Heat-transfer at the interface between a metal and a non-metal: influence of ultra-thin interlayers, interface chemistry and atomic order

The Thermal Boundary Conductance (TBC) at the interface between metals and dielectrics is of key importance for heat transport in structures heterogeneous on a scale from 100 µm downwards. In this thesis the TBC of a large number of metal/dielectric couples was measured using Time-Domain Thermoreflectance (TDTR). Besides creating a large and coherently assessed number of metal dielectric pairs, a particular focus was laid on the effect of ultra-thin interlayers, as well as on the role of interfacial disorder and intermixing on the TBC. For those instances a framework to rationalize the observed phenomena was developed. The large number of consistently evaluated TBC-values allowed comparing the predictive capacity of the widely used Diffuse Mismatch Model (DMM), with the more recently developed approach that combines the Maximum Transmission Limit (MTL) with an average transmission probability that characterizes phonons transmission across real interfaces. It is found that the MTL based prediction of TBC yields consistently good precision whatever substrate is used, while the prediction quality of the DMM decreases with increasing mismatch between the materials on either side of the interface. This work served as a reference to quantify the TBC changes observed in the rest of this work. The influence of a coupling layer on the TBC of a given metal/dielectric couple was experimentally and theoretically assessed by using i) ultra-thin Cu interlayers (1.5 ¿ 25 nm) at the interface between Au and silicon, sapphire and diamond, as well as between Al and diamond, ii) ultra-thin interlayers of Mo and Ni at the interface between Ag or Au and diamond, and iii) intermixed interfaces in the Au-Si and Ti-Si couples with changes in the atomic order and chemical composition induced by various heat treatments. For case i) the TBC was observed to increase (Au-Cu-Si, Au-Cu-Al2O3, Au-Cu-diamond) or decrease (Al-Cu-diamond) monotonically for interlayer thicknesses up to 10 nm roughly, before reaching a plateau very close to the Cu-dielectric TBC value. The evolution of TBC was attributed to the finite electron-phonon coupling factor of the interlayer material for the Au-Cu-Si, Au-Cu-Al2O3, and Au-Cu-diamond cases. The apparent inconsistency between experimental evidence for the Al-Cu-diamond case and theory was rationalized by a variable coverage of the Cu-diamond interface by diffused aluminium evidenced by local chemical analysis. The importance of the electron-phonon coupling factor was confirmed by the use of Ni and Mo interlayers with Au or Ag on diamond, for which the TBC increased monotonically over a much shorter range of interlayer thicknesses than the one observed for Cu, before reaching a plateau. The results were rationalized both with an analytical model developed earlier and a model based on the deviation between temperature of electrons and phonons, a so-called ¿Two Temperature model¿ (TTM) yielding good agreement. In Au/Si samples, a change of the TBC was observed that can be attributed either to disorder or interdiffusion in the interfacial region. Investigations performed on the Ti-Si interface led to significantly decreasing TBC for increased duration of the heat treatment, apparently uncorrelated with the state of crystallization at the interface, but that may be due to interdiffusion.

Thermal Boundary Conductance between metals and dielectrics

Christian Monachon

This work consists in an experimental study of the main parameters governing the transport of heat across an interface between two solids, when it is dominated by phonons. The main experimental tool used is Time-Domain ThermoReflectance (TDTR), which is an optical technique able to measure the Thermal Boundary Conductance (TBC) of single interfaces between metallic layers about 100 nm thick and mm-sized, flat dielectric substrates. Emphasis is put on diamond as a dielectric, because the diamond/metal TBC is among the important parameters governing the thermal conductivity of diamond-based Metal Matrix Composites (MMC) with potential applications as heat sink materials. In a first part, TDTR as a technique is reviewed and its main advantages are identified. Experimental parameters that influence it the most strongly are the size of the laser spots used and the thickness of the metallic layer investigated. An experimental procedure is presented, that provides a reliable way of measuring these quantities. In a second part, the effect on the TBC of surface treatments of the dielectric substrate prior to the metallic layer deposition is investigated. On an AlN substrate, it is found that the formation of a native oxide on its surface decreases the thermal transport across its interface with an Al layer. Etching away this oxide improves the measured TBC from 43 to 241 MWm−2K−1. On a diamond substrate, the results are more nuanced. The as-received surface is found to be hydrogen-terminated and has traces of organic contaminants. Ridding the surface of these contaminants and terminating it with hydrogen using an Ar:H plasma treatment improves TBC in a way that depends on the diamond surface orientation, from 23 to 32 ([111] orientation) or 23 to 54 ([100] orientation) MWm−2K−1. Doing so using a mixture of H2SO4 and HNO3 (1:1) at 200°C partly terminates the surface with oxygen and yields a TBC of 125 MWm−2K−1. Forcing a graphitic sp2 termination of the surface by sputtering Ar ions on it further improves TBC, up to 150 MWm−2K−1. Finally, forcing oxygen termination using an Ar:O plasma yields a high TBC of 180 MWm−2K−1. Still on the oxygenated surface, the deposition of the Al layer by DC sputtering instead of evaporation results in the highest TBC value measured between Al and diamond, of 230 MWm−2K−1, an order of magnitude higher than the TBC of 23 MWm−2K−1 between Al and as-received diamond, and thrice as large as the highest value of 90 MWm−2K−1 reported in the literature. All the treatments applied except for the Ar:H plasma are found to yield TBCs independent of the diamond surface orientation. In a third part, some attempts are made to explain the origin of the observed increase in TBC. By comparing the temperature dependence of the TBC between Al on oxygenated and sp2-terminated diamond, we find that the latter case leads to a distinctly different temperature-dependent behavior. This suggests that the presence of oxygen atoms, presumably forming an interfacial oxide, is the main factor influencing TBC in this system. To confirm this hypothesis, the thickness of this presumed oxide is increased by depositing Al2O3 using Atomic Layer Deposition (ALD) of 1.6, 4.5, 6.2 and 10 nm on the substrate before the Al layer. It is found that the difference in temperature dependence of the TBC between the case where these layers are present and the case when the diamond surface is only oxygen-terminated can be explained simply by the resistive contribution of the deposited layer. This suggests that interfacial states created by the reaction of Al and O are a crucial parameter explaining the high TBC found. In another experiment, the work of adhesion of Cu and Ni on clean diamond is calculated using Density Functional Theory. Using known values for the work of adhesion between Al and Ti on diamond, the TBC between diamond and Al, Cu, Ni or Ti is found to scale roughly with the work of adhesion of each of these systems. Furthermore, the presence of hydrogen at the diamond surface is found to dramatically decreases both the work of adhesion and the thermal transfer across its interface with these metals, confirming the previous results obtained between Al and diamond. Still in the same approach, the TBC between diamond and Cr, Mo, Nb and W is measured before and after a high vacuum heat treatment at 800°C. After careful characterization of the samples both before and after heat treatment, it is found that carbides have formed in the metal layers after heat treatment. Despite the presence of these carbides, the TBC between the diamond substrate and the layers stays the same, suggesting that even before the heat treatment, an interfacial carbide is present between the metal and the diamond and governs heat transfer through the interface. In a final experiment, very thin layers of Ni (of 1.8, 3.2 and 7 nm) are inserted between Al or Ag and diamond. Once these layers have been carefully characterized, it is found that these interfacial layers increase the measured TBC between the top layer and diamond to values that, within error and accounting for electron-phonon coupling, equal 260 MWm−2K−1 measured for a layer of pure Ni on diamond, up from TBCs of 47 and 170 MWm−2K−1 measured in the same study for Ag/diamond and Al/diamond interfaces respectively. Finally, throughout this whole thesis, values for TBC between several metals (Ag, Al, Au, Cr, Cu, Mo, Nb, Pt, Ti, W) as well as some carbides (Cr, Mo, Nb, W) and diamond are provided. They are measured in clean conditions and thus are expected to set a maximum value to the TBC in non-ideal systems such as diamond reinforced metals with potential applications as heat sinks. Based on the results presented, solutions to improve thermal transport in diamond-based MMCs are proposed.

EPFL2013

Multi-configuration evaluation of a megajoule-scale high-temperature latent thermal test-bed

Maurizio Barbato, Selmar Rudolf Binder, Sophia Haussener, Nithin Mallya, Alberto Ortona, Clemens Gregor Suter

Thermal energy storage via latent heat provides an energy dense solution and, during discharge, a hot stream at a well-defined temperature. Utilizing metal phase change materials (PCMs) and high-temperature operation might enable fast (dis)charging and application in previously unexplored areas (e.g. high-temperature processing industry). But detailed characterization and design guidelines of high-temperature metal latent heat storage systems with tailored characteristics are missing. Here, we introduce a combined experimental-numerical characterization and design tool for high-temperature heat storage units. We apply it to a megajoule-scale test-bed operated with steel encapsulated Al68.5Cu26.5Si5 (weight%) (melting temperature 791 K) as the PCM and air as heat transfer fluid (HTF) for charging and discharging. Thermocouples positioned at multiple locations throughout the storage unit are used to characterize the performance and heterogeneity. For the inaugural experimental campaign, three encapsulated tubes with a total of 1.83 kg PCM were vertically arranged in one of the modular stacks and several multi-hour charging/discharging cycles were performed with the HTF heated up to 30 - 70 K above and below the PCM melting point at a flow rate of 1500 lmin(-1). Specifically designed open-cell cellular Si-SiC lattices were wrapped around the PCM tubes to enhance the heat transfer. The experimental results showed a near-isothermal (+/- 10 K) exit temperature discharge maintained for 0.39 2.67 h. Temperature variations throughout the test-bed indicated that test-bed design is important to ensure homogeneous usage of the PCM and controlled phase change. A quasi-1D lumped parameter multi-mode heat transfer model was developed to quantify the thermal stratification within the PCM, heat losses, and phase change characteristics in the thermal storage, and provided explanation and quantification for the experimentally observed heterogeneities. The model was used to extrapolate the heat storage characteristics to larger scales: a 16.84 MJ and 50.51 MJ latent heat storage with the modular stacks filled with 25.7 kg (42 encapsulated tubes) and 77 kg (126 encapsulated tubes) of the PCM, respectively. The coupled experimental- numerical approach allowed for model validation, explanation of experimental variation, and to provide general design guidelines for practically relevant latent high-temperature (metal) thermal energy storage.

PERGAMON-ELSEVIER SCIENCE LTD2022

Heat Transfer and Pressure Drop in the Dryout Region of Intube Evaporation with Refrigerant/Lubricant Mixtures.

Daniel Favrat, John Richard Thome, Olivier Zürcher

A summary of the objectives and conclusions reached in this project are: •A litterature search on post dryout heat transfer for pure refrigerants and for refrigerant-oil mixtures was performed and a comprehensive review written (Chapters 9, 10, and 11); •The correct thermodynamic definition of the heat transfer coefficient for evaporation of refrigerant-oil mixtures was presented and then used in the project, i.e. defining the heat transfer coefficient using the local bubble point temperature Tbub of the refrigerant-oil mixture rather than with the saturation temperature of the pure refrigerant Tsat incorrectly used in prior studies (Chapter 3); •A new generalized approach, that is simple to implement, was developed for predicting bubble point temperatures of refrigerant-oil mixtures for miscible oils that can be applied to any refrigerant-oil combination and is accurate over the local oil concentration range from 0-50 wt.% oil range confronted in direct- expansion evaporators with 0-5 wt.% oil in their refrigerant charge (Chapter 4); •A new thermodynamic method for preparation of temperature-enthalpy- vapor quality (T-h-x) curves for refrigerant-oil mixtures for general application was developed and validated against test data (Chapters 5 and 6), including a simple expression for calculating local oil concentrations as a function of vapor quality; •New, accurate thermodynamic methods for preparation of temperature-enthalpy-vapor (T-h-x) curves for the refrigerant blend R-407C and R-407C/oil mixtures were developed for thermal design of evaporators and for the present experimental test, and was validated against measured test data (Chapter 12); •Recommendations were made on how to include oil effects and refrigerant-oil T-h-x curves into evaporator design methods (Chapter 7); •The effects of oil on set-point parameters for control devices were analyzed and some recommendations made (Chapter 8); •An online oil concentration measurement system was perfected using a high accuracy density flowmeter that allowed oil concentrations to be measured accurately and continuously during experiments, such that oil holdup in the heat transfer test sections at high vapor quality could be identified and the correct inlet oil concentrations be measured, and thus utilized to reduce experimental data; a simpler industrial method for applying the measurement system was also developed and presented (Chapter 15); •Experimental results (local heat transfer coefficients, two-phase pressure drops and some two-phase flow patterns) were obtained for R-134a and R-134a/oil mixtures evaporating in plain and microfinned tubes over a wide range of test conditions (Chapters 16 and 17); •Experimental results (local heat transfer coefficients, two-phase pressure drops and some two-phase flow patterns ) were obtained for R-407C and R- 407C/oil mixtures evaporating in plain and microfinned tubes over a wide range of test conditions (Chapters 18 and 19); •The recently proposed flow boiling model and flow pattern map of Kattan-Thome-Favrat, that importantly models heat transfer coefficients based on local flow pattern and predicts the onset of dryout in horizontal tubes and local heat transfer coefficients in partial dryout regimes, was described in detail; the flow pattern map is also useful to designers wishing to design in specific flow pattern regimes and avoid inefficient heat transfer regimes, such as mist flow and stratified flow (Chapters 20 and 21); •The stratified-wavy flow regime model was modified based on the new test data at high vapor quality for pure R-134a and R-407C, which increased the accuracy of the method significantly in this flow regime, now referred to as the “modified” Kattan- Thome-Favrat flow boiling model (Chapter 22); •The modified Kattan- Thome-Favrat flow boiling model and flow pattern map were shown to accurately predict R-407C heat transfer and flow pattern data and hence is recommended for industrial use for designing direct-expansion evaporators with refrigerant blends [the original version was also verified for R-402 and R-404A blends, see Chapter 21] (Chapter 22); •The effect of local refrigerant-oil viscosity on liquid-phase convection in flow boiling heat transfer and on flow patterns was successfully incorporated into the modified Kattan-Thome-Favrat model, establishing the first flow boiling design method that predicts oil effects on heat transfer (with quite reasonable accuracy too), and included a simple method for calculating the values of µref-oil for use in the model (Chapter 23); •The oil effects on microfin heat transfer coefficients were analyzed and heat transfer augmentation ratios were determined for R-134a/oil and R-407C/oil mixtures (Chapter 25); •Plain tube, two-phase pressure drop gradients for R-134a and R-407C at three mass velocities were compared to the Friedel frictional two-phase pressure drop correlation, attaining accurate results and also microfin pressure drop augmentation ratios were determined (Chapter 25); •The ratio of [µoil/µref]mw, derived from the Arrhenius logrithmic viscosity mixing rule and local oil concentration w, was shown to accurately predict the effect of oil on two-phase pressure drop gradients at high vapor qualities, with an empirical exponent m = 0.18355 found for R-134a/oil mixtures (no foaming) and an empirical expression for m for R-407C/oil mixtures (with foaming). This ratio incorporated into the Friedel correlation accurately predicts two-phase pressure drops of evaporating refrigerant-oil flows (Chapter 25).

1996