The

rmal

Eng

inee

ring

Labo

rato

ry,V

ande

rbilt

Uni

vers

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

1/12

The

rmal

Eng

inee

ring

Labo

rato

ry,V

ande

rbilt

Uni

vers

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

2/12

The

rmal

Eng

inee

ring

Labo

rato

ry,V

ande

rbilt

Uni

vers

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

3/12

The

rmal

Eng

inee

ring

Labo

rato

ry,V

ande

rbilt

Uni

vers

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.)

4/12

The

rmal

Eng

inee

ring

Labo

rato

ry,V

ande

rbilt

Uni

vers

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◦

5/12

The

rmal

Eng

inee

ring

Labo

rato

ry,V

ande

rbilt

Uni

vers

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.

6/12

The

rmal

Eng

inee

ring

Labo

rato

ry,V

ande

rbilt

Uni

vers

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

7/12

The

rmal

Eng

inee

ring

Labo

rato

ry,V

ande

rbilt

Uni

vers

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)

8/12

The

rmal

Eng

inee

ring

Labo

rato

ry,V

ande

rbilt

Uni

vers

ityTemperature distribution

• Typical average temperature distribution from all data after equilibration

9/12

The

rmal

Eng

inee

ring

Labo

rato

ry,V

ande

rbilt

Uni

vers

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

10/12

The

rmal

Eng

inee

ring

Labo

rato

ry,V

ande

rbilt

Uni

vers

ityThermal conductivity with substitution

3

4

5

6

7

8

9

10

0 20 40 60 80 100

ther

mal

con

duct

ivity

(W

/m K

)

substitution percent

50Å100Å400Åbulk

11/12

The

rmal

Eng

inee

ring

Labo

rato

ry,V

ande

rbilt

Uni

vers

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

12/12