3D Modeling and Simulation of Hg2Cl2
Crystal Growth by Physical Vapor
Transport
Joseph Dobmeier
Advisor: Patrick Tebbe
Minnesota State University
November 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]
Image from Kima et. al., 2008
 Applications include: laser Q-switches, fiber-optic
signal modulators, spectrometer frequency control
Introduction
 Two technologically
mature and
commercially available
materials for this region
are Terillium Oxide
(TeO2) and Thalium
Arsenide-Selenide
(TAS)
Image from http://www.olympusfluoview.com/theory/aotfintro.html
 TeO2 is fragile and prone to damage
 TAS is extremely toxic and requires specialized
handling
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. 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
Simulation
RaT=8.19e5, Pe=2.96, Pr=0.758, Le=0.500, Cv=1.06
RaT=8.19e5, Pe=2.96, Pr=0.758,Le=0.5,Cv=1.06
20
8
6
10
4
2
0
0
u
u
-2
-10
-4
-6
-20
-8
-10
-30
-12
-14
-40
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
t
RaT=8.19e5, Pe=2.96, Pr=0.758, Le=0.500, Cv=1.06
0.9
1
0
0.075 0.15 0.225
0.3 0.375 0.45 0.525 0.6 0.675 0.75 0.825
t
RaT=8.19e5, Pe=2.96, Pr=0.758, Le=0.500, Cv=1.06
100
10
121x121 node
61x61 node
31x31 node
90
80
5
70
60
u
Power*
0
50
40
-5
30
20
-10
10
-15
0
0.1
0.2
0.3
0.4
0.5
t
0.6
0.7
0.8
0.9
1
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Frequency (Hz)
1
1.1 1.2 1.3 1.4 1.5
Simulation
 Table of parameters used in study (Ts = 330°C):
Case ΔT (K)
n
1
2
1
2
7.5
1
3
20
1
4
30
1
5
7.5
0.01
6
7.5
0.001
7
7.5
0.0001
Rat
Pr
Le
Pe
Cv
3.83 x 104
1.80 x 105
8.19 x 105
1.92 x 106
1.80 x 103
1.80 x 102
1.80 x 101
0.871
0.831
0.758
0.717
0.831
0.831
0.831
0.411
0.366
0.500
0.540
0.366
0.366
0.366
0.876
1.90
2.96
3.50
1.90
1.90
1.90
1.71
1.28
1.06
1.03
1.28
1.28
1.28
time step Δt*
0.00125
0.00125
0.000125
0.000125
0.00125
0.00125
0.00125
Outline
 Modeling
 Simulation
 Results
 Future Research Directions
Results
 Case 1:
Results
 Case 2:
Results
 Case 5:
Results
Case 1 (0, 0, 0.5)
Case 2 (0, 0, 0.5)
Case 3 (0.49, 0, 0.4)
Case 5 (0.33, 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.