Heat transfer process during the crystallization of benzil grown by the Bridgman–Stockbarger method $ F. Barvinschi a,n , A. Stanculescu b , F. Stanculescu c a Department of Physical Foundation of Engineering, ‘‘Politehnica’’ University of Timisoara, Bv. V. Parvan, No. 2, Timisoara 300223, Romania b National Institute of Materials Physics, P.O. box MG-7, Bucharest-Magurele 077125, Romania c University of Bucharest, Faculty of Physics, 405 Atomistilor Street, P.O. Box MG-11, Bucharest-Magurele 077125, Romania article info Presented at the Romanian Conference on Advanced Materials—ROCAM 2009, August 25–28, 2009, Brasov, Romania. Available online 18 November 2010 Keywords: A1. Crystal growth A1. Heat transfer B1. Organic materials B2. Benzil C1. Numerical modelling abstract The temperature distribution and solid–liquid interface shape during benzil growth have been studied both experimentally and numerically. The heat transfer equation with appropriate boundary conditions has been solved by modelling a vertical Bridgman–Stockbarger growth configuration. Two models have been developed, namely a global numerical model and a pseudo-transient approximation in an ideal configuration. & 2010 Elsevier B.V. All rights reserved. 1. Introduction Organic solids are a class of materials for which there is an increasing interest in various fields of application in photonics for the manufacturing of nonlinear and electro-optical devices [1–4]. Benzil is an aromatic compound, which in solid-state could have potential applications in nonlinear optics because of the: (i) high nonlinear coefficient, (ii) large birefringence, (iii) high damage threshold and (iv) large transparency domain [5,6]. Large single crystals of benzil (length: 35 mm diameter: 12 mm) were grown by employing a vertical Bridgman–Stockbarger (BS) two-zone crystal growth system [7]. Compositional homogeneity and crystalline structure are deter- mined by the macroscopic shape of the interface between solid and liquid phase during directional solidification, which is the result of the conjugated action of different factors such as the: (i) heat transport process, (ii) moving speed of the growth ampoule and (iii) anisotropic growth speed. We present in this paper the details with regard to growth of benzil single crystals by Bridgman–Stockbarger technique and the results of numerical modelling of heat transfer during the crystal- lization process. Numerical calculations have been performed with the commercial software package Fluent TM . A first steady-state heat transport model in the whole furnace is solved (Section 3). In Section 4, the model is restricted to the central part of the Bridgman furnace, taking into account the pseudo-transient heat transfer. 2. Experimental Benzil has a tendency of supercooling and low thermal conductiv- ities in the solid and melt phase and is characterized by a high enthalpy of fusion (DH f ¼ 23.56 kJ/mol [8]). The high value of 4.6  1024 mol 1 [9] computed for the ratio (DH f k/T m ), where k is the Boltzmann constant and T m is the melting temperature of the compound, sustains a tendency to facetted growth morphology and high constitutional supercooling [10] that must be compensated by a steep gradient at the crystal/melt interface. This thermal profile is obtained in a transparent quartz tubular furnace with a variable spacing kanthal coil covered by a supplementary external quartz wall to reduce thermal losses and radial temperature gradients. Temperature is adjusted by a control system connected with a thermocouple situated in the hot zone. A clock mechanism assures the slow moving speed of the ampoule in order to compensate low thermal conductivity of the organic compound. The starting material is sealed under vacuum in a glass ampoule with a conical shaped tip. The narrower zone, situated at 1.5 cm from the tip, controls nucleation and solidification processes (Fig. 1a). Thermal transfer near the interface is controlled by thermal conduction, the convection being reduced through the use of small diameter ( o15 mm) ampoules. Because the pure melted benzil is a transparent light yellow material we have used a transparent furnace for a direct visualization, in real time, of the interface shape as a parameter of the growth process and an indicator for subsequent control of the crystal quality [9]. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jcrysgro Journal of Crystal Growth 0022-0248/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2010.11.028 $ Presented at the Romanian Conference on Advanced Materials – ROCAM 2009, August 25–28, 2009, Brasov, Romania. n Corresponding author. Tel.: + 40256203417; fax: + 40256403392. E-mail address: fbarvinschi@gmail.com (F. Barvinschi). Journal of Crystal Growth 317 (2011) 23–27