Particularidades en la legislación autonómica

Figure 2.5 shows a typical polarisation hysteresis curve for a 0.5 mm thick virgin lithium niobate single crystal, taken from a paper by Gopalan and Gupta (1997) (the units of spontaneous polarisation have been corrected). It illustrates the two spontaneous polarisation states in which lithium niobate can exist and the coercive field required to switch between these states.

Figure 2.5:The hysteresis loop of az-cut LiNbO3single crystal from Gopalan and Gupta (1997) with corrected units of Ps.

Gopalan and Gupta noticed a large asymmetry in the hysteresis loop, indicating the presence of an internal field (Eintin the diagram). In a later study Gopalan et al. (1999) found that the exact value of the internal field varied from sample to sample, within a range of 2.7 – 3.5 kV/mm.

The internal field is measured by the difference in coercive field required to pole lithium niobate in the ‘forward’ direction compared to the ‘reverse’ direction. Forward poling is defined as starting with a virgin crystal (state I) and then domain inverting a region. Reverse poling is the process of poling this area (state II) back to its original domain orientation (state I). The forward and reverse coercive fields are then defined as:

• Forward poling:Ef =Ec+Eint • Reverse poling: Er=Ec−Eint

Consequently a larger field is required for forward poling than for reverse poling. This is because in a virgin crystal (state I) the internal field is parallel to the polarisation direction. After poling the internal field initially maintains the same direction, so reverse poling needs a smaller field. However, the internal field gradually realigns itself along the new polarisation direction. Gopalan found that this process takes many days at room temperature, but is 80 % complete within two minutes when the sample is heated to over 200 °C. Subsequent work by Ro and Cha (2000) suggests that there are two distinct relaxations, one with a subsecond time scale and another which occurs over several days at room temperature. The origin of the internal field in lithium niobate was quite a source of controversy. Some early results suggested that hydroxyl ions (OH−) present in lithium niobate were responsible, on the basis of infrared absorption measurements (Gopalan and Gupta, 1996). The shape of the three peak OH−band showed changes after forward poling of a crystal which were reversed when the crystal was repoled back to the original state. However in 1998 it was proven that the internal field is actually a result of non-stoichiometric point defects in the congruent material. Stoichiometric lithium niobate showed the same OH− infrared bands as the congruent material, but experiments showed that no internal fields were present (Gopalan et al., 1998). Consequently the coercive field required for poling of a stoichiometric crystal is much less (by about four times) than is required for congruent lithium niobate. However the crystal composition was found to have very little effect on the spontaneous polarisation.

Lithium niobate may contain several types of lattice imperfections (Malovichko et al., 1999):

• Oxygen vacancies (vO)2+

• Niobium vacancies (vNb)5−

• Niobium antisites (NbLi)4+

• Niobium on structural vacancy (Nbv)5+

• Lithium on structural vacancy (Liv)+

• Interstitial oxygen (Oi)

The relative concentrations of these defects are unknown, however there are several charge-balanced models of which types of defect are most common:

1. Lithium vacancies and oxygen vacancies (Prokhorov and Kuuzminov, 1990) 2. Niobium antisites and niobium vacancies, 5(NbLi)4++4(vNb)−(Schirmer et al.,

1991)

3. Niobium antisites and lithium vacancies, (NbLi)4++4(vLi)−

4. Ilmenite ordering, Li Nb v Nb Li Li Nb v, etc

The relative merits of each model has been discussed by Kim et al. (2001). The first model, featuring lithium and oxygen vacancies is thought to be unlikely due to an incompatibility with density measurements, while Donnerberg et al. (1991) showed that the formation of niobium vacancies, as suggested by the second model, is energetically unfavourable. However the combination of the niobium and lithium vacancies models essentially results in areas of ilmenite ordering. Yatsenko et al. (1997) used NMR spectra and simulations of 7Li and 93Nb nuclei to study the different models, and reported that the most probable defects are a complex of (NbLi+3vLi) and a single isolated vLi.

Kim et al. (2001) describe how the niobium antisites and lithium vacancies model ((NbLi)4++4(vLi)−) affects the internal field and the poling process in lithium niobate

(and lithium tantalate if the niobium is exchanged for tantalum). A NbLi antisite

combined with four vLi vacancies will posses an electric dipole moment with two

components, one related to the antisite defect, and the other due to the lithium vacancies. For poling to occur, the niobium and lithium ions have to move from their original positions; the niobium simply moves along thezaxis, to an opposite position across the centre of the oxygen octahedron. The lithium ion has to pass

through an opening in the close packed oxygen layer, of similar size to the ion itself. When the lithium is replaced by niobium in a NbLiantisite defect, the niobium will

also have to pass through the oxygen layer. The niobium ionic radius is actually slightly smaller than that for lithium,∼_{64 pm compared to}∼_{76 pm (Shannon, 1976),}

so steric considerations should not be an issue. However, once the antisite niobium has moved, the lithium vacancies around the defect will also need to rearrange to reach a stable state. But as these are thought to only move at temperatures above 150 °C (Battle et al., 2000), a high temperature anneal is required to restore the defect complex to a low energy state. The dipole moment associated with the niobium antisite will be reversed after domain reversal, but at room temperature the lithium vacancy component is not immediately reversed.

Kim et al. (2002) suggest that the dipolar defects give rise to equivalent defect fields,

Ede f ect, which tend to increase the coercive field. They state that the defect field is not a real electric field in lithium niobate, but instead can be considered as “the formal equivalent to the energetic difference between the two domain states +Ps and−_{Ps, one stabilized by the dipolar defects by an amount of energy}−_{Ede f ectPs}

and another raised in energy by the same amount.”

Recent studies of the internal field by the use of the electro-optic effect (Paturzo et al., 2004) and an interferometric method (de Angelis et al., 2004) have been reported. The electro-optic response of a recently poled domain shows a different response to that of a virgin domain, and Paturzo et al. interpret this as the consequence of an elastic dipole component associated with lattice distortions.

In summary, the internal field in lithium niobate can be observed by recording the polarisation hysteresis curve. It is related to the lithium deficiency and resulting crystal defects in congruent lithium niobate, as no internal field has been detected in stoichiometric material. The internal field is also related to the larger coercive field required to induce domain inversion in congruent crystals, however the exact nature of defects responsible are still uncertain. The most likely defect, supported by a variety of experimental evidence, is a charge-balanced complex of a niobium antisite (NbLi)4+with four lithium vacancies (vLi)−.