Die kristallstruktur des kaliumtetragermanats K2[Ge4O9]

Zusammenfassung Die Kristallstruktur des Kaliumtetragermanats, K₂[Ge₄O₉], wurde mit Hilfe dreidimensionaler Röntgendaten bestimmt. K₂[Ge₄O₉] kristallisiert trigonal mit der Raumgruppe P033034c1 (Nr. 165) und den Gitterparametern:a=11.84 undc=9.80 Å. Die vorgeschlagene strukturchemische Beziehung zum Wadeit, K₂Zr[Si₃O₉], wird durch die Existenz tetraedrischer [Ge₃O₉]-Ringe, die über [GeO₆]-Oktaeder zu einem dreidimensionalen Gerüst verknüpft sind, bestätigt. Es wurden folgende mittlere Ge–O-Abstände gefunden: 1.762 (Tetraeder) und 1.886 Å (Oktaeder).

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The crystal structure of potassium tetragermanate K₂[Ge₄O₉]

The crystal structure of potassium tetragermanate K₂[Ge₄O₉] has been determined by means of three-dimensional x-ray data. K₂[Ge₄O₉] crystallizes trigonal with space group P033034c1 (No. 165) and lattice parametersa=11.84 andc=9.80 Å. The proposed structural relationship to wadeite K₂Zr[Si₃O₉] is confirmed by the existence of [Ge₃O₉] rings built by tetrahedra, which are linked by [GeO₆] octahedra forming a three-dimensional network. The mean Ge–O distances are found to be: 1.762 (tetrahedra) and 1.886 Å (octahedra).

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Herrn Prof. Dr.H. Nowotny in Verehrung gewidmet.     

Synthesis and crystal structures of CaY2Ge3O10 and CaY2Ge4O12

New compounds CaY₂Ge₃O₁₀ and CaY₂Ge₄O₁₂ were prepared by heating mixtures of CaCO₃, Y₂O₃ and GeO₂ at 1200 °C. CaY₂Ge₃O₁₀ is stable at 1300 °C, while CaY₂Ge₄O₁₂ decomposes into a melt and CaY₂Ge₃O₁₀ at approximately 1250 °C. We obtained single crystals of CaY₂Ge₃O₁₀ by cooling a sample with an initial composition of Ca:Y:Ge=1:2:8 from 1300 °C with a rate of −6 °C/h. The crystal structure of CaY₂Ge₃O₁₀ was determined by single crystal X-ray diffraction. CaY₂Ge₃O₁₀ crystallizes in the monoclinic space group P2₁/c with a=6.0906(8), b=6.8329(8), and β=109.140(3)°, Z=4, and R₁=0.029 for I>2σ(I). In the structure of CaY₂Ge₃O₁₀, Ca and Y atoms are situated disorderly in three 7-fold coordination sites between isolated germanate groups of triple GeO₄ tetrahedra, Ge₃O₁₀. The structural formula of CaY₂Ge₃O₁₀ is expressed as (Ca_0.45Y_0.55)(Ca_0.46Y_0.54)(Ca_0.09Y_0.91)Ge₃O₁₀. The crystal structure of CaY₂Ge₄O₁₂ was analyzed by the Rietveld method for the X-ray powder diffraction pattern. CaY₂Ge₄O₁₂ is isotypic with SrNa₂P₄O₁₂, crystallizing in the orthorhombic space group P4/nbm, a=9.99282(6), , Z=2, R_wp=0.092, R_p=0.067. CaY₂Ge₄O₁₂ contains four-membered GeO₄-tetrahedra rings, Ge₄O₁₂. Eight-fold coordinated square-anitiprism sites and 6-fold octahedral sites between the layers of the Ge₄O₁₂ rings are occupied by Y atom and Ca/Y atoms, respectively The structural formula is Y(Ca_0.5Y_0.5)₂Ge₄O₁₂.     

Die Kristallstruktur des Tetragermanats K2Ba[Ge4O9]2

The crystal structure of the compound K₂Ba[Ge₄O₉]₂ has been determined by means of three-dimensional X-ray data resulting a finalR-value of 0.034. The lattice constants of the trigonal unit cell ( ) are:a=11.729 (I) andc=19.278 (3) Å. There is a close structural relationship to the tetragermanates K₂Ge₄O₉ and BaGe₄O₉. The new compound also consists of three-membered rings built up by [GeO₄] tetrahedra, which are linked by [GeO₆] octahedra forming a three-dimensional network.According to their powder diagrams the following compounds are isostructural to K₂Ba[Ge₄O₉]₂: Na₂Ba[Ge₄O₉]₂, Rb₂Ba[Ge₄O₉]₂, Na₂Sr[Ge₄O₉]₂ and K₂Sr[Ge₄O₉]₂.     

Die Kristallstruktur der Verbindung LiNa[Ge4O9]

Zusammenfassung Die Kristallstruktur der Verbindung LiNa[Ge₄O₉] wird durch dreidimensionale Patterson- und Fourier-Synthesen bestimmt und mit Hilfe der Methode der kleinsten Quadrate verfeinert. Die rhombische Elementarzelle (Pcca-D _2h ⁸ ) mit den Abmessungen:a=9,31,b=4,68,c=15,88 Å enthält 4 Formeleinheiten. Die Struktur wird aus [GeO₃] _n -Ketten mit tetraedrisch koordiniertem Germanium aufgebaut, die über [GeO₆]-Oktaeder zu einem dreidimensionalen Gerüst vernetzt sind. Als mittlere interatomare Ge-O-Abstände wurden erhalten: 1,758 [4] und 1,866[6] Å. Die Verbindung LiNa[Ge₄O₉] stellt ein Endglied der Mischreihe Li_2–x Na _x [Ge₄O₉] dar.

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Crystal structure of LiNa[Ge₄O₉]

The crystal structure of LiNa[Ge₄O₉] has been determined by means of three-dimensional Patterson and electron density syntheses and refined by least-squares methods. The orthorhombic unit cell (Pcca-D _2h ⁸ ) having the lattice parametersa=9.31,b=4.68 andc=15.88 Å contains 4 formula units. The crystal structure consists of [GeO₃] _n -chains of tetrahedrally coordinated Ge-atoms which are connected by [GeO₆]-octahedra to form a three-dimensional framework. The interatomic Ge-O-distances are found to be 1.758[4] and 1.866[6] Å. The compound LiNa[Ge₄O₉] represents a member of the solid solution series Li_2–x Na _x [Ge₄O₉].

     

M4Ge9O20碱金属锗酸盐晶体、玻璃及熔体结构的拉曼光谱研究

本文研究了M₄Ge₉O₂₀型锗酸盐(M=Na,K)273～1 373 K常温、高温及熔体拉曼光谱。应用量子化学从头计算方法计算了系列二元钠锗酸盐离子簇模型振动频率。M₄Ge₉O₂₀型锗酸盐晶体结构四配位锗、六配位锗共存。研究表明,随温度升高六配位锗将逐渐转变为四配位锗,产生非桥氧,并观察到在熔点以后全部转变为四配位锗,且其桥氧角分布范围为94～145°,其高频区非桥氧对称伸缩振动频率与其精细结构密切相关,振动频率等性质主要依赖于其精细结构而非其初级结构单元-GeO₄,非桥氧对称伸缩振动频率随锗氧四面体应力指数SIT(Stress Index of Tetrahedron)的增大而增大,与实验所得到的频率与SIT的线性关系一致。玻璃结构以四配位锗为主,存在少量六配位锗,其含量取决于冷速的大小。     

Structure, crystal chemistry and thermal evolution of the δ-Bi2O3-related phase Bi9ReO17

The thermal evolution and structural properties of fluorite-related δ-Bi₂O₃-type Bi₉ReO₁₇ were studied with variable temperature neutron powder diffraction, synchrotron X-ray powder diffraction and electron diffraction. The thermodynamically stable room-temperature crystal structure is monoclinic P2₁/c, a=9.89917(5), b=19.70356(10), c=11.61597(6) Å, β=125.302(2)° (R_p=3.51%, wR_p=3.60%) and features clusters of ReO₄ tetrahedra embedded in a distorted Bi–O fluorite-like network. This phase is stable up to 725 °C whereupon it transforms to a disordered δ-Bi₂O₃-like phase, which was modeled with δ-Bi₂O₃ in cubic Fm3¯m with a=5.7809(1) Å (R_p=2.49%, wR_p=2.44%) at 750 °C. Quenching from above 725 °C leads to a different phase, the structure of which has not been solved but appears on the basis of spectroscopic evidence to contain both ReO₄ tetrahedra and ReO₆ octahedra.     

Original close-packed structure and magnetic properties of the Pb4Mn9O20 manganite

The crystal structure of the Pb₄Mn₉O₂₀ compound (previously known as “Pb_0.43MnO_2.18”) was solved from powder X-ray diffraction, electron diffraction, and high resolution electron microscopy data (S.G. Pnma, a=13.8888(2) Å, b=11.2665(2) Å, c=9.9867(1) Å, R_I=0.016, R_P=0.047). The structure is based on a 6H (cch)₂ close packing of pure oxygen “h”-type (O₁₆) layers alternating with mixed “c”-type (Pb₄O₁₂) layers. The Mn atoms occupy octahedral interstices formed by the oxygen atoms of the close-packed layers. The MnO₆ octahedra share edges within the layers, whereas the octahedra in neighboring layers are linked through corner sharing. The relationship with the closely related Pb₃Mn₇O₁₅ structure is discussed. Magnetization measurements reveal a peculiar magnetic behavior with a phase transition at 52 K, a small net magnetization below the transition temperature, and a tendency towards spin freezing.     

A novel germanate, Cu2Fe2Ge4O13, with a four tetrahedra oligomer

The structure of Cu₂Fe₂Ge₄O₁₃, previously thought to be CuFeGe₂O₆, has been determined from single-crystal X-ray diffraction data to be monoclinic, P2₁/m, a=12.1050(6), b=8.5073(4), c=4.8736(2) Å, β=96.145(1)°, Z=2, with R1=0.0231 and wR2=0.0605. The unique structure has an oligomer of four germanate tetrahedra, cross-linked laterally by square-planar copper ions, joined end-to-end by a zigzag chain of edge-sharing iron oxide octahedra. Running along the a-direction the metal oxide chain consists of alternating Cu-Cu and Fe-Fe dimers. A hypothetical series of homologous structures (Cu_n−2Fe₂Ge_nO_3n+1 with n=3,4,…,∞) with different length germanate oligomers is proposed, where as n increases, the infinite chain of the CuGeO₃ is approached. In this context, Cu₂Fe₂Ge₄O₁₃ is viewed as being built from blocks of CuGeO₃ and the Fe oxide chains. This material has significance to the study of low-dimensional mixed-spin systems.     

Crystal structure and magnetic properties of Sr4Mn2NiO9

The crystal structure of Sr₄Mn₂NiO₉ has been refined on single crystal. This phase belongs to the series A_1+x(A^′_xB_1–x)O₃ (x=1/3) related to the 2H-hexagonal perovskite. The structure contains transition metals in chains of oxide polyhedra (trigonal prisms and octahedra); neighboring chains are separated from each other by the Sr atoms. The sequence of the face sharing polyhedra along the chains is two octahedra + one trigonal prism. Mn occupies the octahedra and Ni is disordered in the trigonal prism with ≈80% in the pseudo square faces of the prism and ≈20% at the centre. This result has been confirmed by XANES experiments at Mn K and Ni K edges, respectively. Sr₄Mn₂NiO₉ is antiferromagnetic with a Néel temperature at T=3 K. The Curie constant measured at high temperature is in good agreement with ≈80% of the Ni²⁺ ions in the spin state configuration S=0.     

Cluster self-organization of Na-TR-Ge-O-H (TR = La-Lu, Y, and Sc) germanate systems: Suprapolyhedral precursor clusters and self-assembly of Na2Pr6Ge8O26, Na4Sc2Ge4O13, and Na5ScGe4O12 crystal structures

In an M-T-O model system (M is a polyvalent metal; T = Ge or Si), we consider initial stages of formation of cyclic MT clusters and the mechanism of their modification by T tetrahedra. The polyhedron ratio T/M in clusters increases progressively during modeling from one in M₂T₂ to two (M₂T₂ + 2T = M₂T₄), three (M₂T₂ + 2T₂ = M₂T₆), and four (M₂T₂ + 2T + 2T₂ = M₂T₈). These types of clusters were used to find precursor clusters for T-condensed structures of Na₂Pr₆Ge₈O₂₆, Na₄Sc₂Ge₄O₁₃, and Na₅ScGe₄O₁₂. The TOPOS program package was used to carry out the complete 3D reconstruction of the self-assembly of Na,TR germanates: precursor cluster → primary chain → microlayer → microframework (supraprecursor) → ... framework. In all structures, as previously in six orthotetrahedral Na,TR germanate structures, the basic invariant type of four-polyhedral cyclic precursor cluster M₂T₂ was identified; this cluster is built of TR polyhedra, with CN = 6 or 7, linked via orthotetrahedra. The features of the generation of a Ge radical were considered in the form of a Ge₂O₇ chain and a Ge₄O₁₂ ring in various layers of the Na₂Pr₆Ge₈O₂₆ composite structure, a Ge₄O₁₃ chain in Na₄Sc₂Ge₄O₁₃, and a Ge₁₂O₃₆ ring in the Na₅ScGe₄O₁₂ superionic conductor. Original Russian Text ? G.D. Ilyushin, L.N. Dem’yanets, 2009, published in Zhurnal Neorganicheskoi Khimii, 2009, Vol. 54, No. 3, pp. 484–496.     

Die Kristallstruktur der Verbindung Cd2Ge7O16

The crystal structure of Cd₂Ge₇O₁₆ has been determined by means of three-dimensional single-crystal data. A finalR-value of 6.3% was obtained by least squares refinement based on 230 observed reflexions. The tetragonal unit cell with the lattice parametersa=11.31 andc=4.63 Å contains two formula units Cd₂Ge₇O₁₆. The compound is built up by [GeO₄]-tetrahedra and [GeO₆]-octahedra forming a three-dimensional framework with the Cd atoms located in the cavities. The average interatomic distances are found to be: Ge–O=1.74 (tetrahedra), 1.89 (octahedra) and Cd–O=2.36 Å.

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Die Kristallstruktur von Ge5O[PO4]6

Zusammenfassung Die Kristallstruktur der Verbindung Ge₅O[PO₄]₆ wurde auf Grund dreidimensionaler Einkristalldaten ausWeissenberg-Aufnahmen ermittelt und nach der Methode der kleinsten Quadrate verfeinert: Raumgruppe ;a=7,994±0,004 undc=24,87±0,01 Å;Z=3; 467 unabhängige Reflexe;R=0,086.Die Kristallstruktur wird aus singulären [GeO₆]-Oktaedern und [Ge₂O₇]-Doppeltetraedern aufgebaut, die über [PO₄]-Tetraeder zu einem dreidimensionalen Strukturverband vernetzt sind. Die mittleren Abstände betragen: Ge^[6]–O=1,863, Ge^[4]–O=1,704 und P–O=1,525 Å.

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The crystal structure of Ge₅O[PO₄]₆

The crystal structure of Ge₅O[PO₄]₆ has been determined and refined by least-squares, using three-dimensional x-ray data fromWeissenberg-photographs: space group ;a=7.994±0.004 andc=24.87±0.01 Å;Z=3; 467 independent reflections;R=0.086.The crystal structure consists of isolated [GeO₆] octahedra and [Ge₂O₇] double tetrahedra which are linked by [PO₄] groups forming a three-dimensional network. The average interatomic distances are: Ge^[6]–O=1.863, Ge^[4]–O=1.704 and P–O=1.525 Å.

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Synthesis and Crystal Structure of the First Fully Characterized Vanadoborate Na3[B6O9(VO4)]

Single crystals of synthetic Na₃VB₆O₁₃ were obtained by heating a mixture of Na₂CO₃.H₂O, V₂O₅, and H₃BO₃; its formula has been determined by the resolution of the structure from X-ray diffraction data. The compound is orthorhombic, space group P2₁2₁2₁; the unit cell parameters are a=7.723(7), b=10.155(4), c=12.505(4) Å, Z=4. The crystal structure was solved from 1535 reflections until R=0.029; it contains hexaborate units formed by three triangular BO₃ (3Δ) and three tetrahedral BO₄ (3T). These hexaborate groups are joined together to form sheets which are linked by VO₄ tetrahedra leading to a three-dimensional network. The shorthand notation of the vanadoborate ion is 6: ∞³ (3Δ+3T)+VO₄. The sodium atoms are inside the channels that exist in the compound, whose structural formula may be written Na₃[B₆O₉(VO₄)]. This compound melts incongruently; powder may be obtained by annealing a mixture of Na₂B₄O₇ and V₂O₅ at 630°C. It is the first vanadoborate for which the formula and the structure have been unambiguously established.     

Über die Silbergermanate Ag4Ge9O20 und Ag2Ge4O9

Zusammenfassung Der Germanat-Zeolith Ag₃HGe₇O₁₆·4 H₂O wird durch Ionenaustausch aus dem isotypen Ammonium-Zeolith hergestellt. Nach Dehydratation des Ag-Zeoliths bildet sich bei 460°C das zuMe ₄Ge₉O₂₀ (Me=Na, K) isotype Ag₄Ge₉O₂₀. Durch Erhitzen auf 650°C entsteht das zuMe ₂Ge₄O₉ (Me=Na, K, Rb, Tl) isotype Ag₂Ge₄O₉. Oberhalb 760°C erfolgt unter Dissoziation die Bildung von metallischem Silber und GeO₂ (Rutilform).

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The zeolithic germanate Ag₃HGe₇O₁₆·4 H₂O has been prepared by ion-exchange from the analogous ammonium compound. After dehydration at 460°C Ag₄Ge₉O₂₀ is formed, which is isostructural withMe ₄Ge₉O₂₀ (Me=Na, K). By heating up to 650°C Ag₂Ge₄O₉ is obtained, having the structure ofMe ₂Ge₄O₉ (Me=Na, K, Rb, Tl). Above 760°C the compound decomposes into silver, oxygen and GeO₂ (rutile).

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Structure and magnetism of NaRu2O4 and Na2.7Ru4O9

The structures of NaRu₂O₄ and Na_2.7Ru₄O₉ are refined using neutron diffraction. NaRu₂O₄ is a stoichiometric compound consisting of double chains of edge sharing RuO₆ octahedra. Na_2.7Ru₄O₉ is a non-stoichiometric compound with partial occupancy of the Na sublattice. The structure is a mixture of single, double and triple chains of edge-shared RuO₆ octahedra. NaRu₂O₄ displays temperature independent paramagnetism with . Na_2.7Ru₄O₉ is paramagnetic, χ₀= with and a Curie constant of 0.0119 emu/mol Oe K. Specific heat measurements reveal a small upturn at low temperatures, similar to the upturn observed in La₄Ru₆O₁₉. The electronic contribution to the specific heat (γ) for Na_2.7Ru₄O₉ was determined to be15 mJ/mole_Ru K².     

Structural study of the NaCdVO4-Cd3V2O8 and CdO-V2O5 sections of the ternary system Na2O-CdO-V2O5

The NaCdVO₄-Cd₃V₂O₈ and CdO-V₂O₅ sections of the ternary system Na₂O-CdO-V₂O₅ have been studied and the crystal structures of Cd₃V₂O₈ and Cd₁₈V₈O₃₈ compounds were determined from single-crystal X-ray diffraction data. Cd₃V₂O₈ crystallizes with the maricite-type structure in space group Pnma, a=9.8133(10) Å, b=6.9882(10) Å, c=5.3251(10) Å and Z=4, whereas Cd₁₈V₈O₃₈ crystallizes in space group P1 with a new-type structure, a=8.5761(14), b=8.607(3), c=12.896(2) Å, α=95.64(1), β=102.45(1), γ=108.42(1)° and Z=1. The Cd₃V₂O₈ structure is made up of Cd1O₄ infinite chains of edge-sharing Cd1O₆ octahedra which are parallel to the b direction. The Cd1O₄ chains are linked together by VO₄ tetrahedra and strongly distorted Cd2O₄ tetrahedra. The structure of Cd₁₈V₈O₃₈ is based on an ordered three-dimensional framework of cadmium and vanadium polyhedra that share corners. The distorted CdO₆ octahedra, CdO₅ trigonal bipyramids and CdO₅ square pyramids share corners, edges or faces.     

Cu2Sc2Ge4O13, a novel germanate isotypic with the quasi-1D compound Cu2Fe2Ge4O13 between 100 and 298 K

The germanate compound Cu₂Sc₂Ge₄O₁₃ has been synthesized by solid-state ceramic sintering techniques between 1173 and 1423 K. The structure was solved from single-crystal data by Patterson methods. The title compound is monoclinic, a=12.336(2) Å, b=8.7034(9) Å, c=4.8883(8) Å, β=95.74(2), space group P2₁/m, Z=4. The compound is isotypic with Cu₂Fe₂Ge₄O₁₃, described very recently. The structure consists of crankshaft-like chains of edge-sharing ScO₆ octahedra running parallel to the crystallographic b-axis. These chains are linked laterally by [Cu₂O₆]⁸⁻ dimers forming a sheet of metal-oxygen-polyhedra within the a-b plane. These sheets are separated along the c-axis by [Ge₄O₁₃]¹⁰⁻ units. Cooling to 100 K does not alter the crystallographic symmetry of Cu₂Sc₂Ge₄O₁₃. While the b, c lattice parameter and the unit cell volume show a positive linear thermal expansion (α=6.4(2)×10⁻⁶, 5.0(2)×10⁻⁶ and 8.3(2)×10⁻⁶ K⁻¹ respectively), the a lattice parameter exhibits a negative thermal expansion (α=−3.0(2)×10⁻⁶ K⁻¹) for the complete T-range investigated. This negative thermal expansion of a is mainly due to the increase of the Cu-Cu interatomic distance, which is along the a-axis. Average bond lengths remain almost constant between 100 and 298 K, whereas individual ones partly show both significant shortages and lengthening.     

The polar phase of Li2Ge4O9 at 298, 150 and 90 K

Dilithium tetragermanate is orthorhombic, space group P2₁ca, at 298 K, and is thus in a polar and probably a ferroelectric state. The structure contains two independent Li, four Ge and nine O atoms, all on general positions with site symmetry 1. Three tetrahedrally coordinated Ge positions form crumpled crankshaft‐like chains, forming sheets within the ac plane, and these are interconnected by the fourth, octahedrally coordinated, Ge sites along the b direction. The GeO₄ tetrahedra and GeO₆ octahedra form a three‐dimensional framework containing two different cavities, hosting the two 4+1‐coordinated Li sites. Cooling to 90 K does not alter the space‐group symmetry; the tetrahedral chains behave as a rigid unit and changes occur mainly within the Li coordination spheres.     

Multianvil high-pressure/high-temperature synthesis, crystal structure, and thermal behaviour of the rare-earth borogermanate Ce6(BO4)2Ge9O22

The new monoclinic cerium borogermanate Ce₆(BO₄)₂Ge₉O₂₂ was synthesized under high-pressure and high-temperature conditions in a Walker-type multianvil apparatus at 10.5 GPa and 1200 °C. Ce₆(BO₄)₂Ge₉O₂₂ crystallizes with two formula units in the space group P2₁/n with lattice parameters a=877.0(2), b=1079.4(2), c=1079.1(2) pm, and β=95.94(3)°. As the parameter pressure favours the formation of compounds with cations possessing high coordination numbers, it was possible to produce simultaneously BO₄-tetrahedra and GeO₆-octahedra in one and the same borogermanate for the first time. Furthermore, the cerium atoms show high coordination numbers (C.N.: 9 and 11), and one oxygen site bridges one boron and two germanium atoms (O^[3]), which is observed here for the first time. Besides a structural discussion, temperature-dependent X-ray powder diffraction data are presented, demonstrating the metastable character of this high-pressure phase.     

High-pressure preparation, crystal structure, and properties of the new rare-earth oxoborate β-Dy2B4O9

In this work we report about a new rare-earth oxoborate β-Dy₂B₄O₉ synthesized under high-pressure/high-temperature conditions from Dy₂O₃ and boron oxide B₂O₃ in a B₂O₃/Na₂O₂ flux with a walker-type multianvil apparatus at 8 GPa and 1000°C. Single crystal X-ray structure determination of β-Dy₂B₄O₉ revealed: , a=616.2(1) pm, b=642.8(1) pm, c=748.5(1) pm, α=102.54(1)°, β=97.08(1)°, γ=102.45(1)°, Z=2, R1=0.0151, wR₂=0.0475 (all data). The compound exhibits a new structure type which is built up from bands of linked BO₃- (Δ) and tetrahedral BO₄-groups (□). The Dy³⁺-cations are positioned in the voids between the bands. According to the conception of fundamental building blocks β-Dy₂B₄O₉ can be classified with the notation 2Δ6□:Δ3□=4□=3□Δ. Furthermore we report about temperature-resolved in situ powder diffraction measurements and IR-spectroscopic investigations on β-Dy₂B₄O₉.