**1. Introduction**

Ferroelectric lithium niobate is a material that has been extensively studied because of its many technological applications, including optical integrated circuits, electro-optical modulators, optical memories, acoustic filters, high-frequency beam deflectors, frequency converters and holographic volume storage [1–9], for which holographic volume storage performance is very important [10–15]. This paper looks at the doping of LiNbO3 with vanadium and molybdenum ions in different charge states, with the aim of predicting the optimum location of dopants, and charge compensation mechanisms where needed.

Previous work on vanadium and molybdenum doped lithium niobate has included experimental studies of how its photorefractive properties are enhanced by doping with molybdenum ions [16,17] where it is suggested that the Mo6<sup>+</sup> ion dopes at the Nb5<sup>+</sup> site. Another study looks at LiNbO3 co-doped with Mg and V, concluding that some of the vanadium dopes at the Nb site in the 5+ charge state, but that V4<sup>+</sup>Li, V3<sup>+</sup>Li and V2<sup>+</sup>Li defects are also observed [18]. Finally, another recent publication [19] has looked at the photorefractive response of Zn and Mo co-doped LiNbO3 in the visible region, and concluded that the presence of Mo6<sup>+</sup> ions helps promote fast response and multi-wavelength holographic storage, which is attributed to their occupation of regular niobium sites in the lattice.

In a Density Functional Theory (DFT) study [20], vanadium doping was modelled, and it was concluded that vanadium substitutes at the Li<sup>+</sup> site as V4+, but that it dopes at the Nb site as a neutral defect as the Fermi level is increased. In another DFT study [21], molybdenum doping was modelled and it was concluded that the most stable configuration involves doping at the Nb5<sup>+</sup> site, in agreement with the previously mentioned experimental studies [16,17]. It is noted that in the DFT

studies, predictions were made on the basis of defect formation energies, as opposed to the solution energy approach adopted in this paper.

This paper presents a computer modelling study of V2<sup>+</sup>, V3<sup>+</sup>, V4<sup>+</sup> and V5<sup>+</sup> as well as Mo3<sup>+</sup>, Mo4<sup>+</sup>, Mo5<sup>+</sup> and Mo6<sup>+</sup> doping in LiNbO3 using interatomic potentials. Such calculations enable predictions to be made of the sites occupied by dopant ions, and the form of charge compensation adopted, if needed. These calculations provide information about how the defects behave in the material, and how they influence its properties in the applications mentioned previously. It follows a series of papers by the authors on LiNbO3 doped with a range of ions [22–27].
