Neutron scattering study of the one-dimensional ionic conductor β-eucryptite

The phase transitions in $\beta$-eucryptite have been investigated by the slow neutron scattering technique. In the temperature range $430<~T<~490$°C an incommensurate structure is found which coexists with the well-known low-temperature superstructure in the range $430<~T<~482.5$°C. A pronounced temperature dependence of the satellite positions is observed. Interpretations of the observed scattering are based on a simple model which accounts only for the Li chains within the quartz channels. The width of the diffuse scattering at 525°C indicates that the Li correlations within a chain are effective over 19 ± 3 Li-Li distances while chain-chain correlations are relatively weak. A rather profound analogy to the triangular Ising lattice in the presence of an external field is discussed. At present this model does not explain the incommensurate structure.