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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 ... – PowerPoint PPT presentation

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


1
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

2
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

3
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)
4
Interface thermal conductance
  • Thermal conductivity L is a property of the
    continuum
  • Thermal conductance (per unit area) G is a
    property of an interface

5
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)

6
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

7
2005 Factor of 60 range at room temperature
8
Modulated pump-probe apparatus
9
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

10
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)
11
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

12
Iterative solution for layered geometries
13
Two basic types of experiments on solid samples
  • thermal conductivity of bulk samples and thermal
    conductance of interfaces
  • thermal conductivity of thin films

14
Flexible, convenient, and accurate technique...
  • ...with 3 micron resolution

thermal conductivity map of cross-section of
thermal barrier coating, with J.-C. Zhao (GE)
15
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)
16
Thermoreflectance data for Bi and Pb interfaces
17
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.

18
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

19
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).

20
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

21
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

22
ZrO2Y thermal barrier
  • after 500 thermal cycles (1 h)
  • 25 C gt1135 Cgt25 C

23
ZrO2Y thermal barrier
  • after 500 thermal cycles (1 h)
  • 25 C gt1135 Cgt25 C

24
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.

25
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.

26
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

27
Hydrophilic metal nanoparticles 4 nm diameter
AuPd nanoparticles in water
  • transient absorption data

28
22 nm diameter AuPd nanoparticles in water CTAB
surfactant
29
Nanoparticle summary
In Toluene
In water
G 200 MW m-2 K-1
G 15 MW m-2 K-1
30
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
31
Thermoreflectance of solid-liquid interfaces
  • hydrophobic
  • 37 MW/m2-K

no water
  • hydrophilic
  • 150 MW/m2-K

32
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.
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