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Research Papers: Conduction

# Measurement of Interface Thermal Resistance With Neutron Diffraction

[+] Author and Article Information
Seung-Yub Lee

Department of Applied Physics and
Applied Mathematics,
Columbia University,
New York, NY 10027
e-mail: sl3274@columbia.edu

Harley Skorpenske

Neutron Scattering Science Division,
Oak Ridge National Laboratory,
Oak Ridge, TN 37831
e-mail: skorpenskehd@ornl.gov

Alexandru D. Stoica

Neutron Scattering Science Division,
Oak Ridge National Laboratory,
Oak Ridge, TN 37831

Ke An

Neutron Scattering Science Division,
Oak Ridge National Laboratory,
Oak Ridge, TN 37831
e-mail: kean@ornl.gov

Xun-Li Wang

Department of Physics & Materials Science,
City University of Hong Kong,
Tat Chee Avenue,
Kowloon, Hong Kong
e-mail: xlwang@cityu.edu.hk

I. C. Noyan

Department of Applied Physics and
Applied Mathematics,
Columbia University,
New York, NY 10027
e-mail: icn2@columbia.edu

In this discussion, the volume element centered at point $P$ will be identified by the coordinates of its center point, $P(x,y,z)$.

If the material composition changes during the measurement through diffusion, or through phase changes, and/or the residual strains from past processing change due to these processes or through local yielding, the local lattice parameter will have changes that are not due to temperature and the temperature calculated will be inaccurate. In a numerical model, such processes can be taken into account if the equations linking these parameters to the lattice spacing are known.

$kI$ is an artificial parameter which accurately represents the temperature drop across the interface without attempting to differentiate the contributions from acoustic, asperity and thermal distortion components to the total thermal resistance. Using the equivalent interface film construction eliminates the need for local modeling of the contacting and non-contacting irregularities [29-30].

This equation was obtained by computing the $kM$ values over the temperature range of interest at 10 K intervals from the eighth order polynomial reported by Marquardt et al. [44], and fitting these data to a third order polynomial. Due to the limited temperature range used in this work this procedure did not yield significant error.

The strain data in Fig. 11(a) is calculated from the lattice parameter data shown in Fig. 8.

For these calculations, as a first approximation, the relatively small strain gradients within each plate were averaged to obtain the corresponding average strain values.

Comparing the temperatures computed from the thermal strain data to thermocouple values is insufficient to select the most accurate CTE equation; the thermocouples are far away from the regions interrogated by the neutron beam. Comparison of CT3, CT4 temperatures with the CT5, CT8 temperatures, respectively, shows that the temperature distribution in the central plate is not homogeneous in the zy plane.

The simple cases are treated first to highlight the important parameters before the general solutions are presented.

The computed and measured temperature profiles did not coincide if the variation of the $(kIj/kM)$ ratio was outside this range.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 14, 2012; final manuscript received July 11, 2013; published online November 28, 2013. Assoc. Editor: Robert D. Tzou. The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Heat Transfer 136(3), 031302 (Nov 28, 2013) (12 pages) Paper No: HT-12-1504; doi: 10.1115/1.4025500 History: Received September 14, 2012; Revised July 11, 2013

## Abstract

A noncontact, nondestructive neutron diffraction technique for measuring thermal resistance of buried material interfaces in bulk samples, inaccessible to thermocouple measurements, is described. The technique uses spatially resolved neutron diffraction measurements to measure temperature, and analytical or numerical methods to calculate the corresponding thermal resistance. It was tested at the VULCAN instrument of the Spallation Neutron Source, Oak Ridge National Laboratories on a stack of three 6061 alloy aluminum plates (heat-source, middle-plate, and heat-sink), held in dry thermal contact, at low pressure, in ambient air. The results agreed with thermocouple-based measurements. This technique is applicable to all crystalline materials and most interface configurations, and it can be used for the characterization of thermal resistance across interfaces in actual engineering parts under nonambient conditions and/or in moving/rotating systems.

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## Figures

Fig. 1

Schematic of traditional apparatus for measuring thermal contact resistance. In the current technique, the thermocouples are replaced by collimated neutron diffraction measurements (adapted from Ref. [9]).

Fig. 2

Schematic of the overall experimental geometry (a), and the central strip within which the internal temperatures are measured via neutron diffraction. Figures 2(c) and 2(d) depict the expected temperature distribution for finite interface resistances and the equivalent resistance circuit, respectively.

Fig. 3

Sample stack mounted on the Vulcan diffractometer. The welded membrane covers the cooling serpentine through which liquid nitrogen is circulated. The system is held together with spring-loaded struts at four corners. Figure 3(b) shows the thermocouple placement. Thermocouple pairs TC3-TC4 and TC5-TC8 yield the temperature gradient in the middle-plate.

Fig. 4

The temperatures recorded from thermocouples TC3-TC8 in the middle-plate as a function of time, for hot-plate set-points of 343 K (a) and 293 K (b), respectively. These data were correlated with thermal strain measurements to define the precision of the temperatures determined from neutron thermal strains. The corresponding mean temperatures after stabilization are 344.6 ± 0.2 K and 296.6 ± 0.1 K.

Fig. 5

Temperatures recorded from thermocouples TC0-TC9 as a function of time, with the hot-plate controller set-point at 323 K and liquid nitrogen introduced into the heat-sink. The temperature range of Fig. 5(a) is 3.5× of Fig. 5(b).

Fig. 6

Schematic of the neutron diffraction geometry. The probe volume is defined by the intersection of the apexes of the acceptance cones of the radial collimators and the incident beam. The sample can be moved along three orthogonal directions so that any position within the sample stack can be interrogated (inset).

Fig. 7

Typical time-of-flight (TOF) neutron diffraction data from the central plate refined via the GSAS program [40]. The measured data are depicted by the “+” symbols. The solid trace is the intensity computed from the refined model. The difference between the refined model output and the measured values form the residual line. In this plot, the tick-marks indicate the TOF positions of Bragg reflections.

Fig. 12

Modeled temperature values within the stack as a function of (k_I/k_M). In the calculation, the effective interface thickness was conservatively assumed to be 2 μm, which is twice the experimentally measured maximum asperity height.

Fig. 13

Computed thermal conductivity across the 25 mm thick Al middle-plate as a function of the variables (kI/kM) and tI. For hot and cold boundary temperatures of 306 K and 112 K, complete, intermediate and negligible thermal conductivities occur in regions I, II, and III (depicted by the in-set schematics). For 2 μm thick (identical) interfaces, the (ΔTM)A-E corresponding to the marked points A to E in Region II are 1.2, 11, 74, 167, and 191 K, respectively for ΔTHC = 194 K.

Fig. 11

Variation of thermal strain with x-position for stacks with full (a) and partial (b) nitrogen flow. In these figures, the lines connecting the data points are from the finite element simulation. The average temperature values in each plate are shown in Table 1. The error in the strain values is smaller than ±30 microstrain, which is comparable to the symbol size in the graph.

Fig. 10

abaqus model of the Al plate stack at steady state. The inset shows the interface detail on the heat-source side.

Fig. 9

Variation of the linear coefficient of thermal expansion, α, of the Al plates with temperature for the four expressions used in modeling. The boiling temperature of liquid nitrogen (77 K) is marked as the lower bound of temperature range.

Fig. 8

Neutron diffraction measurements of the Al lattice spacing as a function of position through the center of the stack at room temperature (RT) equilibrium and at steady state with thermal gradient. The error bars associated with the data points are similar in size to the symbols. The gaps in the data for the heat-sink plate correspond to the hollowed-out region where the coolant serpentine had been machined. The data for the cold-plate reflect the presence of additional residual strains due to the machining and welding steps. These strains did not change during the measurements. Typical error associated with each data point is ±0.0002 Å.

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