Thermal Properties of Yttrium Aluminum Garnet from...
Transcript of Thermal Properties of Yttrium Aluminum Garnet from...
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ity Thermal Properties of Yttrium Aluminum Garnet fromMolecular Dynamics Simulations
ASME/JSME Thermal Engineering ConferenceHonolulu, Hawaii
March 15, 2011
Majid “Magic” S. al-DosariD. Greg Walker
Vanderbilt University
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ityWhy YAG?
• YAG is interesting in generalbecause of its applications
– solid-state lighting
– thermographic phosphor
– thermal barrier coating
– lasing medium
• YAG is particularly interesting to usbecause
– radiation hardness
– luminescence and transport areaffected by substitutional species
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ityAbout YAG (Y3Al5O12)
• Low electrical conductivity means thermal transport is phonon dominated
• Some (experimental) thermal properties
– thermal conductivity 10−14W/mK
– melting temperature 2213K
– Debye temperature θD = 750K
– thermal expansion 7.0×10−6 K−1 at 300K
– specific heat 600kJ/kgK
• 160 atoms in unit cell
– 24 Y
– 40 Al
– 96 O
• lattice constant is 12.01A
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ityPolyhedra in YAG
L. Dobrzycki, E. Bulska, D.A. Pawlak, Z. Frukacz and K. Wozniak, “Structure of YAG crystals doped/substituted with erbium and
ytterbium,” Inorganic Chemistry, 43(2), pp. 7656–7664, 2004. (Used with permission.)
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ityYAG model
• LAMMPS with custom potential
• Two-body potential
– Coulomb electrostatics (Ewald summation)
– Repulsive force
• Three-body potential
– O–Al/Y–O, 109.5◦
– A/Y–O–O, 109.5◦
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ityVerification and Validation
• Simulation parameters
– 0.002ps timestep
– 10−4 PPPM precision
– 7A cutoff
– periodic boundaries
– NPT ensemble; 1ps damping
– each temperature equilibrated for80,000 time steps (160ps)
Quantity LAMMPS Chen∗ experimentalmelting temperature (K) 1900 2131 2213thermal expansion (K−1) 7.8×10−6 7.0×10−6
lattice constant (A) at 300K 12.43 12.35 12.01specific heat (kJ/kg K) 0.87 0.6
∗ J. Chen et al., 2007, Chin. Phys., 16(9):2779.
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ityNon-equilibrium configuration
• Periodic boundaries are required because of long-range forces, so two “mirror”domains are simulated
• Imposed bath temperature; amount of energy added computed.
k = −
qA
dxdT
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ityNon-equilibirum simulation
• Simulation settings
– 0.001ps timestep
– 4A exponential cutoff; 7A Coulombic cutoff
– 10−5 PPPM precision
• Simulation parameters
– NVE integrator
– Aluminum substitutions: 0%, 50%, 100%
– Average temperature: 300K; ∆T = 40K
– Lengths: 4, 8, 16, and 32 unit cells (height and width are 1 unit cell each)
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ityTemperature distribution
• Typical average temperature distribution from all data after equilibration
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ityBulk Thermal Conductivity
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
0 0.005 0.01 0.015 0.02
1/k
(m K
/W)
1/length (Å−1)
0% Ga50% Ga
100% Ga
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ityThermal conductivity with substitution
3
4
5
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7
8
9
10
0 20 40 60 80 100
ther
mal
con
duct
ivity
(W
/m K
)
substitution percent
50Å100Å400Åbulk
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ityConclusions
• Simulations showed decent agreement with several thermalproperties (experimental and other equivalent model
• More data (other substitution percentages) are needed forfurther confidence.
• The interatomic potential for the gallium substitution was notaltered becasue no potential exists for this configuration.Density functional calculations can be used to determinepotential parameters.
• In the process of performing equilibirum analysis to validatefurther the foregoing results
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