The triple molybdates K_3–xNa_1+xM₄(MoO₄)₆ (M = Ni, Mg, Co) and K_3+xLi_1–xMg₄(MoO₄)₆ were found upon studying the corresponding ternary molybdate systems, and their structures, thermal stability and electrical conductiviplusmnty were investigated. The compounds crystallize in the space group R3c and are isostructural with the sodium‐ion conductor II‐Na₃Fe₂(AsO₄)₃ and yurmarinite, Na₇(Fe³⁺, Mg, Cu)₄(AsO₄)₆; their basic structural units are flat polyhedral clusters of the central M1O₆ octahedron sharing edges with three surrounding M2O₆ octahedra, which combine with single NaO₆ octahedra and bridging MoO₄ tetrahedra to form open three‐dimensional (3D) frameworks where the cavities are partially occupied by disordered potassium (sodium) ions. The split alkali‐ion positions in K_3–xNa_1+xM₄(MoO₄)₆ (M = Ni, Mg, Co) give their structural formulae as [(K,Na)_0.5□_0.5)]₆(Na)[M1][M2]₃(MoO₄)₆, whereas the lithium‐containing compound (K_0.5□_0.5)₆(Mg_0.89K_0.11)(Li_0.89Mg_0.11)Mg₃(MoO₄)₆ shows an unexpected (Mg, K) isomorphism, which is similar to (Mn, K) and (Co, K) substitutions in isostructural K_3+xLi_1–xM₄(MoO₄)₆ (M = Mn, Co). The crystal chemistry of the title compounds and related arsenates, phosphates and molybdates was considered, and the connections of the cationic distributions with potential 3D ionic conductivity were shown by means of calculating the bond valence sum (BVS) maps for the Na⁺, Li⁺ and K⁺ ions. Electrical conductivity measurements gave relatively low values for the triple molybdates [σ = 4.8 × 10⁻⁶ S cm⁻¹ at 390°C for K₃NaCo₄(MoO₄)₆ and 5 × 10⁻⁷ S cm⁻¹ at 400°C for K₃LiMg₄(MoO₄)₆] compared with II‐Na₃Fe₂(AsO₄)₃ (σ = 8.3 × 10⁻⁴ S cm⁻¹ at 300°C). This may be explained by a low concentration of sodium or lithium ions and the blocking of their transport by large potassium ions.

中文翻译：

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同型同型II-Na3Fe2（AsO4）3和褐铁矿的三钼酸盐K3-xNa1 + xM4（MoO4）6（M = Ni，Mg，Co）和K3 + xLi1-xMg4（MoO4）6同型：合成，钾无序，晶体化学和离子电导率

通过研究相应的三元化合物，发现了三钼酸盐K _{3– x} Na _{1+ x} M ₄（MoO ₄）₆（M  = Ni，Mg，Co）和K _{3+ x} Li _{1– x} Mg ₄（MoO ₄）_6。研究了钼酸盐体系及其结构，热稳定性和导电性。这些化合物在空间群R 3 c中结晶，并与钠离子导体II-Na ₃ Fe ₂（AsO ₄）₃同构褐铁矿，Na ₇（Fe ³⁺，Mg，Cu）₄（AsO ₄）₆；它们的基本结构单元是中央M 1O ₆八面体的平坦多面体簇，与三个周围的M 2O ₆八面体共享边，并与单个NaO ₆八面体结合并桥接MoO ₄四面体以形成开放的三维（3D）框架，其中的空腔部分被无序的钾（钠）离子占据。在K _{3– x} Na _{1+ x} M ₄（MoO ₄）₆（M  = Ni，Mg，Co）的结构式为[（K，Na）_0.5 □ _0.5）] ₆（Na）[ M 1] [ M 2] ₃（MoO ₄）₆，而锂含有化合物（K _0.5 □ _0.5）₆（Mg _0.89 K _0.11）（Li _0.89 Mg _0.11）Mg ₃（MoO ₄）₆表现出意外的（Mg，K）同构，类似于（Mn，K）和（Co ，K）等结构K _{3+ x中的}取代Li _{1– x} M ₄（MoO ₄）₆（M  = Mn，Co）。考虑了标题化合物及其相关的砷酸盐，磷酸盐和钼酸盐的晶体化学性质，并通过计算Na ⁺，Li ⁺的键合价和（BVS）图，显示了阳离子分布与潜在3D离子电导率的联系。和K ⁺离子 对于K ₃ NaCo ₄（MoO ₄）_6，在390°C下，_三价钼酸盐的电导率测量值相对较低[σ= 4.8×10 ^-6  S cm ^-1K ₃ LiMg ₄（MoO ₄）₆ ]和II-Na ₃ Fe ₂（AsO ₄）₃在400°C时为5×10 ^-7  S cm ^-1（σ= 8.3×10 ^-4  S cm ^-1在300°C下）。钠或锂离子浓度低以及大钾离子阻碍了它们的运输，可以解释这一点。