Title: Thermal%20conductance%20of%20solid-solid%20and%20solid-liquid%20interfaces
1Thermal conductance of solid-solid and
solid-liquid interfaces
- David G. Cahill,
- Zhenbin Ge, Ho-Ki Lyeo, Xuan Zheng, Paul Braun
- Frederick Seitz Materials Research Lab and
Department of Materials Science - University of Illinois, Urbana
2Interfaces are critical at the nanoscale
- Low thermal conductivity in nanostructured
materials - improved thermoelectric energy conversion
- improved thermal barriers
- High thermal conductivity composites and
suspensions
3Interfaces are critical at the nanoscale
- High power density devices
- solid state lighting
- high speed electronics
- nanoscale sensors
Micrograph of tunneling magnetoresistive
sensor for 120 GB drives, M. Kautzky (Seagate)
4Interface thermal conductance
- Thermal conductivity L is a property of the
continuum
- Thermal conductance (per unit area) G is a
property of an interface
5Interface thermal conductance (2001)
- Observations (2001) span a very limited range
- Al/sapphire ? Pb/diamond
- no data for hard/soft
- lattice dynamics (LD) theory by Stoner and Maris
(1993) - Diffuse mismatch (DMM) theory by Swartz and Pohl
(1987)
6Acoustic and diffuse mismatch theory
- Acoustic mismatch (AMM)
- perfect interface average transmission
coefficient lttgt given by differences in acoustic
impedance, Zrv - lattice dynamics (LD) incorporates microscopics
- Diffuse mismatch (DMM)
- disordered interface lttgt given by differences in
densities of vibrational states - Predicted large range of G not observed (2001)
- For similar materials, scattering decreases G
- For dissimilar materials, scattering increases G
72005 Factor of 60 range at room temperature
8Modulated pump-probe apparatus
9psec acoustics andtime-domain thermoreflectance
- Optical constants and reflectivity depend on
strain and temperature - Strain echoes give acoustic properties or film
thickness - Thermoreflectance gives thermal properties
10Modulated pump-probe
- four times scales
- pulse duration, 0.3 ps
- pulse spacing, 12.5 ns
- modulation period, 100 ns
- time-delay, t
t
Bonello et al. (1998)
11Analytical model for modulated time-domain
thermoreflectance
- frequency domain solution for heat flow in
cylindrical coordinates using gaussian beams. - G(k) given by iterative solution (transfer
matrix) - In-phase and out-of-phase signals by series of
sum and difference over sidebands
12Iterative solution for layered geometries
13Two basic types of experiments on solid samples
- thermal conductivity of bulk samples and thermal
conductance of interfaces
- thermal conductivity of thin films
14Flexible, convenient, and accurate technique...
- ...with 3 micron resolution
thermal conductivity map of cross-section of
thermal barrier coating, with J.-C. Zhao (GE)
15Interfaces between highly dissimilar materials
- high temperature limit of the radiation limit
R. J. Stoner and H. J. Maris, Phys.Rev.B 48, 22,
16373 (1993)
16Thermoreflectance data for Bi and Pb interfaces
17Room temperature thermal conductance
- Pb and Bi show similar behavior. Electron-phonon
coupling is not an important channel. - Weak dependence on Debye velocity of the
substrate. - Pb/diamond 50 smaller than Stoner and Maris but
still far too large for a purely elastic process.
18Temperature dependence of the conductance
- Excess conductance has a linear temperature
dependence (not observed by Stoner and Maris). - Suggests inelastic (3-phonon?) channel for heat
transport
19Application can we use interfaces to beat the
minimum thermal conductivity?
- If the small thermal conductance of Bi/diamond
could be reproduced in a multi-layered film, then
placing interfaces every 10 nm would give an
incredibly low thermal conductivity of 0.1 W/m-K
(factor of 2 smaller than a polymer).
20W/Al2O3 nanolaminates
- room temperature data
- sputtered in pure Ar
- atomic-layer deposition at 177 and 300 C, S.
George (U. Colorado) - G 220 MW m-2 K-1
21Unexpected advance Thermal conductivity imaging
- At t100 ps,
- in-phase signal is mostly determined by the heat
capacity of the Al film - out-of-phase signal is mostly determined by the
effusivity (LC)1/2 of the substrate
22ZrO2Y thermal barrier
- after 500 thermal cycles (1 h)
- 25 C gt1135 Cgt25 C
23ZrO2Y thermal barrier
- after 500 thermal cycles (1 h)
- 25 C gt1135 Cgt25 C
24Solid-liquid interfaces Two approaches
- Transient absorption measurements of
nanoparticles and nanotubes in liquid
suspensions. - Measure the thermal relaxation time of a suddenly
heat particle. If the particle is small enough,
then we have sensitivity to the interface - limited to interfaces that give good stability of
the suspension - Thin planar Al and Au films. Same as before but
heat flows both directions into the fluid and
into the solid substrate.
25Transient absorption
- Optical absorption depends on temperature of the
nanotube - Cooling rate gives interface conductance
- G 12 MW m-2 K-1
- MD suggests channel is low frequency squeezing
and bending modes strongly coupled to the fluid.
26Application Critical aspect ratio for a fiber
composite
- Isotropic fiber composite with high conductivity
fibers (and infinite interface conductance)
- But this conductivity if obtained only if the
aspect ratio of the fiber is high
27Hydrophilic metal nanoparticles 4 nm diameter
AuPd nanoparticles in water
- transient absorption data
2822 nm diameter AuPd nanoparticles in water CTAB
surfactant
29Nanoparticle summary
In Toluene
In water
G 200 MW m-2 K-1
G 15 MW m-2 K-1
30Application Critical particle radius for
nanocomposite
- Interface conductance and thermal conductivity of
the fluid determine a critical particle radius
rc L/G
- For particles in water, rc 3 nm.
- For high thermal conductivity particles, dilute
limit of effective medium theory
r gtgt rc DL (13f)L r ltlt rc DL
(1-1.5f)L
31Thermoreflectance of solid-liquid interfaces
no water
32Conclusions
- Much to learn about transport of heat across
interfaces but we now have good tools. - Pb/diamond, Bi/diamond interfaces show a
temperature dependent conductance far above the
radiation limit. What is the correct description
of this inelastic channel? - Can circumvent the minimum thermal conductivity
with high densities of interfaces. - Conductance of hydrophilic nanoparticle/surfactant
/water interfaces is essentially independent of
the surfactant layer. - Heat transfer is reduced by a factor of 4 at
hydrophobic interfaces with water.