Introduction

Due to its various applications in non-linear optics and electro-optics, the ferroelectric material LiNbO₃ has been extensively studied in recent several years. Its transition temperature of 1480 K is among the highest known ferroelectric transition temperatures. In the ferroelectric phase, LiNbO₃ has 10 atoms in the unit cell; the space group is R3c. The atomic arrangement is given by oxygen octahedra stapled along the polar trigonal axis. Each Nb atoms is displaced from the center of the oxygen octahedron along the polar axis; the next octahedron (along the polar axis) is empty, and the following one contains a Li atom, displaced from the oxygen face along the trigonal axis. In the paraelectric phase, the space group of LiNbO₃ is $R\bar{3}c$. In this case, the Nb atoms are centered inside the oxygen octahedra, and the Li atoms lie inside the common face of two adjacent oxygen octahedra(1).

The mechanism of the structural phase transition from paraelectric to ferroelectric phase is still not completely clear. Temperature dependence measurements of Raman scattering (2) and temperature dependence measurements of far infrared reflectivity in LiNbO₃(3) suggest the displacive type phase transition. In contradiction with this picture, the absence of the A 1 mode softening reported in certain papers(4) is an indication towards the order-disorder type phase transition.

The study of electronic structure and lattice dynamics from first principles was hindered by a relative complexity of structure. Inbar and Cohen (5) analyzed the ferroelectric instability and shown that it cannot be attributed to the net displacement of Li atoms in the course of ferroelectric transition; in addition to that, the displacement (with respect to Nb) and distortion of the oxygen octahedra plays a crucial role. These results have been essentially reproduced by Yu and Park (6). The aim of our present study is to optimize the structure of the ferroelectric phase fully from first principles, adjusting the values of all internal parameters constrained only by the crystal symmetry. In the course of that, the energetics of individual atomic displacements can be analyzed and applied for the zone-center lattice dynamics simulation within the frozen-phonon scheme. With such simulation so far missing, the attribution of different experimentally measured zone-center phonon modes (with respect to atomic displacement patterns) is problematic.