A molecular dynamics simulation on the static calibration test of a revised thin-film thermopile heat-flux sensor

Measurement 150 (2020) 107039

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A molecular dynamics simulation on the static calibration test of a revised thin-film thermopile heat-flux sensor Kai Yang a,⇑, Qingtao Yang a, Xinxin Zhu a, Hui Wang a, Tao Zhu a, Jianhua Liu b a b

Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center (CARDC), Mianyang 621000, People’s Republic of China Beijing Research Institute of Telemetry, Beijing 100076, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 7 March 2019 Received in revised form 3 September 2019 Accepted 7 September 2019 Available online 11 September 2019 Keywords: Thin-film thermopile heat-flux sensor Sensitivity coefficient Thermal conductivity None-equilibrium molecular dynamics Substrate effect

a b s t r a c t A revised thin-film thermopile heat-flux sensor with cooper-based heat sink is calibrated at a static calibration system that provides a stable heat flux source in the range of 0.1–10.0 MW/m2. The calibration results show that sensitivity coefficients (SCs) of the revised heat-flux sensor are quadratically dependent on surface temperatures, which is different from the linear SCs of original heat-flux sensors. A molecular dynamics simulation is applied to predict the thermal conductivity (TC) of thin-film thermal resistance layer and the interfacial thermal resistivity at the interface with film thickness and substrate material being considered. With the aid of the molecular dynamics simulation and finite element method, the reason for such a difference is analyzed to be the coupled effect of temperature-dependent thermal conductivity (TC) of thin-film thermal resistance layer and the interfacial thermal impedance at the interface. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Heat flux that used to determine the amount of thermal energy passed through a given area per unit of time is a critical parameter in the research field of thermal protection system design, thermal energy engineering, etc [1,2]. With appropriate assumption and materials properties, heat flux is mostly determined by the measured temperature or temperature difference [3]. Consequently, different kinds of heat flux sensors have been developed and some are frequently applied in the aerospace engineering, such as Gardon gages [4], slug-type calorimeters, Schmidt-Boelter gages, coaxial thermocouples [5,6] and Null-point calorimeters [1]. As is known to all, water-cooled Gardon gages can survive temperatures up to 1000 °C and have a time response about 0.2–5.0 s; the primary disadvantages for slug-type calorimeters are their short lifetime, though slug-type calorimeters are simple to fabricate [7]; Schmidt-Boelter gages have a time response
0.05 s, frequently used in temperature below 350 °C; coaxial thermocouples and Null-point calorimeters have a short run time (<0.5 s), though designed for high heat flux measurement [8]. Hence, these flux sensors cannot meet the demands of long run-time (>10 s), fast time-response (<0.1 ms) and high heat flux (>1MW/m2), which are required in hypersonic flight tests. Thin-film thermopile heat-flux sensors [9], which are first reported in 1980s, are made with the aid of Physical Vapor Depo⇑ Corresponding author. E-mail address: [email protected] (K. Yang). https://doi.org/10.1016/j.measurement.2019.107039 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved.

sition or Chemical Vapor Deposition techniques. A new version of such a heat-flux sensor has been developed to survive temperature up to 1000 °C and high heat flux [8]. However, the new sensors cannot be exposed to a high temperature, high heat flux environment for more than 10 s because of no heat-sink design. Hence, a cooper-based heat sink is added to extend its application range in hypersonic flight tests. And the revised heat-flux sensors are calibrated at our static calibration system, a radiation facility. Moreover, this study focuses on analyzing calibration data and discussing the reasons for the different SCs between the new version and the revised heat-flux sensors. The measuring principle for thin-film thermopile heat-flux sensors is that the temperature difference across the thermal resistance layer is proportional to the heat flux, which would be detailly presented in Section 2. Hence, thermal conductivity (TC) of the thermal resistance layer is a primary parameter that has a dominant influence on the SCs of thin-film thermopile heat-flux sensors. As is well known, TC is temperature-dependent. And several methods are developed to measure TCs of thin films [10–13]. It is said in Ref. [11] that TCs of thin films are mainly dependent on film thickness, film materials, temperature and methods of thin film deposition. In recent years, Molecular Dynamics (MD) is applied to predict TCs of thin films [14,15]. Film thickness, temperature and substrate materials are easy embedded in MD simulations, since thin film fabrication and TC measuring platform construction are money-consuming, and moreover there is no a standard method for measuring TC of thin films that is recommended by any institution. In this study, LAMMPS (Large-scale

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K. Yang et al. / Measurement 150 (2020) 107039

atomic/molecular massively parallel simulator) [16] distributed by Sandia National Laboratories [17] is used to calculate TC of the thermal resistance layer with considering substrate material, what helps understand our static calibration test results of the thin-film thermopile heat-flux sensors. Namely, MD simulation would be applied to help design thin-film heat-flux sensors. The correspondence is organized as follows: the thin-film thermopile heat-flux sensor and the calibration facility are briefly introduced in Section 2, including the derived sensitive coefficient, the uncertainty analysis for the calibration facility and a typical profile of original calibration data. Section 3 presents the analyzed results of calibration data and the MD simulation results, which help understand the different sensitive coefficients between the new version and the revised heat-flux sensors. Conclusions are given in Section 4.

with the thermoelectric voltage output V, V; Seebeck coefficient of the thermocouples se , V/°C; the number of thermocouple pairsN. The SC is defined as K ¼ V=q, namely we have

K¼N

2.1. Thin-film thermopile heat-flux sensor As illustrated in Fig. 1, the sensitive element consists of a thermal resistance layer and a series of thermocouple junctions, which are called thermopile that used to amplify the temperature difference signal because the thermal resistance layer (about 1 lm) is so thin that the temperature difference across the thermal resistance layer is really small [8]. Then we have

k q ¼ ðT 1  T 2 Þ d

ð1Þ

where, q is heat flux density, W/m2; k is TC of the thermal resistance layer, W/(m.°C); d is the thickness of the thermal resistance layer, m; DT ¼ T 1  T 2 is the temperature difference across the thermal resistance layer with the upper surface temperature T 1 and the lower surface temperature T 2 , °C. What’s more,

DT ¼

V Nse

ð2Þ

ð3Þ

For a fabricated heat-flux sensor, the thickness of thermal resistance layer d and the number of thermocouple pairs N are two constants, which are known in advance. So the SC K is a function of TC of the thermal resistance layer and Seebeck coefficient of the thermocouple. As mentioned above, TC is temperature-dependent. Hence, the SC K is related to the temperature. Consequently, the new version of the thin-film thermopile heat-flux sensors applies a kind of corrected SC [18].

q¼ 2. Static calibration test

se d k

V V ¼ K c a þ bT

ð4Þ

Namely, K c ¼ a þ bTwith a and b being two parameters, which can be determined with the aid of static calibration tests. T  ðT 1 þ T 2 Þ=2 is the surface temperature, which is measured by the thermal resistor. 2.2. The radiation facility for calibrating heat-flux sensors The revised thin-film thermopile heat-flux sensors, as shown in Fig. 2, are calibrated at our calibration system. The calibration system, a radiation facility, provides a stable heat flux in the range of 0.1–10.0 MW/m2. As shown in Fig. 3, the ellipsoidal mirror focuses most of the rays from the 10 kW short-arc Xenon lamp located at the first focal point F1 on the other focal point F2. To calibrating heat flux sensors, a water-cooled optical integrator is applied to obtain a uniform distributed light spot. Owing to the stable light source, a transfer calibration method [19] is used: when the shuttles are open, a commercial water-cooled Gardon gauge, which is regularly corrected by a transfer standard Electrically calibrated radiometer (ECR), is exposed to the uniform distributed light spot and a reference heat flux is obtained; then the shuttles are closed

Fig. 1. The sensitive element of a thin-film thermopile heat-flux sensor.

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K. Yang et al. / Measurement 150 (2020) 107039

Fig. 2. The revised thin-film thermopile heat-flux sensor.

and a to-be-calibrated heat flux sensor is moved to the same position, where it is exposed to the same incident heat flux. In addition, Pyromark 1200, a kind of high-temperature black paint, is sprayed on the front surface of to-be-calibrated heat flux sensors for a stable absorptivity and the absorptivity is 0.946, which is calculated with the aid of measured spectral reflectivity provide by the National Institute of Metrology, China. Detailed information about the calibration system can be found in Ref. [20]. With regard to the transfer calibration method, the measurement uncertainties are grouped under two categories: Type A, evaluated using statistical methods, and Type B, evaluated by other

means, such as the instruction manuals provided by the manufacturers. The individual uncertainties are simply discussed below and the values tabulated in Table 1, which are then combined using the square root of the sum-of-the squares to arrive at the combined standard measurement uncertainty [21]. As shown in Table 1, (I) the uncertainty for ECR is estimated to be 0.6% [21], which is obtained from previous measurements [19]; the plane nonuniformity and time stability of the light spot that generated by the water-cooled optical integrator have a great influence on the transfer calibration, since the light spot is used to calibrate heatflux sensors and different heat-flux sensors have different sensing areas and response times from those of the water-cooled Gardon gauge. A horizontal scanning method, with which the watercooled Gardon gauge is placed at different heights of the light spot and continuously measures the heat flux when horizontally traveling at a low speed (about 1.9 mm/s) through the light spot, is used to determine the plane non-uniformity of the light spot. (II) And the uncertainty for the plane non-uniformity is estimated to be 1.5%; three consecutive tests are conducted at each constant power of the short-arc Xenon lamp and five constant powers are selected over the power range. (III) Then the uncertainty for the time stability is estimated to be 1.0% [20]; a high-precision stepping-motordriven transfer device is applied to transfer to-be-calibration heat-flux sensors and the water-cooled Gardon gauge. Assuming a maximum error of about 0.25 mm in the position of the watercooled Gardon gauge, (Ⅳ) the corresponding uncertainty is tested to be about 0.1%; the experimental data is sampled via a DH5927N data acquisition unit, and (V) the uncertainty is reported to be 0.5 in its manual; in this study, Pyromark 1200 is sprayed on the front

Fig. 3. The Xenon short arc lamp calibration system for calibrating heat flux sensors [20].

Table 1 Estimate of uncertainties for the heat-flux sensor calibration facility. Uncertainty Source I Transfer Standard ECR II Water-cooled Gardon gauge III IV V Data acquisition unit VI High-temperature paint Relative expanded uncertainty (U ¼ kuc *) qffiffiffiffiffiffiffiffiffiffiffi P 2ffi ** * uc ¼ i ui ; k ¼ 2 means that it is equivalent to an uncertainty of 2

Non-uniformity of the light spot Repeat tests at the same position Position alignment

Type

Uncertainty (%)

B A A A B B k ¼ 2**

0.6 1.5 1.0 0.1 0.5 1.0 4.42

standard deviations about the mean of a normalized Gaussian distribution.

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K. Yang et al. / Measurement 150 (2020) 107039

surface of to-be-calibrated heat flux sensors and (VI) the uncertainty for the paint is 1%, which is provided by the National Institute of Metrology, China. 2.3. A typical profile of original calibration data In this study, each sensor is calibrated at three different heatflux levels. The calibration setup is illustrated in Fig. 4 and a typical profile of original calibration data is depicted in Fig. 5. In general, thermal resistor is used for high-precision temperature measurement on the principle of temperature-dependent resistance, and the thermal resistor is thin film Pt, which is deposited on the front surface. For the purpose of synchronously collecting the temperature difference DT and surface temperature T signals, a constant current (1 mA) is supplied to the thermal resistor, and then the corresponding resistance is converted into voltage. In addition, the surface temperature T is calculated with the aid of resistance-temperature calibration data, which is shown in Fig. 6. 3. Results and discussion

ence heat flux is determined by the water-cooled Gardon gage that is regularly corrected by ECR. The calibration results of a revised sensor are shown in Fig. 7. Obviously, a quadratically temperature-dependent SC seems reasonable. Then we have

q¼

V

ð5Þ

a þ bT þ cT 2 

where K c ¼ a þ bT þ cT 2 is the corrected temperature-dependent SC for the revised thin-film thermopile heat-flux sensors, and a, b and c are three parameters to be determined by calibration tests. To employ the least square method for determining the three parameters a, b and c, Eq.(5) is converted to the following form.

min

X

qi 

j

V ij

!2 ð6Þ

a þ bT ij þ cT 2ij

in which, subscript ‘‘j” denotes the data number in the three calibration tests, subscript ‘‘i” indicates the order number of calibration tests. qi is a constant heat flux measured by the water-cooled Gardon gage in a single calibration test. Then we have 

K c ¼ 4:03 þ 0:012T  1:23  105 T 2

3.1. Static calibration results

ð7Þ

5 2

The transfer calibration method [19] is employed to calibrate the revised thin-film thermopile heat-flux sensors, and the refer-

optical integrator water-cooled Gardon gage

shutter the revised heat-flux sensor Fig. 4. The calibration test on the revised heat-flux sensors.

1:2310 T It is obvious that 4:03þ0:012T1:2310 5 2 is a monotonically increasT

ing function in the temperature range of 20–550 °C. When T  222:5 C,

1:23105 T 2 4:03þ0:012T1:23105 T 2

 0:1. Hence, for the revised thin-

film thermopile heat-flux sensor presented in this section, a linear temperature-dependent SC, as shown in Eq. (4), is feasible if the surface temperature is below 222.5 °C. As mentioned above, SC is a function of temperature-dependent TCs of thermal resistance layers and Seebeck coefficients of thermocouples. The thermal resistance layer is amorphous SiO2, whose thickness is 5 lm, and the thin-film thermopiles are made of Platinum/Platinum-13% Rhodium (Pt/Pt13Rh). It is reported in Ref. [22–24] that the thin-film Pt/Pt13Rh (or Pt/Pt10Rh) thermopiles have a temperature-dependent Seebeck coefficient and the ITS-90 inverse polynomials are used in this study. Then we have the calculated TCs of thin-film amorphous SiO2 with the thickness of thermal resistance layer d ¼ 5lm and the number of thermocouple pairs N ¼ 150. As shown in Fig. 8, TC of the thermal resistance layer has a decreasing trend with the increasing temper-

Fig. 5. A typical profile of original calibration data.

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K. Yang et al. / Measurement 150 (2020) 107039

Fig. 6. the resistance-temperature calibration data for the thin-film thermal resistor.

Fig. 7. Calibration results of a revised thin-film thermopile heat-flux sensor.

ature. To the authors’ knowledge, most of measured TCs of SiO2 thin films increase as temperature increases [11–13,25]. And no reliable TCs of SiO2 thin films can be found for reference, because TC is dependent on thin film materials, film thickness [26], temperature and substrate materials, even though SiO2 thin films are widely used in Micro-electromechanical System (MEMS). 3.2. MD simulation As a needed supplement to experimental measurements, MD is frequently employed to calculate physical properties of materials by solving Newton’s equations of motion for a system of atoms interacting with a given potential [27]. In this study, noneequilibrium molecular dynamics (NEMD) [28] is used to calculate TC of amorphous SiO2 with film thickness, temperature and substrate being considered, what helps understand the calculated TC of the thermal resistance layer based on calibration tests. As shown in Fig. 9, the simulated structure has a size of 4.35  6.46 nm2 in the x and y coordinate directions. And periodic boundary condi-

tions are used in the two coordinate directions while a fixed boundary condition is applied in the z-direction. The SiO2 layer is released at an initial distance of 3 Å above the substrate AlN layer. LAMMPS is used to conduct all the MD simulations with a time step of 0.2 fs. The interatomic interaction within the SiO2 layer is modeled with the Tersoff-based potential [29,30], and the Tersoff-based potential is recommended in Ref. [31] to calculate thermal transport properties of AlN layer. To the nature of van der Waals interactions between the SiO2 layer and AlN substrate, the LennardJones (LJ) potential is used to model their interatomic interactions.

" Eij ¼ 4eij

rij rij

12

 

rij r ij

6 # ð8Þ

where eij is the potential well depth, rij is the distance at which the potential energy reaches zero, r ij is the interatomic distance between atoms i and j. The LJ parameters are listed in Table 2 while the potential cutoff radius is set as 10 Å. It should be noted that

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K. Yang et al. / Measurement 150 (2020) 107039

Fig. 8. The calculated thermal conductivity of the thermal resistance layer based on calibration tests.

AlN layer

Heat flux

Amorphous SiO2 layer Fig. 9. The simulated structure of amorphous SiO2 layer and substrate layer AlN ceramic.

Table 2 LJ parameters used to characterize the interatomic interactions between SiO2 and AlN.

eij (meV) rij (Å)

Al-Si

Al-O

N-Si

N-O

19.54 3.9173

7.548 3.5631

7.222 3.544

2.79 3.189

Lorentz-Berthelot mixing rules [32] are used to calculate the LJ parameters listed in Table 2 with the aid of the universal force parameters [33]. Three groups of MD simulations are conducted on SiO2 layer of three thicknesses, and five matrix temperatures are considered in each group. The simulation time under different ensembles is listed in Table 3, while the NVT ensemble is used to equilibrate the whole system at the target temperature and the NVE ensemble is for simulating the heat-transfer process. And typical steady-state temperatures are shown in Fig. 10, in which the sampled temperatures are linearly distributed along the thickness direction. In MD simulation, the thermal conductivity is defined as

k¼

Pl A 1 DT 1

ð9Þ

in which, P is the power, which is added to the hot region and equally subtracted from the cold region. l is the thickness of SiO2 layer, A1 is the cross-section area of SiO2 layer, DT 1 is the temperature difference between the upper and bottom surfaces of SiO2 layer. As mentioned above, five temperatures are considered in the three groups of MD simulations. Then we have the predicted TCs. As shown in Fig. 11, it is obvious that TCs of SiO2 thin films are thickness-dependent, no matter that the substrate AlN is considered or not. When substrate AlN is taken into account in MD simulations, the predicted TCs of SiO2 thin films have a linearly temperature-dependent decreasing trend along with the increasing temperature in the simulated temperature range. Hence, the predicted TCs are not sufficient to explain the quadratically temperature-dependent SCs of thin-film thermopile heat-flux sensors. In addition, the reason for different temperature-dependent TCs is frequently referred to be substrate effect. As a matter of fact, the lower thermocouples would be affected by the upper-surface temperature of the substrate AlN, since the lower thermocouples firmly attach the substrate. Hence, the interfacial thermal resistivity should be considered. And the interfacial thermal impedance is defined as

7

K. Yang et al. / Measurement 150 (2020) 107039 Table 3 the simulation time under different ensembles for two thicknesses of SiO2 layer. 19.2 nm (time :ns)

NVT NVE NVE (Sample)

64.18 nm (time :ns)

100.5 nm (time :ns)

SiO2

AlN-SiO2

SiO2

AlN-SiO2

SiO2

AlN-SiO2

2.0 7.0 5.0

2.2 10.0 5.0

3.0 8.0 6.0

3.0 10.0 4.0

3.0 8.2 5.0

3.0 12.0 5.0

Fig. 10. The typical steady-state temperature profiles at 26.85 °C; (I), (III) and (V) pure SiO2; (II), (IV) and (VI) SiO2 with substrate AlN.

Fig. 11. The predicted TCs by MD simulations; (I) pure SiO2; (II) SiO2 with substrate AlN.

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K. Yang et al. / Measurement 150 (2020) 107039

c¼

A 2 DT 2 P

ð10Þ

in which, A2 is the cross-section area of the SiO2-AlN interface, DT is the temperature drop at the SiO2-AlN interface. And then as shown in Fig. 12, the predicted interfacial thermal impedance seems to be quadratically temperature-dependent with a decreasing trend in the simulated temperature range. To present the coupled effect of temperature-dependent TC of SiO2 with the substrate and the inter-

facial thermal impedance on the measured temperature difference, a finite element (FE) model is used to simulate the heat-transfer procedure with a constant heat-flux density 1 MW/m2 applied, in which the thickness of SiO2 layer is extended to be 1 mm, and TCs of SiO2 thin film are proportionally amplified with a proportionally reduced interfacial thermal resistivity for a reasonable response time and temperature difference across SiO2 layer and temperature drop at the SiO2-AlN interface with Table 4 recording parameters used in the finite element simulation. As shown in Fig. 13, the mea-

Fig. 12. The predicted interfacial thermal resistivity by MD in the temperature range of 26.85–526.85 °C.

Table 4 Parameters used in the finite element simulation.

AlN-SiO SiO2

AlN

Thermal Impedance (106 °C.m2/W) Thermal Conductivity (W/m. °C) Specific heat (J/kg. °C) Density (g/cm3) Thermal Conductivity (W/m. °C) Specific heat (J/kg. °C) Density (g/cm3)

26.85 °C

226.85 °C

356.85 °C

426.85 °C

526.85 °C

2.3502 26.62 7547.1 2.2 170 7396.4 3.27

2.1134 25.238

1.9466 23.862

1.4945 22.801

0.9241 22.102

Fig. 13. The simulated temperature difference by the finite element method.

K. Yang et al. / Measurement 150 (2020) 107039

sured temperature difference is quadraticlly temperaturedependent when the temperature-dependent interfacial thermal impedance is considered. In addition, the FE simulation is processed in ANSYS workbench and automatic meshing is used with locally refined grids at the SiO2 layer and the interaction region. 4. Conclusions A revised thin-film thermopile heat-flux sensor with copper heat sink is calibrated with our heat-flux sensor calibration system, since it is necessary for this kind of heat-flux sensors to get the sensitive coefficient by calibration tests. The calibration results show a quadraticlly temperature-dependent SC. With the aid of MD simulation and finite element method, the coupled effect of linearly temperature-dependent TCs of SiO2 thin film and the quadraticlly temperature-dependent interfacial thermal resistivity causes the quadraticlly temperature-dependent SCs of the revised thin-film thermopile heat-flux sensor. And TCs shown in Fig. 8 should be referred to as effective thermal conductivities, because calibration tests cannot reveal the real reason for different temperaturedependent sensitivity coefficients. Hence, results of the MD simulation and finite element method help understand the calibration data, and they can be used to predict output performance of this temperature-difference-based heat flux sensors, when new thermal resistance and substrate materials are used to design new sensors. Acknowledgment The research is supported by the National Key Research and Development Program of China (Grant No. 2016YFA0401200) and the National Science Foundation of China (Grant No. 11802321 and 11872068). And the authors are grateful to Yunfeng Shi and Henggao Xiang for sharing the Tersoff-based potential file of wurtzite AlN. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.measurement.2019.107039. References [1] C.P. Liu, Heat flux measurement in aerothermodynamic test, National Defend Industry Press, Beijing, 2013 (In Chinese). [2] N. Yilmaz, F. Vigil, J. Height, B. Donaldson, W. Gill, Rocket motor exhaust thermal environment characterization, Meas. J. Int. Meas. Confed. 122 (2018), https://doi.org/10.1016/j.measurement.2018.03.039. [3] D.G. Holmberg, T.E. Diller, High-frequency heat flux sensor calibration and modeling, J. Fluids Eng. Trans. ASME. 117 (1995), https://doi.org/10.1115/ 1.2817319. [4] C. Purpura, E. Trifoni, O. Petrella, L. Marciano, M. Musto, G. Rotondo, Gardon gauge heat flux sensor verification by new working facility, Meas. J. Int. Meas. Confed. 134 (2019), https://doi.org/10.1016/j.measurement.2018.10.076. [5] K.J. Irimpan, N. Mannil, H. Arya, V. Menezes, Performance evaluation of coaxial thermocouple against platinum thin film gauge for heat flux measurement in shock tunnel, Meas. J. Int. Meas. Confed. 61 (2015), https://doi.org/10.1016/j. measurement.2014.10.056. [6] S.K. Manjhi, R. Kumar, Transient surface heat flux measurement for short duration using K-type, E-type and J-type of coaxial thermocouples for internal combustion engine, Meas. J. Int. Meas. Confed. 136 (2019), https://doi.org/ 10.1016/j.measurement.2018.12.070. [7] ASTM Standard E457-08, Standard test method for measuring heat-transfer rate using a thermal capacitance (slug) calorimeter, https://www.astm.org/ Standards/E457.htm (2015).

9

[8] J.P. Terrell, J.M. Hager, S. Onishi, T.E. Diller, Heat flux microsensor measurements and calibrations, in: the 1992 NASA Langley Measurement Technology Conference, 1992, pp. 69–80 [9] J.M. Hager, L.W. Langley, S. Onishi, et al., Microsensors for high heat flux measurements, J. Thermophys Heat Tr. 7 (3) (1992), https://doi.org/10.2514/ 3.452. [10] D. Zhao, X. Qian, X. Gu, S.A. Jajja, R. Yang, Measurement techniques for thermal conductivity and interfacial thermal conductance of bulk and thin film materials, J. Electron. Packag. Trans. ASME. 138 (2016), https://doi.org/ 10.1115/1.4034605. [11] S.R. Mirmira, L.S. Fletcher, Review of the thermal conductivity of thin films, J. Thermophys. Heat Transf. 12 (1998), https://doi.org/10.2514/2.6321. [12] M.B. Kleiner, S.A. Kühn, W. Weber, Thermal conductivity measurements of thin silicon dioxide films in integrated circuits, IEEE Trans. Electron Devices. 43 (9) (1996), https://doi.org/10.1109/16.535354. [13] H.A. Schafft, J.S. Suehle, P.G.A. Mirel, Thermal conductivity measurements of thin-film silicon dioxide, in: Proceedings of the 1989 International Conference on Microelectronic Test Structures, Edinburgh, UK, 13-14 March, 1989, pp. 121–125. [14] P. Jund, R. Jullien, Molecular-dynamics calculation of the thermal conductivity of vitreous silica, Phys. Rev. B – Condens. Matter Mater. Phys. 59 (21) (1999), https://doi.org/10.1103/PhysRevB.59.13707. [15] Z. Huang, Z. Tang, J. Yu, S. Bai, Thermal conductivity of amorphous and crystalline thin films by molecular dynamics simulation, Phys. B Condens. Matter. 404 (2009), https://doi.org/10.1016/j.physb.2009.02.022. [16] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117 (1995), https://doi.org/10.1006/jcph.1995.1039. [17] http://lammps.sandia.gov. [18] Vatell Corporation, HFM-6, HFM-7, & HFM-8 Operator’s Manual http://vatell.com/vatellwebfiles/HFM%20Use%206,7,&%208%20v1.pdf (2015). [19] A.V. Murthy, B.K. Tsai, C.E. Gibson, Calibration of high heat flux sensors at NIST, J. Res. Natl. Inst. Stand. Technol. 102 (4) (1997), https://doi.org/10.6028/ jres.102.032. [20] H. Wang, Q.T. Yang, X.X. Zhu, et al., Inverse estimation of heat flux using linear artificial neural networks, Int. J. Therm. Sci. 132 (2018), https://doi.org/ 10.1016/j.ijthermalsci.2018.04.034. [21] A.V. Murthy, B.K. Tsai, R.D. Saunders, Transfer calibration validation tests on a heat flux sensor in the 51 mm high-temperature blackbody, J. Res. Natl. Inst. Stand. Technol. 106 (5) (2001), https://doi.org/10.6028/jres.106.039. [22] X. Zhao, X. Liang, S. Jiang, W. Zhang, H. Jiang, Microstructure evolution and thermoelectric property of Pt-PtRh thin film thermocouples, Crystals. 7 (96) (2017), https://doi.org/10.3390/cryst7040096. [23] Y. Chen, H. Jiang, W. Zhao, W. Zhang, X. Liu, S. Jiang, Fabrication and calibration of Pt-10%Rh/Pt thin film thermocouples, Meas. J. Int. Meas. Confed. (2014), https://doi.org/10.1016/j.measurement.2013.11.018. [24] J.D. Wrbanek, G.C. Fralic, S.C. Farmer, A. Sayir, C.A. Blaha, J.M. Gonzalez, Development of thin film ceramic thermocouples for high temperature environments, in: 40th AIAA/ASME/SAE/ASEE Jt. Propuls. Conf. Exhib., Florida, USA, 11-14 July, 2004. [25] W. Zhu, G. Zheng, S. Cao, H. He, Thermal conductivity of amorphous SiO2 thin film: A molecular dynamics study, Sci. Rep. 8 (2018), https://doi.org/10.1038/ s41598-018-28925-6. [26] F.R. Brotzen, P.J. Loos, D.P. Brady, Thermal conductivity of thin SiO2 films, Thin Solid Films. 207 (1992), https://doi.org/10.1016/0040-6090(92)90123-S. [27] J.R. Lukes, D.Y. Li, X.G. Liang, C.L. Tien, Molecular dynamics study of solid thinfilm thermal conductivity, J. Heat Transfer. 122 (2000), https://doi.org/ 10.1115/1.1288405. [28] R.J. Stevens, L.V. Zhigilei, P.M. Norris, Effects of temperature and disorder on thermal boundary conductance at solid-solid interfaces: Nonequilibrium molecular dynamics simulations, Int. J. Heat Mass Transf. 50 (2007), https:// doi.org/10.1016/j.ijheatmasstransfer.2007.01.040. [29] S. Munetoh, T. Motooka, K. Moriguchi, A. Shintani, Interatomic potential for SiO systems using Tersoff parameterization, Comput. Mater. Sci. 39 (2007), https://doi.org/10.1016/j.commatsci.2006.06.010. [30] M. Tungare, Y. Shi, N. Tripathi, P. Suvarna, F. Shahedipour-Sandvik, A Tersoffbased interatomic potential for wurtzite AlN, Phys. Status Solidi Appl. Mater. Sci. 208 (7) (2011), https://doi.org/10.1002/pssa.201001086. [31] H. Xiang, H. Li, X. Peng, Comparison of different interatomic potentials for MD simulations of AlN, Comput. Mater. Sci. 140 (2017), https://doi.org/10.1016/ j.commatsci.2017.08.042. [32] A.K. Al-Matar, D.A. Rockstraw, A Generating Equation for Mixing Rules and Two New Mixing Rules for Interatomic Potential Energy Parameters, J. Comput. Chem. 25 (5) (2004), https://doi.org/10.1002/jcc.10418. [33] A.K. Rappé, C.J. Casewit, K.S. Colwell, W.A. Goddard, W.M. Skiff, UFF, a Full Periodic Table Force Field for Molecular Mechanics and Molecular Dynamics Simulations, J. Am. Chem. Soc. 114 (1992), https://doi.org/ 10.1021/ja00051a040.