordered Li4SiO4 and with the substructure of ordered Li4SiO4. The ionic conductivity of Li3.75Si0.75P0.25O4 is more than three orders of magnitude higher than for ordered Li4SiO4 for which it is 10−5(Ωm)−1 at room temperature. All Li sites are only partially occupied. The highest probability of close Liue5f8Li approaches exists between the octahedral site and an adjoining tetrahedral location. These two sites define a lithium pathway parallel to the b-direction in the structure.

A three dimensionally periodic, eleven coordinated, dense packing of symmetry equivalent spheres

Abstract Symmetry equivalent equal size spheres can be packed in an array filling 71.87% of space. Each sphere in this packing has eleven neighbors at unit distance. The density of this tetragonal close packing is second only to closest packing with twelve coordination. Anions in numerous compounds, including some which are solid electrolytes, arrange themselves in this pattern. It occurs among others in rutiles, β-BeO, Li4GeO4 and CaSO4.

Observed wurtzite derivatives and related dipolar tetrahedral structures

Abstract Eight lower-symmetry ordered derivatives of the wurtzite type and an additional six related dipolar tetrahedral structure types were observed. All these structures are based on hexagonal closest packing of anions. Their mutual symmetry relationships can be summarized in a Barnighausen diagram. Dipolar tetrahedral structures are characterized by centrosymmetric space groups, thus resulting in a dipolar distribution of the coordination tetrahedra. Dipolar tetrahedral structures often exhibit disorder and random statistical occupations and several good ionic conductors are found among them. The wurtzite-type derivatives are characterized by polar space groups and all coordination tetrahedra in them are pointing in the same direction. Some simple, geometrically possible wurtzite derivatives have never been observed. Their absence can be rationalized on the basis of a poor geometrical fit between tetrahedral chains as demonstrated by computer simulations of their hypothetical structures. The ratio ϵ (quotient of the thickness of one hexagonal layer in [001] over one measure of the mean diameter of one atom within this layer) is useful for ordering the wurtzite derivatives on the basis of their chemical composition, since ϵ increases from the oxides, over the nitrides to the sulfides. The ϵ ratio also distinguishes clearly between the oxidic wurtzite types (0.79) and the tetrahedral rutile types of β-BeO derivatives (0.86), while the dipolar tetrahedral types have ϵ values around 0.82, that is, close to the value expected for hexagonal closest packing.

Solid Solutions between octahedral and tetrahedral olivine types in LiZn-germanates

The solid electrolytes Li2+2xZn1−xGeO4 (LISICON) are solid solutions between the HTue5f8Li3PO4 type and the olivine type. A reevaluation of the HTue5f8Li3PO4 data confirms that all Li is in tetrahedral coordination.

Enumeration of wurtzite derivatives and related dipolar tetrahedral structures

Abstract Polyas theorem and related results are used to count and classify by space group all possible wurtzite derivatives with small unit cells having composition ABX2, AB2X3, AB3X4, or ABC2X4. The same arguments are applied to the dipolar tetrahedral structures, which resemble wurtzite but have a different pattern of occupancy of the tetrahedral voids in the hcp anion framework. Covalent molecular orbital and electrostatic calculations are used to study the two real and eight hypothetical structures for Li3PO4. Both predict shared edges to be destabilizing, in keeping with Paulings rules.

Hexaaquocopper (II) ions in Tutton's salts

HEXAAQUOCOPPER (II) IONS IN TUTTONS SALTS Werner H. Baur Department of Geological Sciences University of lllinois at Chicago Chicago, lllinois 60680 (Received 3 A u ~ s t l~2J The EPR s p e c t r a o f s e v e r a l o f T u t t o n s s a l t s CuX2(YO4) 2.6HzO (whe re X i s NH4, K, Rb o r Cs ; Y i s S o r Se) h a v e b e e n m e a s u r e d and i n t e r p r e t e d as b e i n g c o n n e c t e d w i t h a r h o m b i c s y m m e t r y o f t h e l i g a n d f i e l d a r o u n d t h e Cu 2+ i o n s ( 1 , 2 , 5 ) , and n o t w i t h t h e more common t e t r a g o n a l f i e l d f o u n d u s u a l l y as a r e s u l t o f t h e J a h n T e l l e r d i s t o r t i o n a r o u n d Cu 2+. I n t e r e s t i n g l y t h e maximum g v a l u e s w e r e f o u n d t o be o r i e n t e d i n two d i f f e r e n t d i r e c t i o n s i n t h e d i f f e r e n t c o m p o u n d s . An i n s p e c t i o n o f t h e c r y s t a l s t r u c t u r e o f C u ( N H 4 ) 2 ( S O 4 ) 2 . 6 H 2 0 d e t e r m i n e d by n e u t r o n d i f f r a c t i o n (4) shows t h a t t h e d i r e c t i o n o f t h e maximum v a l u e o f g c o i n c i d e s w i t h t h e v e c t o r Cu-O(w7) i n t h e c r y s t a l s t r u c t u r e ( T a b l e l a ) . In t h e c r y s t a l s t r u c t u r e s o f CuK2(SO4)26H20 (5) and C u C s 2 ( S O 4 ) 2 . 6 N 2 0 (6) t h e maximum g v a l u e i s i n t h e d i r e c t i o n o f C u O ( w 8 ) . T h e r e f o r e , i n a l l t h r e e c a s e s t h e maximum g v a l u e i s w e l l a l i g n e d w i t h t h e l o n g e s t 2+ CuO(w) d i s t a n c e o f t h e Cu(OH2) 6 i o n . In s p i t e o f t h e p r o n o u n c e d d i f f e r e n c e s i n i n d i v i d u a l bond l e n g t h s , t h e a v e r a g e Cu-O(w) d i s t a n c e s a r e a l m o s t i d e n t i c a l i n t h e t h r e e s a l t s (maximum A = 0 . 0 0 8 ~ ) . Ghosh , P a l and B a g c h i (2) r e c o g n i z e d t h a t . . . t h e l i g a n d f i e l d n e a r . . . t h e Cu 2+ i o n . . . i s n o t d e p e n d e n t on t h e s i x n e i g h b o u r i n g w a t e r d i p o l e s a l o n e b u t a l s o upon how t h e more d i s t a n t n e i g h b o u r s a r e s i t u a t e d . . . . At t h e t i m e o f t h e i r w r i t i n g ( e a r l y 1965) no 2 + r e s u l t s o f t h e c r y s t a l s t r u c t u r e d e t e r m i n a t i o n s o f Cu c o n t a i n i n g T u t t o n s s a l t h~d b e e n p u b l i s h e d y e t . S i n c e t h e t h r e e a b o v e m e n t i o n e d compounds h a v e b e e n d e t e r m i n e d r e c e n t l y w i t h h i g h a c c u r a c y

Variation of mean SiO bond lengths in silicon-oxygen octahedra

Abstract The mean bond length Siue5f8O in silicon-oxygen octahedra is a function of the mean coordination number of the oxygen atoms (CN) in the octahedron: (Siue5f8O)mean = 1.729 + 0.013CN. The radius of Si in six coordination against oxygen is 0.407 A.