CRYSTAL CHEMISTRY OF SODIUM ION CONDUCTING TITANATES

V.B.Nalbandyan

Rostov State University, 7, Zorge str., Rostov-on-Don, 344090, Russia
E-mail: vnalband@uic.rnd.runnet.ru

Keywords: superionic conductors, crystal structure, non-stoichiometry, single crystals, ceramics, bottlenecks, conduction paths

A review is given. Some recent results obtained in this laboratory are included.

Stable Na₂O - TiO₂ phases are poor ionic conductors, even after heterovalent doping. About 130 compounds of about 40 structure types are known in Na₂O - TiO₂ - RO_n (-NaF) systems, and some of them exhibit fast cation conduction and other ion transport phenomena such as cation exchange and cation extraction/insertion reactions [see Refs 1-3 and references therein]. These compounds usually contain R cations close in size to Ti⁴⁺, and Na⁺ non-stoichiometry is charge-compensated via heterovalent R/Ti substitution. A common feature of all the structures (except Na₄TiO₄) is TiO₆ octahedron, distorted by asymmetric -bonding [4]. Even in formally centrosymmetric sites, the local environment must be acentric due to random occupation of adjacent sites.

Many R cations (Mg²⁺, Sc³⁺, V³⁺, Cr³⁺, Mn²⁺, Fe²⁺, Fe³⁺, Co²⁺, Ni²⁺) mix randomly with Ti⁴⁺ in all known structures, and almost identical set of structure types is formed with variuos R²⁺ and R³⁺. In other systems, the same structure types exist only at low R concentrations. At higher R content, different structures are formed, where R = Al³⁺, Ga³⁺, Zn²⁺, Li⁺ adopt tetrahedral coordination, R = Mn³⁺, Cu²⁺ adopt square-pyramidal one, and R = Ti³⁺ forms clusters with short Ti-Ti distances. The Ti(3+, 4+) compounds (bronzes) are n-type semiconductors [3]. Most other compounds have negligible electronic conductivity.

Major factor influencing Na⁺ mobility is the type of a rigid lattice: its connectivity, bottleneck radius for Na⁺ movement [1], sodium sites connectivity and the jump distance.

With increasing Na/(R,Ti) ratio, the following sequence is usually observed: frameworks with isolated cavities (e.g. freudenbergite type), then frameworks with one-dimensional (1D) channels (single, double, triple, quadruple and even ten-barrelled [4]), then layered structures, and, finally, structures with finite oxoanions. No chain structures or frameworks with intersecting tunnels were found so far. The latter class of structures seems hardly probable because mean coordination number of oxygen with respect to (Ti,R) is usually too high (about 3). Short translation vectors of about 300 pm (octahedron edge) or 400 pm (octahedron diagonal) are characteristic of most of the structures. In accordance with our prediction [5], "300 pm structures" (10 types) show relatively high Na⁺ mobility along the short translation, whereas "400 pm structures" are poor cation conductors.

For the given structure type, Na⁺ non-stoichiometry and bond ionicity [6] are of great importance for the ion conduction. However, deviation from stoichiometry, bottleneck size and stability of the structure type are not independent features. Comparing the related structure types (see below), or samples of the given type with varying x parameter, or non-equivalent channels in the same structure, clearly shows a negative correlation between bottleneck radius and channel occupancy: the widest channel is the least populated one. Na⁺ site splitting and/or interstitial Na⁺ sites are usually found in such a channel. These enable Na⁺-Na⁺ distance to be in the excess of a short translation and thus stabilize the structure. Another stabilizing factor is greater entropy due to the static sodium disorder and to enhanced cation movement via wide bottlenecks. Na⁺ deficiency in a channel with narrow bottleneck cannot give rise to essential static or dynamic displacements and therefore has little stabilizing effect. On the other hand, increased bottleneck radius may be considered not only as a cause of Na⁺ disorder, but also as a result of it: Na⁺ displacement shifts anions away.

The two layered structure types described earlier in K_xIn_xSn_1-xO₂ system [6] are also found in Na_x(R,Ti)O₂ systems. Both have identical ideal formula and identical octahedral brucite-like (R,Ti)O_6/3 layers. The first one is rhombohedral with Na⁺ in octahedra (O3), and the second one is hexagonal with Na⁺ in trigonal prisms (P2). The P2 structure is more favourable for ion conduction [6], and this is the case for Na compounds too, Na_0.6Cr_0.6Ti_0.4O₂ being one of the most conductive sodium electrolytes (12 S/m at 300C for 90% dense ceramics) [2]. However, the prismatic environment is electrostatically less favourable than octahedral (antiprismatic) one. Therefore, the formation of P2 phases seems to violate the classical crystal chemical rules, especially taking into account the occupancy of interstitial prisms having two faces in common with (R,Ti) octahedra. The explanation is given above. In fact, P2 phases are formed only as non-stoichiometric and disordered (x = 0.6-0.7).

Similar results are obtained when comparing another pair of structure types with identical ideal formula Na(R,Ti)₂O₄. From the classical point of view, the CaFe₂O₄ type with narrow bottlenecks seems to be more stable than Na_xFe_xTi_2-xO₄ type because of the lower degree of octahedral edge sharing and closer oxygen packing around sodium. Experimentally, this is the case for x = 1, but sodium deficiency favours formation of the Na_xFe_xTi_2-xO₄ type with wide channels and high ion conductivity.

With increasing mean (R,Ti) radius, the short period is increased thus diminishing Na⁺-Na⁺ repulsion. So the preference of the P2 and Na_xFe_xTi_2-xO₄ types vanishes. That is why these structures do not exist with large R cations such as Sc³⁺, Mn²⁺. Neither are they formed with very little cations (Al³⁺, Be²⁺). However, partial Al substitution for Cr is possible. Decreasing mean R radius shifts homogeneity range of P2 phases towards lower x values and increases interlayer distances and bottleneck radii, thus enhancing ion conduction [2]. This is in contrast with the behaviour of frameworks with intersecting tunnels (e.g. of the NASICON type).

For 2D ion conductors, the specific conductivity of the single phase ceramics is only 2-3 times lower than that of the single crystal in "easy" direction, and activation energy is essentially the same. However, for 1D conductors, conductivity of the ceramics is 2-3 orders lower than that of the crystal, and activation energy is greater. A method is developed to prepare high-conducting polycrystalline textures of 2D and 1D materials.

Na⁺ extraction under oxidizing conditions (both electrochemical and chemical) is possible when R is not in higher oxidation state (e.g. Ti³⁺, V³⁺, Cr³⁺, Mn²⁺, Mn³⁺, Co²⁺, Cu²⁺) [2, 3]. The rate of extraction is limited not only by R redox properties and sodium mobility or electron conduction, but also by destabilizing effects of increased oxygen-oxygen repulsion and bond valence discrepancies.

Ion transport mechanisms are discussed. A great similarity between the two pairs of fast ion conducting structures (P2/O3 and /"-aluminas) is shown.

The work was supported by the Russian Foundation for Basic Research under the grant No. 97-03-33807a.

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