1. 3D Modeling and Simulation of Hg 2 Cl 2 Crystal Growth by Physical Vapor Transport Joseph Dobmeier Advisor: Patrick Tebbe Minnesota State University November 2011

2. Introduction  Hg 2 Cl 2 crystals are useful for their acousto-optic properties  Used to construct acousto-optic modulators and tunable filters in the low UV and long wave infrared regions 8-10μm [1]  Applications include: laser Q-switches, fiber-optic signal modulators, spectrometer frequency control Image from Kima et. al., 2008

3. Introduction  Two technologically mature and commercially available materials for this region are Terillium Oxide (TeO 2 ) and Thalium Arsenide-Selenide (TAS)  TeO 2 is fragile and prone to damage  TAS is extremely toxic and requires specialized handling Image from http://www.olympusfluoview.com/theory/aotfintro.html

4. Introduction Images from Kima et. al., 2008

5. Outline  Modeling  Simulation  Results  Future Research Directions

6. Modeling  Four conservation equations [2-4] :

7. Modeling  Geometry:  Vertically oriented 5x5cm cylinder with the source at the bottom  Boundary conditions:  Walls: no slip, adiabatic, and impermeable  Source and sink: constant temperature, tangential velocity of zero, normal velocity calculated using Fick’s law and Dalton’s law of partial pressures [6]

8. Outline  Modeling  Simulation  Results  Future Research Directions

9. Simulation  Performed by a commercially available code FIDAP, a product of Fluent Inc.  Capabilities extended to physical vapor transport process through the use of a subroutine  Subroutine determines the boundary nodal velocities by a finite difference calculation of the mass fraction derivatives  Each nodal velocity was then scaled to ensure source and crystal mass flux average values satisfied the continuity equation [2]  Initial conditions for velocity were zero, a linear profile was selected for the concentration profile

10. Simulation  Mesh density:  Parametric studies were performed in 2D on the mesh density  Three sizes were compared: 1.31x31 2.61x61 3.121x121  Flowfield development was found to be identical, but some small-scale recirculation cells were not captured  A frequency analysis was undertaken comparing the oscillatory regions which agreed across densities

11. Simulation

12. Case ΔT (K) nRa t PrLePeCvCv time step Δt * 1213.83 x 10 4 0.8710.4110.8761.710.00125 27.511.80 x 10 5 0.8310.3661.901.280.00125 32018.19 x 10 5 0.7580.5002.961.060.000125 43011.92 x 10 6 0.7170.5403.501.030.000125 57.50.011.80 x 10 3 0.8310.3661.901.280.00125 67.50.0011.80 x 10 2 0.8310.3661.901.280.00125 77.50.00011.80 x 10 1 0.8310.3661.901.280.00125  Table of parameters used in study (T s = 330°C):

13. Outline  Modeling  Simulation  Results  Future Research Directions

14. Results  Case 1:

15. Results  Case 2:

16. Results  Case 5:

17. Results Case 5 (0.33, 0, 0.5) Case 2 (0, 0, 0.5) Case 3 (0.49, 0, 0.4) Case 1 (0, 0, 0.5)

18. Outline  Modeling  Simulation  Results  Future Research Directions

19. Future Research  Complete bifurcation graph showing flowfield regime transition  Perform phase-space analysis of transient and oscillatory regions  Simulate more cases for current geometry  Modify geometry for different furnace layouts  Reduce total run time through parallel implementation of simulation with newer commercial software code

20. Questions ???

21. References [1] Joo-Soo Kima, Sudhir B. Trivedia, Jolanta Soosa, Neelam Guptab, Witold Palosza. Growth of Hg 2 Cl 2 and Hg 2 Br 2 single crystals by physical vapor transport. Journal of Crystal Growth 310 (2008) 2457–2463. [2] P. A. Tebbe, S.K. Loyalka, W. M. B. Duval. Finite element modeling of asymmetric and transient flowfields during physical vapor transport. Finite Elements in Analysis and Design 40 (2004) 1499-1519. [3] W. M. B. Duval, Convection in the physical vapor transport process-I: thermal, J. Chem. Vapor Deposition 2 (1994) 188-217. [4] W. M. B. Duval, Convection in the physical vapor transport process-II: thermosolutal, J. Chem. Vapor Deposition 2 (1994) 282-311. [5] D. W.Greenwell, B. L. Markham and F. Rosenberger. Numerical modeling of diffusive physical vapor transport in cylindrical ampoules, Journal of Crystal Growth, 51 (1981) 413-425. [6] R. B. Bird, W.E Stewart and E. M. Lightfoot. Transport Phenomena 2 nd Ed., John Wiley & Sons Inc., (2002) 268, 353-356. [7] F.C. Moon. Chaotic and Fractal Dynamics. John Wiley & Sons Inc., (1992) 53-55.