Thermal analysis for LiNaSO4 single crystals by differential scanning calorimetry (DSC) had shown a clear endothermic peak at 796.9 K. The enthalpy energy of the structural phase transition, Delta H = 11.94 kJ/mol, was measured. The corresponding entropy change, Delta S was 14.98 J/K mol. The dielectric response of LiNaSO4 single crystal under ac electric field was investigated by impedance spectroscopy. Two distinct relaxations in the sample crystal were detected: dielectric dipolar relaxation and ionic conductivity relaxation. The dipolar relaxation peak due to SO4- reorientation was found at around 1.5 x 10(5) Hz, which is temperature independent. The ionic conductivity relaxation due to Li+ was found at the lower frequency and it was temperature dependent. The dc conductivity varied from 6.7 x 10(-8) Omega(-8) cm(-1) at 423 K to 1.0 x 10(-4) Omega(-1) cm(-1) at the temperatures above 793 K. The activation enthalpy of Li+ is 1.63 eV in the temperature range between 593 and 793 K. The sample crystal became a fast ionic conductor in the high-temperature phase with the activation energy of 0.08 eV. The ionic conductivity and dipolar relaxations are synchronized in the high-temperature phase of the sample crystal. (C) 2010 Elsevier B.V. All rights reserved.