**Abstract**

Li2O fnds several important technological applications, as it is used in solid- state batteries, can be used as a blanket breeding material in nuclear fusion reactors, etc. Li2O exhibits a fast ion phase, characterized by a thermally induced dynamic disorder in the anionic sub-lattice of Li+, at elevated temperatures around 1200 K. We have car- ried out lattice-dynamical calculations of Li2O using a shell model in the quasi-harmonic approximation. The calculated phonon frequencies are in excellent agreement with the reported inelastic neutron scattering data. Thermal expansion, speci¯c heat, elastic con- stants and equation of state have also been calculated which are in good agreement with the available experimental data.

**Introduction**

Lithium oxide (Li2O) belongs to the class of superionics, which allow macroscopic movement of ions through their structure. This behavior is characterized by the rapid di®usion of a significant fraction of one of the constituent species within an essentially rigid framework of the other species. In Li2O, Li is the di®using species, while oxygens constitute the rigid framework [1,2].

This material finds several technological applications ranging from lightweight high power-ensity lithium-ion batteries to being a possible candidate for blanket material in future fusion reactors [3,4]. Li2O crystallizes in the anti-fuorite structure with a face-centered cubic lattice and belongs to the Fm3m (O5 h) space group [1,2], lithium being in the tetrahedral coordination. Like other fuorites [5], this also shows a decrease in the elastic constant C11 [6] with emperature around the transition the fast ion phase.In several other fuorites, the fast ion phase is characterized by a specific heat anomaly [7], a Schottky hump in the speci¯c heat. However, no such anomaly has been observed in Li2O [6,8,9].

This paper reports the lattice dynamics calculations done to understand dynamics of anti-fuorite Li2O. Lattice dynamics calculations have been done to calculate the phonon spectrum, specific heat and elastic constants of the oxide. These results are in very good agreement with the available experimental data [6,9{11].

**Lattice dynamics calculations**

Calculations have been carried out in the quasi-harmonic approximation using inter-atomic potential consisting of both long and short-range terms, using DISPR [12].The form of the potential is given below:

where a and b are empirical parameters [13], and a = 1822 eV and b = 12:364. Oxygen ions have been modeled using a shell model [13,14]. Group theoretical considerations classify the phonons in the entire Brillouin zone into the following representations:

The phonon dispersion relation at ambient conditions is given in figure 1. The zone center modes and the phonons in the entire Brillouin zone are in very good agreement with the available inelastic neutron scattering data [10,11]. The phonon density of states at ambient conditions along with the partial densities of lithium and oxygen is given in figure 2. Both lithium and oxygen contribute almost in the entire Brillouin zone. Lithium's contribution is higher on the higher energy side, with a prominent peak in the region between 50 and 75 meV. Oxygen contribution is greater on the lower energy side with prominent peaks below 60 meV. The specisic heat, CP(T) can be calculated from the knowledge of the phonon density of states. The calculated ratio CP(T)=T has been compared with the ex-perimental result in ¯gure 3. The variation of the Debye temperature (µD) with temperature is given in ¯gure 4. Table 1 gives the calculated values of the elas-tic constants and equilibrium lattice parameters using the model calculations as compared with the experimental results.

**Conclusions**

A shell model has been successfully used to study the phonon properties of Li2O. The interatomic potential is able to reproduce the equilibrium lattice constant

elastic constants (except C12) and phonon frequencies, which are in unison with the experimental data [1,6]. The phonon dispersion in the entire Brillouin zone agrees well with reported experimental data. The calculated specific heat is in good agreement with the experimental data. The interatomic potential formulated for Li2O oxide may be transferred to other similar °uorites and anti°uorites like Na2O, K2O, UO2, ThO2 etc., with suitable modifications.

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C.I.V.- 18.991.089

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