NASA/TM—2010-215670

The Lattice and Thermal Radiation Conductivity of

Thermal Barrier Coatings: Models and Experiments

Dongming Zhu and Charles M. Spuckler

Glenn Research Center, Cleveland, Ohio

February 2010
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NASA/TM—2010-215670

The Lattice and Thermal Radiation Conductivity of

Thermal Barrier Coatings: Models and Experiments

Dongming Zhu and Charles M. Spuckler

Glenn Research Center, Cleveland, Ohio

Prepared for the

33rd International Conference and Exposition on Advanced Ceramics and Composites

sponsored by the American Ceramic Society

Daytona Beach, Florida, January 18–23, 2009

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

February 2010
This work was sponsored by the Fundamental Aeronautics Program

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management.

Available from

NASA Center for Aerospace Information National Technical Information Service

7115 Standard Drive 5301 Shawnee Road

Hanover, MD 21076–1320 Alexandria, VA 22312

Available electronically at http://gltrs.grc.nasa.gov
The Lattice and Thermal Radiation Conductivity of Thermal

Barrier Coatings: Models and Experiments

Dongming Zhu and Charles M. Spuckler

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

The lattice and radiation conductivity of ZrO2-Y2O3 thermal barrier coatings was evaluated using a

laser heat flux approach. A diffusion model has been established to correlate the coating apparent thermal

conductivity to the lattice and radiation conductivity. The radiation conductivity component can be

expressed as a function of temperature, coating material scattering, and absorption properties. High

temperature scattering and absorption of the coating systems can be also derived based on the testing

results using the modeling approach. A comparison has been made for the gray and nongray coating

models in the plasma-sprayed thermal barrier coatings. The model prediction is found to have a good

agreement with experimental observations.

NASA/TM—2010-215670
National Aeronautics and Space Administration

Revolutionary Ceramic Coatings Greatly

Impact Gas Turbine Engine Technology

— Ceramic thermal and environmental barrier coating system development

goals

- Meet engine temperature and performance requirements

- Ensure long-term durability

- Improve technology readiness

- Develop design tools and lifing methodologies

— Crucial for envisioned supersonic vehicles: reduced engine emission,

improved efficiency and long-term supersonic cruise durability

www.nasa.gov 1

National Aeronautics and Space Administration i

Revolutionary Ceramic Coatings Impact Gas

Turbine Engine Technology

(Continued)

Step increase in temperature capability

Temperature 

n

3100 OF SiC/SiC

Capability (T/EBC) surface / CMC coatings

2800 °F ------------- 3000 °F+ (1650 °C+

combustor 2700 °F SiC/SiC CMC

TBC 2700 °F (1482 °C)^ and Si3N4 coatings

Increase in AT

2500 °F across T/EBC

Turbine TBC

Ceramic Matrix Composite _ _ 2400 °F (1316 °C)

Single Crystal Superalloy

--- 2000 °F (1093 °C)

Ge

Gen. IV

Gen I I – Current commercial

Gen I Year

www.nasa.gov 2

NASA/TM—2010-215670 2
National Aeronautics and Space Administration ZO Objectives

• Evaluate thermal conductivity and thermal radiation resistance of

ceramic coatings at high temperatures (2700 to 3200 °F), under

realistically thermal gradient conditions

• Facilitate the development advanced thermal and environmental

barrier coatings

• Improve understanding of the coating thermal radiation performance

Laser heat flux Laser heat flux Laser heat flux

High emissivity layer

1 1 1 1 1 1

Radiation emitter

1 1 1

Ceramic coating Ceramic coating Ceramic coating

(a) Internal radiation (b) Combined internal & (c) External radiation

external radiation

www.nasa.gov 3

National Aeronautics and Space Administration : ^t

NASA Steady-State Laser Heat-Flux Approach for

Ceramic Coating Thermal Conductivity Measurements

— A uniform laser (wavelength 10.6 μm) power distribution achieved using integrating

lens combined with lens/specimen rotation

— The ceramic surface and substrate temperatures measured by 8 μm and two-color

pyrometers and/or by an embedded miniature thermocouple

— Thermal conductivity measured at 5 sec intervals in real time

® DDD DDD

laser beam/ o

integrating lens o 3. 0 KW CO 2 High Power Laser

reflectometer / \ pyrometer

300 RPM /^O3 aluminum laser

aperture plate

camera

specimen

r `_ slip ring

thermocouple

cooling air

air gap platinum flat coils

bond coat

miniature

thermocouple

TBC coated

back aluminum

plate edge

aluminum back plate

air tube CMSX4 substrate

Ni-base superalloy or CMC substrate

www.nasa.gov 4

NASA/TM—2010-215670 3
8 μm pyrometer

for Tceramic-surface

qreflected

N

qdelivered

qradiated

ceramic coating

National Aeronautics and Space Administration .'

Ceramic Coating Thermal Conductivity Measurement

Approach by the Laser High-Heat-Flux Testing

kceramic(t) = qthru ⋅ lceramic /ΔTceramic(t) Where

V qthru = qdelivered −qreflected −qradiated and ΔTeraic(t)=Teramic-s urafce − Tmetal−back −

d qth (

l

substrate qthru ⋅dl (T) b ksubstrr«re(T)

ΔT c =ΔTmeasured

−ΔT.mbstrate −ΔTbond

Two-color and 8 μm /^

pyrometers for <\//,<\// \

Tsubstrate-back

ΔTtc \

substrate

Optional miniature

thermocouple for additional

17 qthru heat-flux calibration

www.nasa.gov 5

National Aeronautics and Space Administration /I

Thermal Conductivity of Fully Dense Oxides

— The radiation conductivity component evaluated

— Significant conductivity increase due to increased radiation at high

temperatures especially under thermal gradients

Laser heat flux Laser heat flux Laser heat flux

High emissivitylayer Radiation emitter

1 1 1 1 1 1

Ceramic coating Ceramic coating Ceramic coating

(a) Internal radiation (b) Combined internal & (c) External radiation

external radiation

5

La2Zr2O7 0 rO

2

-8wt%Y

2

O

3

 plasma-sprayed porous coating

3.0

u Hot-pressed specimens u

k measured

4 6 2.5 — k fit due to lattice conduction-radiation

3 increasing porosity 3

2.0 Free-standing coating

^

3

'Sa

• - ,^ 1.5 radiation

2 ^

La

2

Zr

2

O7 sol-gel hot-press 1.0

sintering induced 1 _ _ La

2

Zr

2

O7

 sol-gel hot-press a

0.5 conductivity rise lattice conduction

•.. . .. La

2

Zr

2

O7 hot-press F

0 0.0

200 400 600 800 1000 1200 1400 1600 200 400 600 800 1000 1200 1400 1600 1800

Surface temperature, °C Surface temperature, °C

www.nasa.gov 6

NASA/TM—2010-215670 4
National Aeronautics and Space Administration

Thermal Conductivity of Fully Dense Oxides

(Continued)

5

4

.y 3

U

b

O 2

U

y^^

1

t-^

0 I 1 1 1 I

200 400 600 800 1000 1200 1400 1600

Surface temperature, °C

www.nasa.gov 7

National Aeronautics and Space Administration

Evaluation of Lattice and Radiation Thermal

Conductivity of TEBC Systems at High Temperatures

— ZrO2-8wt%Y2O3/BSAS/mullite+20wt%BSAS/Si coating on SiC/SiC CIVIC substrate

— Conductivity determined by a steady-state laser heat-flux technique

— Coating surface radiation can contribute 5 to 15% total heat transfer at 1650 °C

—^ Tsurface ack

— Tucc 

k

Tb21ac Laser power

— Laser power

1.40 1600 1.40 1600

1400 ........

1.30 ----

--

I °' 130

1400 3

1200

3 o

°o, .p --------- :.........y ......... ;......... :

----.....-.. 1200 m

k 1.20 -----

^vty

1000 v 1.20 -.....-. -

0.35 ".......... 

1000 o

emt5

- ------- '----------`---------t-------

...--

-

0.40 U

t" 0.3 ^ I ^ . o --; -^ .,,

0.40

------- ------

i.. 800 U o — 0.45 i-. ____ __

0.45

w w 0.50 ...... . 800 w

1.10 f ------^ -- - 0.510::: - 1---::::::__k''::-- 1.10 .... ..... .... .....

......... a .........:......

- ^ 600 ^ m

i 600

- 400 { r d .^ 100 = ¢

..

-

00

N 1.00

p 200 

H •^ ......... .... ..:............ .........

o

z 0.90 0 z 0.90 200

0 5 10 15 20 25 30 35 40 1350 1400 1450 1500 1550 1600 1650

Time, min Surface temperature, C

www.nasa.gov 8

NASA/TM—2010-215670 5
National Aeronautics and Space Administration

Radiative Diffusion Models

- The diffusion conduction equations

dT 16σ ⋅ n 2⋅ Twe dT _r 16σ⋅ n 2⋅T dT

qtotal = kcond dx + 3 (a + σs

dx — 



kcond + 3 (a + σs ) )dx

16σ⋅ n 2 ⋅ T 3

e

q

total = Total heat flux

k^ective = kcond + = kcond + k ad kcond = Intrinsic lattice conductive thermal conductivity

3 (a +σs krad = radiation thermal conductivity

qr1 < qr2

Tg1

Tg2

Ts1 D

keffective = effective thermal conductivity

σ = Stefan-Boltzman constant 5.6704x10-8 W/(m2-K4)

n = Refractive index, 2.2

a = Absorption coefficient, cm-1

σs = Scattering coefficient, c m1

T = Average temperature of the material, K

qr1

Radiative

opaque diffusion transparent

approximation

0 ν c1 ν c2

Regions of optical thickness

www.nasa.gov 9

National Aeronautics and Space Administration i

Radiative Diffusion Models for Nongray Materials ^'r

- The diffusion conduction models established for nongray coating materials

- The diffusion conduction equations

dT σ⋅ n

2

+ 16 ⋅ Tme dT

= kcond +

16

 σ⋅ n

2

⋅ T:

 dT

kco

qtotal =

dx 3 (a + a) dx  3 (a +σs

)



 dx

Gray model

I

16σ ⋅ n

2

⋅ T

3

ave

qtotal

= Total heat flux

keffective = k

cond + = kcond

3(a +σ)

+ k

rad

k

cond

= Intrinsic lattice conductive thermal conductivity

s

krad = radiation thermal conductivity

1

4m^

{ k +

16" ⋅ n

2

 TL [FF ]l 

[T(0) − T(d)1

keffecti ve

= effective thermal conductivity

=

3x K '°`^•`

− 0

i

0 istTave

 d

σ= Stefan-Boltzman constant 5.6704x10-8 W/(m2

-K4)

Nongray

I

n= Refractive index, 2.2

— model F0→xT 

— 15 i [ e ' + 65 + 6 =

l + 3S 1

3 I

aAbsorptioncoefficient,cm-1

aC

L

n n n n 

l

σ

s 

= Scattering coefficient, cm-1

T= Average temperature of the material, K

qr1 < q r 2 qr 1

Radiative

T

g 1 Tg2

opaque diffusion transparent

Ts 1 D

approximation

0 ν

c1

ν

c2

Regions of optical thickness

www.nasa.gov 10

NASA/TM—2010-215670 6
0

1.0

a

0.8

a^

a 0.6

00

0.4

0

x 0.2

U

0.0

0 500 1000 1500

Coating thickness, microns

2000

National Aeronautics and Space Administration

Evaluation of Lattice and Radiation Thermal

Conductivity of 3000 °F Coating Systems 0

- Freestanding coatings and gray layer radiative diffusion assumption models

3 0

x 2.5

2.0

0 1.5 b

0

U

1.0

N

0.5

k^

 dT + 16σ ⋅ n 2⋅T!. dT _



k^ +

16σ ⋅ n2 ⋅ T!.

qtot

 dT

d - '^ dx 3 (a +σ) dx '^ 3(a +σ,) 



dx

k ti k

+ 16σ⋅ n 2⋅ T!. =

k- +k

v = conm rva

3 (a +σ,)

a

0

,o

Radiation component =

0.0 I I 1

200 400 600 800 1000 1200 1400 1600 1800

Surface temperature, °C

Thermal radiation evaluation of advanced coating materials

www.nasa.gov 11

National Aeronautics and Space Administration

Scattering Component of Plasma-Sprayed

Coating Systems

0.0 0.50 1.0 1.5 2.0

www.nasa.gov 12

NASA/TM—2010-215670 7
National Aeronautics and Space Administration

Radiation Conductivity Component of

Ceramic Materials

1.2

1.0

0.8

a

0.6

U

0 0.4 .Y

0.2

I I I% I I

- d7 -

^q —0— Dense materials-1100C_

.nj--0— Dense materials-1200C -

--E] — Dense materials-1300C -

-^ - Dense materials-1400C -

--0- - ^— Coatings-1550C

Coatings-1600C

^— Coatings-1650C

n — Coatings-1700C

0.0

0 200 400 600 800 1000 1200

Thermal gradient, K/mm

Average temperature

www.nasa.gov 13

National Aeronautics and Space Administration

Evaluation of Radiation Flux Resistance of

Oxide Coating Systems

— Preliminary results showed doped HfO2 coatings had better radiation

resistance

1600 150

1400 15 mil Tradiation source Coating thickness, microns

1200 doped Troack "e

1 0 0

200 400 600 800 1000 1200

U HfO2 100 B 1000

G

800

a

9 600

H

q

rad 50 0.5 400 ^— rad-thru

200

or

0 0 \^

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0+'

Time, hours

T radiation source

0.1

0.00 0.02 0.04 0.06 0.08 0.10 0.12

T back Coating thickness, cm

qradthru =hc(Tback-Tair)

www.nasa.gov 14

NASA/TM—2010-215670 8
National Aeronautics and Space Administration

Concluding Remarks

• Laser heat-flux approach established for radiation thermal

conductivity measurements and advanced coating development

• Lattice and radiation conductivity determined for dense materials

and coatings

• The diffusion conduction models established for gray and nongray

coating materials

• Scattering and absorption determined for coatings under realistic

thermal gradients at high temperatures

• Advanced coatings promising in reducing radiation conductivity

www.nasa.gov 15

NASA/TM—2010-215670 9
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The Lattice and Thermal Radiation Conductivity of Thermal Barrier Coatings: Models and

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Zhu, Dongming; Spuckler, Charles, M.

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

The lattice and radiation conductivity of ZrO2-Y2O3 thermal barrier coatings was evaluated using a laser heat flux approach. A diffusion

model has been established to correlate the coating apparent thermal conductivity to the lattice and radiation conductivity. The radiation

conductivity component can be expressed as a function of temperature, coating material scattering, and absorption properties. High

temperature scattering and absorption of the coating systems can be also derived based on the testing results using the modeling approach. A

comparison has been made for the gray and nongray coating models in the plasma-sprayed thermal barrier coatings. The model prediction is

found to have a good agreement with experimental observations.

15. SUBJECT TERMS

Thermal conductivity; Coatings; Scattering; Absorption; Absorbents; Thermal radiation; Oxides

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