**6. Mass transfer with external forces in oxide crystal growth**

In crystal growth, steady convection is always desired because it is helpful for mass transfer and thus provides an enhanced renewal of the melt/solution in the region near the crystallization interface. However, when the temperature gradient gets larger enough, the convective flow may become oscillatory or even turbulent, which inevitably gives rise to generation of striations. In some cases, the unsteady flow may be suppressed by external force such as rotation, vibration or magnetic field. In this part, some experimental results will be given about the effect of external forces on mass transport during oxide crystal growth.

#### **6.1 Suppression of oscillatory flow by transverse magnetic field in NaBi(WO4)2 melt**

For oxide melt, oscillatory convection can be observed if the temperature gradient along the loop heater gets large enough. Fig. 21(a) shows a typical unsteady flow pattern of NaBi(WO4)2 melt. This pattern comprises one main trunk and the branches. The main trunk oscillates with time, and the arrows I, II represent the range of oscillation. Fig. 21(b) shows the schematic diagram of oscillatory pattern. The main trunk oscillates around the position A with the amplitude as shown by the bi-directional arrow 1. The oscillatory frequency reached about 10 Hz, and the amplitude was about 500 μm. Similar convective oscillations have also been observed in KNbO3, BaB2O4 and Bi12SiO20 melts or solutions suspended on a loop heater (Z. H. Liu et al., 1998; W. Q. Jin et al., 2004; Y. Hong et al., 2006).

When a 60 mT transverse static magnetic field is applied, the distinct attenuation of the oscillation is observed and arrows III, IV represent the range of oscillation as shown in Fig. 22(a). The main trunk oscillates around the position A with the amplitude (~200 μm) as shown by the bi-directional arrow 2 in Fig. 22(b), which is smaller than that as shown by arrow 1. So the oscillatory amplitude of main trunk decreased when the magnetic field is applied. The frequency of oscillation is measured to be about 4 Hz. This means that the instability of convective flow has been effectively reduced.

Interfacial Mass Transfer and Morphological Instability of Oxide Crystal Growth 549

(upper part) of the as-grown single crystal obtained with RMF in Fig. 23(c). It is simplified as a schematic drawing in Fig. 23(d). Since such curved lines are observed only at the upper part of the as-grown crystal, they are in correlated with the free surface at the top end of the melt. By contrast with the same position of the single crystal grown in the normal condition without RMF shown in Fig. 23 (b), no similar pattern can be observed on the free surface of the same position. Therefore, it can be concluded that the appeared pattern is definitely

Fig. 23. Bi12SiO20 crystals grown with (a) and without (b) rotation magnetic field, the regular

Optical microscopic observation reveals that the middle part of the crystal grown with RMF has no growth striations. On the other hand, a large number of growth striations could be clearly observed inside the crystal grown without RMF at the same position. This is due to the appearance of steady forced convection in the melt induced by magnetic field. As a result, the transport of heat and mass is enhanced and remains stable, and therefore the

**6.3 Improvement of crystallographic perfection in Bi12SiO20 crystal by axial vibration**  The authors have experimentally investigated the effect of axial vibration on the free surface flows in a vertical Bridgman model under isothermal conditions (X. H. Pan, 2005a, 2005b). Steady forced flows are obtained on the free surface of the liquid phase driven by pure axial vibration. Based on this hinting, axial vibration is introduced into the Bi12SiO20 crystal growth in our laboratory (Y. Zhang et al., 2008, 2009), in order to suppress the unsteady thermocapillary or buoyancy convections. Some results are described in the following. Axial vibration has been introduced in the growth of Bi12SiO20 single crystal by vertical Bridgman technique. The frequency of the axial vibration applied is 50 Hz and its amplitude varies. The quality of the Bi12SiO20 single crystal is identified by the high-resolution X-ray rocking curves as shown in Fig. 24. It can be found that the crystal grown with 70 μm

pattern (c) observed on the surface and its schematic drawing (d)

crystallographic perfection could be improved.

induced by the applied RMF.

Fig. 21. (a) Oscillatory flow pattern in NaBi(WO4)2 melt, (b) The schematic diagram of the flow pattern

Fig. 22. (a) Flow pattern in NaBi(WO4)2 melt under 60 mT transverse magnetic field, (b) The schematic diagram of the flow pattern

In general, attention has seldom been paid to the growth of oxide single crystals in applied magnetic fields since their electrical conductivity is extremely low even in the melt. It is normally assumed that the effect of the magnetic field to be applied is negligible in an oxide melt. However, above experimental result shows that 60 mT static magnetic field is strong enough to affect the mass flow of oxide melt. It should be emphasized that the oscillation of the thermocapillary flow could be completely suppressed by the 60 mT magnetic field if the temperature difference applied on the loop decrease. The suppression of magnetic field on the oscillation flow might be due to the Lorentz force induced by the interaction of dissociated ions with magnetic field (W. Q. Jin, 2007).

#### **6.2 Effect of rotating magnetic field on Bi12SiO20 crystal growth**

In the following, the experiment results about bulk crystal growth by vertical zone-melting technique (VZM) in a rotation magnetic field (RMF) shall be demonstrated. Here Bi12SiO20 crystal is selected as model material due to its excellent photorefractive and electro-optical properties. More details about the RMF-VZM system is described in the reference (Y. Liu et al., 2010).

Fig. 23 shows the photographs of the Bi12SiO20 crystals grown by VZM. The crystal in Fig. 23(a) is grown with 25 mT and 50 Hz RMF and the one in Fig. 23(b) is obtained without RMF. A regular deep pattern with numerous curved lines is observed on the free surface

Fig. 21. (a) Oscillatory flow pattern in NaBi(WO4)2 melt, (b) The schematic diagram of the

Fig. 22. (a) Flow pattern in NaBi(WO4)2 melt under 60 mT transverse magnetic field, (b) The

In general, attention has seldom been paid to the growth of oxide single crystals in applied magnetic fields since their electrical conductivity is extremely low even in the melt. It is normally assumed that the effect of the magnetic field to be applied is negligible in an oxide melt. However, above experimental result shows that 60 mT static magnetic field is strong enough to affect the mass flow of oxide melt. It should be emphasized that the oscillation of the thermocapillary flow could be completely suppressed by the 60 mT magnetic field if the temperature difference applied on the loop decrease. The suppression of magnetic field on the oscillation flow might be due to the Lorentz force induced by the interaction of

In the following, the experiment results about bulk crystal growth by vertical zone-melting technique (VZM) in a rotation magnetic field (RMF) shall be demonstrated. Here Bi12SiO20 crystal is selected as model material due to its excellent photorefractive and electro-optical properties. More details about the RMF-VZM system is described in the reference (Y. Liu et

Fig. 23 shows the photographs of the Bi12SiO20 crystals grown by VZM. The crystal in Fig. 23(a) is grown with 25 mT and 50 Hz RMF and the one in Fig. 23(b) is obtained without RMF. A regular deep pattern with numerous curved lines is observed on the free surface

flow pattern

al., 2010).

schematic diagram of the flow pattern

dissociated ions with magnetic field (W. Q. Jin, 2007).

**6.2 Effect of rotating magnetic field on Bi12SiO20 crystal growth** 

(upper part) of the as-grown single crystal obtained with RMF in Fig. 23(c). It is simplified as a schematic drawing in Fig. 23(d). Since such curved lines are observed only at the upper part of the as-grown crystal, they are in correlated with the free surface at the top end of the melt. By contrast with the same position of the single crystal grown in the normal condition without RMF shown in Fig. 23 (b), no similar pattern can be observed on the free surface of the same position. Therefore, it can be concluded that the appeared pattern is definitely induced by the applied RMF.

Fig. 23. Bi12SiO20 crystals grown with (a) and without (b) rotation magnetic field, the regular pattern (c) observed on the surface and its schematic drawing (d)

Optical microscopic observation reveals that the middle part of the crystal grown with RMF has no growth striations. On the other hand, a large number of growth striations could be clearly observed inside the crystal grown without RMF at the same position. This is due to the appearance of steady forced convection in the melt induced by magnetic field. As a result, the transport of heat and mass is enhanced and remains stable, and therefore the crystallographic perfection could be improved.
