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.