Post on 21-Mar-2016
description
3D Modeling and Simulation of Hg2Cl2 Crystal Growth by Physical Vapor
Transport
Joseph DobmeierAdvisor: Patrick Tebbe
Minnesota State UniversityNovember 2011
Introduction
Hg2Cl2 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
Introduction Two technologically
mature and commercially available materials for this region are Terillium Oxide (TeO2) and Thalium Arsenide-Selenide (TAS)
TeO2 is fragile and prone to damage TAS is extremely toxic and requires specialized
handling
Image from http://www.olympusfluoview.com/theory/aotfintro.html
Introduction
Images from Kima et. al., 2008
Outline
Modeling Simulation Results Future Research Directions
Modeling Four conservation equations[2-4]:
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]
Outline
Modeling Simulation Results Future Research Directions
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
Simulation Mesh density:
Parametric studies were performed in 2D on the mesh density
Three sizes were compared: 1. 31x312. 61x613. 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
Simulation
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50
10
20
30
40
50
60
70
80
90
100
RaT=8.19e5, Pe=2.96, Pr=0.758, Le=0.500, Cv=1.06
Frequency (Hz)
Pow
er*
121x121 node61x61 node31x31 node
0 0.075 0.15 0.225 0.3 0.375 0.45 0.525 0.6 0.675 0.75 0.825
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
t
u
RaT=8.19e5, Pe=2.96, Pr=0.758,Le=0.5,Cv=1.06
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-15
-10
-5
0
5
10
RaT=8.19e5, Pe=2.96, Pr=0.758, Le=0.500, Cv=1.06
t
u
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-40
-30
-20
-10
0
10
20
RaT=8.19e5, Pe=2.96, Pr=0.758, Le=0.500, Cv=1.06
t
u
Simulation
Case ΔT (K)
n Rat Pr Le Pe Cv time step Δt*1 2 1 3.83 x 104 0.871 0.411 0.876 1.71 0.001252 7.5 1 1.80 x 105 0.831 0.366 1.90 1.28 0.001253 20 1 8.19 x 105 0.758 0.500 2.96 1.06 0.0001254 30 1 1.92 x 106 0.717 0.540 3.50 1.03 0.0001255 7.5 0.01 1.80 x 103 0.831 0.366 1.90 1.28 0.001256 7.5 0.001 1.80 x 102 0.831 0.366 1.90 1.28 0.001257 7.5 0.0001 1.80 x 101 0.831 0.366 1.90 1.28 0.00125
Table of parameters used in study (Ts = 330°C):
Outline
Modeling Simulation Results Future Research Directions
Results Case 1:
Results Case 2:
Results Case 5:
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)
Outline
Modeling Simulation Results Future Research Directions
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
Questions ???
References[1] Joo-Soo Kima, Sudhir B. Trivedia, Jolanta Soosa, Neelam Guptab, Witold Palosza. Growth of Hg2Cl2 and Hg2Br2 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 2nd Ed., John Wiley & Sons Inc., (2002) 268, 353-356. [7] F.C. Moon. Chaotic and Fractal Dynamics. John Wiley & Sons Inc., (1992) 53-55.