Materials Science and Engineering B 146 (2008) 41–44 The dependence of the dopant distribution on the pulling rate and on the capillary channel radius in the case of a Nd:YVO 4 cylindrical bar grown from the melt by EFG method L. Braescu ∗ Department of Computer Science, Faculty of Mathematics and Computer Science, West University of Timisoara, Blv: V. Parvan 4, 300223 Timisoara, Romania Abstract The dependence of the Nd 3+ ion distribution on the pulling rate v and on the capillary channel radius R cap , in an YVO 4 cylindrical bar grown from the melt by EFG method with melt replenishment is determined. Using COMSOL Multiphysics 3.3, the coupled incompressible Navier–Stokes and conservative convection–diffusion equations were solved in the stationary and time dependent cases for different pulling rates v in the range [1 × 10 -10 ,1 × 10 -6 ] m/s and for different capillary channel radii. The computations reveal that in the stationary case, for a given R cap , there exist critical pulling rate values v ′ depending on R cap , at which the Nd 3+ ion concentration has a maximum. If v increases in the range [1 × 10 -10 , v ′ ] then the impurity concentration increases, and after that the concentration decreases slowly remaining in average equal to the initial impurity concentration in the melt. In the time dependent case, after a transition period which depends on v and R cap , the impurity concentrations tend to those obtained in the stationary case. In the transition period there exists a slight non-homogeneity of the dopant distribution, and after that the concentration of Nd 3+ ions in the crystal is almost equal to C 0 , as it was reported by practical crystal growers. © 2007 Elsevier B.V. All rights reserved. Keywords: Mathematical simulations; Rare-earth compounds; Solid-state laser 1. Introduction Nd:YVO 4 single crystal is one of the most attractive laser hosts for LD pumped solid-state lasers due to a low-pumping threshold, high-absorption coefficient, and good mechanical and chemical properties. These crystals were produced by many growth techniques (Czochralski, Verneuil, floating zone, laser heated pedestal growth and top-seeded solution growth). The wide application is still limited due to serious difficulties in growing crystals with a good quality; the homogeneity of the dopant concentration and free defects in the grown crystal are very important for the optical applications of Nd:YVO 4 . For solving this problem, researchers have paid attention to the edge- defined film-fed growth (EFG) method [1–3] as a perspective way to attain high-quality rare-earth vanadate single crystals. The central component of the EFG growth system is a die, which controls the shape of the crystal, the interface, the heat and mass transfer from the crucible to the meniscus (the liquid bridge retained between the die and the crystal). ∗ Tel.: +40 256 592 221; fax: +40 256 592 316. E-mail address: lilianabraescu@balint1.math.uvt.ro. Impurity confinement at the die and the meniscus/interface melt region was predicted for EFG system by early models [4]. Stirring of the meniscus does not redistribute impurities rejected back into the melt if the interface and crucible melts are sepa- rated by long capillaries. In the absence of such back mixing, growth takes place with an effective segregation coefficient close to unity. It thus appeared that the grown crystals by EFG method, would be limited in quality and the process would have a low tolerance for rejected melt impurities. In the other melt growth methods, vigorous stirring of the interface melt is utilized to remove the rejected impurities from the interface boundary layer to improve the crystal quality. Modeling was used to examine if the rejected interface impu- rities could be manipulated in EFG cylindrical bar growth so as to improve the crystal quality. The first, this proved was studied through utilization of capillary design to create interface melt convention and redistribute impurities by “die capillary convec- tion”. After that, the rejected impurities were studied through manipulation of the interface shape using an axis-symmetric or “displaced” die shape which would affect mass transport through the cylindrical bar thickness. Recently, the influence of the die geometry and various growth conditions on the fluid flow and on the solute distribu- 0921-5107/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2007.07.057