With very few exceptions the numerous polymorphs of SiO2 all consist of SiO4 tetrahedra linked through their corners, thus forming three-dimensional framework structures. The topology of the tetrahedral linkage and the efficiency of space filling are different for the polymorphs. For a given type of framework, for example, that of quartz or cristobalite, space filling can be improved by so-called displacive transformations from a more open high-temperature form (e.g., “high”, “h”, or β “quartz”) to a denser form stable at lower temperatures (“low” or “α quartz”). These transformations do not change the topology of the framework, i.e., chemical bonds in a crystal can be deformed, but are not broken and rearranged.

The Scientific Basis

Superionic conductors: Transitions, structures, dynamics

A paired interstitialcy model is used as a basis for qualitative comparisons of conductivity and dielectric phenomena in β-alumina crystals and in glass. Thus, the increase in the conductivity of sodium silicate glasses with increasing Na2O activity can be explained if the concentration of (Na2*)2+ interstitial pairs increases with increased polarizability of O2- ions, expressed in terms of the optical basicity parameter, Δ. Similarly, the occurrence of the pronounced minima in conductivity isotherms (the mixed-alkali effect in glass) is attributed to disappearance of mobile interstitial pairs, e.g. (Li2*)2+ or (K2*)2+, and the stabilization (by polarization interactions) of apparently immobile mixed-alkali pairs, (LiK*)2+. The phenomenon of coionic conduction in certain β-alumina crystals is an interesting departure from this general pattern. The orientation dependence of the electrical modulus spectrum of monocrys-talline β-alumina highlights the presence of a bimodal distribution of relaxation times, in which the low-frequency component (v0=1011 Hz) may arise from the rearrangement of interstitial pairs and the high-frequency component (v0=2×1012 Hz) may arise from less hindered ionic motions. It is suggested that the motions of interstitial pairs and surrounding cations are mutually catalytic and that some form of combined motion is responsible for both the electrical and mechanical relaxations in β-alumina and glass.

Conduction and Dielectric Loss Mechanisms in β-Alumina and Glass: A Discussion Based on the Paired Interstitialcy Model

The structures of ordered and disordered β-eucryptite have been determined from Rietveld analysis of powder synchrotron x-ray and neutron diffraction data over a temperature range of 20 to 873 K. On heating, both materials show an expansion within the (001) plane and a contraction along the c axis. However, the anisotropic character of the thermal behavior of ordered β-eucryptite is much more pronounced than that of the disordered compound; the linear expansion coefficients of the ordered and disordered phases are αa = 7.26 × 10−6 K−1; αc = −16.35 × 10−6 K−1, and αa = 5.98 × 10−6 K−1; αc = −3.82 × 10−6 K−1, respectively. The thermal behavior of β-eucryptite can be attributed to three interdependent processes that all cause an increase in a but a decrease in c with increasing temperature: (i) Si/Al tetrahedral deformation, (ii) Li positional disordering, and (iii) tetrahedral tilting. Because disordered β-eucryptite does not exhibit tetrahedral tilting, the absolute values of its axial thermal coefficients are smaller than those for the ordered sample. At low temperatures, both ordered and disordered β-eucryptite exhibit a continuous expansion parallel to the c axis with decreasing temperature, whereas a remains approximately unchanged. Our difference Fourier synthesis reveals localization of Li ions below room temperature, and we suggest that repulsion between Li and Al/Si inhibits contraction along the a axes.

Structural mechanisms underlying near-zero thermal expansion in β-eucryptite: A combined synchrotron x-ray and neutron Rietveld analysis

Lithium magnesium molybdates of the general formula Li2−2xMg2+x(MoO4)3, for 0 ≤
x
≤ 0.3, have been synthesized and their structure and lithium ion conductivity investigated. Determination of crystal structure of one of the members, Li2Mg2(MoO4)3, has revealed a three-dimensional framework consisting of metal–oxygen octahedra and trigonal prisms (where Li and Mg reside) which are interconnected by MoO4 tetrahedra. Although the framework is three-dimensional, lithium-ion conductivity appears to be restricted to the one-dimensional channels formed by interconnected trigonal prisms. Isotypic molybdates, Li3M(MoO4)3
(M = Cr, Fe), where lithium ions occupy exclusively the trigonal prismatic channels, exhibit a higher lithium ion conductivity than Li2−2xMg2+x(MoO4)3, lending support to the idea that the conductivity is one-dimensional in these materials. 7Li NMR spectral data are consistent with this interpretation.

G.H. Talat

Papers

One-dimensional cooperative LI-diffusion in β-eucryptite

β-eucryptite—a one-dimensional Li-ionic conductor