Thermal%20conductance%20of%20solid-solid%20and%20solid-liquid%20interfaces

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Thermal 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

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Interfaces are critical at the nanoscale

• Low thermal conductivity in nanostructured
  materials
• improved thermoelectric energy conversion
• improved thermal barriers
• High thermal conductivity composites and
  suspensions

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Interfaces 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)
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Interface thermal conductance

• Thermal conductivity L is a property of the
  continuum

• Thermal conductance (per unit area) G is a
  property of an interface

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Interface 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)

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Acoustic 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

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2005 Factor of 60 range at room temperature
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Modulated pump-probe apparatus
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psec 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

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Modulated 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)
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Analytical 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

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Iterative solution for layered geometries
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Two basic types of experiments on solid samples

• thermal conductivity of bulk samples and thermal
  conductance of interfaces

• thermal conductivity of thin films

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Flexible, convenient, and accurate technique...

• ...with 3 micron resolution

thermal conductivity map of cross-section of
thermal barrier coating, with J.-C. Zhao (GE)
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Interfaces 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)
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Thermoreflectance data for Bi and Pb interfaces
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Room 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.

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Temperature 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

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Application 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).

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W/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

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Unexpected 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

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ZrO2Y thermal barrier

• after 500 thermal cycles (1 h)
• 25 C gt1135 Cgt25 C

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ZrO2Y thermal barrier

• after 500 thermal cycles (1 h)
• 25 C gt1135 Cgt25 C

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Solid-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.

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Transient 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.

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Application 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

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Hydrophilic metal nanoparticles 4 nm diameter
AuPd nanoparticles in water

• transient absorption data

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22 nm diameter AuPd nanoparticles in water CTAB
surfactant
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Nanoparticle summary
In Toluene
In water
G 200 MW m-2 K-1
G 15 MW m-2 K-1
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Application 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
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Thermoreflectance of solid-liquid interfaces

• hydrophobic
• 37 MW/m2-K

no water

• hydrophilic
• 150 MW/m2-K

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Conclusions

• 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.