${beta}$- Eucryptite (LiAlSiO4) is a potential electrolyte for Li- ion battery due to its high Li- ion conductivity and very small volume thermal expansion coefficient. We have performed ab-initio molecular dynamics simulations of $beta$- Eucryptite to study the origin of high temperature superionic phase transition in this material. The simulations are able to provide the microscopic understanding of the one -dimensional superionicity that occurs along the hexagonal c-axis and is associated with the order-disorder nature of the phase transition. The Li ionic conductivity is found to enhance due to the anisotropic negative thermal expansion along hexagonal c-axis. The introduction of defects in the crystal like, excess Li in interstitial sites, Li vacancy and O vacancy are found to significantly increase the ionic conductivity and hence might reduce the temperature of the superionic phase transition in this material.