In-situ and ex-situ characterization of the effective thermal conductivity of hydride forming materials

In-situ and ex-situ characterization of the effective thermal conductivity of hydride forming materials In-situ und ex-situ Characterisierung der Wärmeleitfähigkeit von Hydridbildenden Materialien 1. Examiner: Prof. Julian Jepsen 2. Examiner: Prof. Thomas Klassen Supervisor: Dr. Julián Puszkiel Institution: Helmholtz-Zentrum Hereon Geesthacht/ Helmut-Schmidt-Universität der Bundeswehr Masters Thesis Author: Sarah Kretschmann Wirtschaftsingenieurwesen (Elektrische Energieversorgung und Energiewirtschaft) of 2021 Student ID: 894770 Submission date: 25.07.2025 i Table of Contents Abstract .................................................................................................................................... iii 1. Introduction....................................................................................................................... 1 2. Experimental and model description .............................................................................. 7 2.1 Materials and preparation ........................................................................................... 7 2.2 Activation and kinetic-capacity measurement .............................................................. 8 2.2.1 Function and Role of the Titration System .................................................................. 9 2.2.2 Activation Procedure and cycling ............................................................................. 11 2.2.3 Thermodynamic consideration ................................................................................. 12 2.3 ETC measurements ........................................................................................................ 13 2.3.1 Overview of the Measurement Setup ....................................................................... 13 2.3.2 In-situ vs. Ex-situ Measurements ............................................................................. 15 2.4 XRD measurements and crystalline phase analysis ....................................................... 16 2.5 Manipulation ................................................................................................................... 18 3. Results ............................................................................................................................ 21 3.1 Activation and cycling ............................................................................................... 21 3.1.1 Hydralloy® C5 with and without ENG ....................................................................... 21 3.1.2 HPM3 with and without ENG .................................................................................... 24 3.2 XRD measurements ....................................................................................................... 27 3.3 Ex-situ ETC-measurements ............................................................................................ 30 3.4 In-situ ETC-measurements ............................................................................................. 31 3.4.1 Hydralloy C5 pure .................................................................................................. 31 3.4.2 Hydralloy C5 + 5 wt% ENG .................................................................................... 34 3.4.3 HPM3 pure .............................................................................................................. 37 3.4.4 HPM3 + 5 wt% ENG ................................................................................................ 39 4. Discussion ...................................................................................................................... 42 4.1 The influence of pressure, temperature, material composition, and hydrogen capacity 43 4.1.1 The influence of pressure ......................................................................................... 43 4.1.2 The influence of temperature ................................................................................... 44 4.1.3 The influence of material composition ...................................................................... 45 4.1.4 The influence of hydrogen capacity .......................................................................... 47 4.2 Evaluation of the obtained results based on the literature review .................................... 49 4.3 Limitations and Uncertainties .......................................................................................... 51 4.4 Modeling the ETC ........................................................................................................... 52 ii 4.4.1 Mathematical model ................................................................................................. 52 4.4.1.1 Hydralloy® C5 with and without ENG .................................................................... 52 4.4.1.2 HPM3 with and without ENG ................................................................................. 54 4.4.2 Physical model ......................................................................................................... 55 4.4.2.1 Analysis of the main influencing parameters of the ETC in the ZBS model ........... 57 4.4.2.2 Comprehensive analysis on the application of the ZBS model for the ETC dependence on the pressure ............................................................................................ 60 5. Conclusions and prospects ........................................................................................... 63 5.1 Conclusions .................................................................................................................... 63 5.2 Prospects ....................................................................................................................... 64 Acknowledgements .................................................................................................................. iii Declaration of Authorship ....................................................................................................... iv References ................................................................................................................................ v List of Figures .......................................................................................................................... x List of Tables ........................................................................................................................... xii Appendix A ............................................................................................................................. xiii Appendix B ............................................................................................................................. xvi Appendix C ........................................................................................................................... xviii Appendix D ............................................................................................................................. xix Appendix E ............................................................................................................................. xxi iii Abstract The integration of hydrogen into the global energy system presents a promising pathway toward decarbonization, particularly when used as a clean, flexible energy carrier for storage and conversion. However, the adoption of solid-state hydrogen storage systems based on metal hydrides is limited by their poor thermal properties, especially their low effective thermal conductivity (ETC), which significantly impacts absorption/desorption kinetics and overall system efficiency. This study examines the ETC behavior of selected AB₂-type Laves phase hydride-forming materials (commercial alloy: Hydralloy® C5 and customized alloy: HPM3) under realistic operating conditions. While Hydralloy® C5 is commonly used in hydrogen storage applications, HPM3 is a high-pressure material specifically designed for metal-hydride-based compression systems to deliver hydrogen up to 350 bar. The materials were evaluated using a combination of ex-situ and in-situ transient plane source (TPS) measurements. Experimental setups included a high-pressure thermal conductivity analyzer and a custom-built Sieverts-type apparatus for parallel characterization of hydrogen capacity. Additionally, X-ray diffraction (XRD) was employed to evaluate the structural changes and crystallite size after cycling. The integration of expanded natural graphite (ENG) was also studied, showing that conductive additives can significantly improve ETC if sufficient packing density and structural integration are achieved. The results indicate that hydrogen pressure is the main factor affecting ETC, followed by material composition. Temperature and hydrogen capacity had only minor impacts within the studied ranges, aligning with recent literature's theoretical expectations. To interpret and generalize the measured data, both a simplified mathematical model and a structure-based physical model were used to describe the ETC behavior as a function of pressure. These models confirmed that gas-phase conduction and particle contact resistance dominate heat transfer in powder beds, and that additive-induced enhancements can be linked to percolation thresholds and crystallite structure. These findings underscore the importance of realistic, pressure-dependent ETC characterization and modeling in the design of metal hydride-based hydrogen storage and compression systems. The results offer a validated framework for future system optimization and support ongoing advancements. 1 1. Introduction The global energy system is currently undergoing a fundamental transformation. Driven by population growth, economic development, and technological progress, global primary energy demand is projected to increase by more than 25 % by 2040 [1]. This rise in energy consumption presents a significant environmental and technological challenge. The heavy reliance on fossil fuels in the current energy mix, accounting for more than 80 % of total energy use, is a pressing issue that needs to be addressed [2]. The challenges associated with this dominance, such as greenhouse gas emissions and resource depletion, underscore the need for alternative energy sources and the importance of research on hydrogen storage materials. The combustion of these resources results in the emission of substantial quantities of greenhouse gases, particularly carbon dioxide. It is the primary contributor to global warming and climate change. In addition, fossil fuels are finite, geopolitically sensitive, and often linked to air pollution, resource conflicts, and market volatility [3–5]. In this context, the transition toward renewable energy sources is not only desirable but necessary. Technologies based on solar, wind, and hydropower offer clean, increasingly costcompetitive, and sustainable alternatives to fossil fuels [5]. However, many renewables suffer from intermittency and decentralization—the sun does not always shine, and the wind does not always blow. Such intermittency is making the storage and redistribution of energy one of the core technical challenges of the coming decades [6]. The development of robust, flexible, and efficient energy storage systems is thus essential to ensure the stability and reliability of future renewable energy grids. Within these challenges, a promising and widely studied solution is the use of hydrogen as an energy carrier. Hydrogen, with its unique properties, offers several key advantages. It can be produced from water using renewable electricity (via electrolysis), emits only water vapor when used in fuel cells or combustion, and can be stored and transported in various forms. It has a high gravimetric energy density of approximately 120 MJ/kg, which is approximately times that of gasoline [7,8]. Its volumetric energy density, however, depends strongly on the storage form: ~0.01–0.02 MJ/L for compressed gas at ambient temperature, 8.5 MJ/L for liquid hydrogen, and up to 9 MJ/L for solid-state storage in metal hydrides [9–11]. Hydrogen is also suitable for longterm and seasonal storage, unlike batteries, due to self-discharging that occurs when no load is connected [4]. Hydrogen can serve as a feedstock for industry, a fuel for transport, and an intermediate energy vector for converting renewable power into chemical energy [10]. Because of this flexibility and 2 cleanliness, hydrogen is increasingly viewed as a cornerstone of future sustainable energy systems. Fig. 1 illustrates the concept of an integrated energy storage system, where unit 2 (hydrogen storage) serves as a buffer between the production of hydrogen through electrolysis and its consumption in a fuel cell to generate clean energy. The introduction of hydrogen storage systems enables the decoupling of renewable energy sources-based systems from the intermittent nature of natural resources. Figure 1. Hydrogen energy storage system process flow [12]. Copyright used with permission. Despite these benefits, the deployment of hydrogen technologies still faces several technical challenges. Among these, hydrogen storage, as shown in Fig. 2, is one of the most critical due to the low density of hydrogen (0.0899 kg/m3) and the small nature of the hydrogen molecule, resulting in leakage issues. Current commercial systems primarily rely on compressed gas storage at pressures ranging from 350 to 700 bar and ambient temperatures (~15 ºC), as used in fuel cell vehicles and stationary tanks [5,8]. These high-pressure systems enable quick refueling and have acceptable gravimetric energy density, but they pose safety risks, require thick-walled vessels, and are limited in volumetric efficiency due to the low gas density even at high pressures (~20–40 kg/m³) [8]. Furthermore, the energy required to compress hydrogen to 700 bar is substantial, typically consuming 15–20 % of its lower heating value (LHV), thereby reducing the overall system efficiency [10,13]. Another option is cryogenic liquid hydrogen at - 253°C, which offers higher energy density but results in significant boil-off losses and requires an energyintensive liquefaction process [5]. Liquefaction alone consumes around 30 % of the hydrogen's 3 LHV, and additional energy must be spent to minimize boil-off losses during storage and handling [10,13]. An alternative is solid-state hydrogen storage in materials capable of reversibly absorbing and releasing hydrogen, such as metal hydrides. Hydrides offer benefits such as high volumetric hydrogen density (50–150 kg/m³) [8,14], safe handling, and mild operating conditions [10]. Unlike compressed or cryogenic systems, metal hydrides operate at lower pressures and temperatures, requiring significantly less auxiliary energy input for storage operation [13]. Figure 2. Different variants of large-scale hydrogen storage [5]. Note: Mg2FeH6 provides the highest volumetric capacity among chemical hydrides; thus, chemical hydrides may extend the volumetric capacity range indicated in this Figure [8,14]. It is possible to distinguish between intermetallic and chemical hydride materials. The intermetallic hydrides are formed from alloys and allocate atomic hydrogen in their interstices. On the one hand, the formation of intermetallic hydrides occurs at room temperature and under relatively low pressures (10–50 bar) [15,16]. On the other hand, the formation of chemical hydrides (complexes and binary hydrides) occurs from metallic and non-metallic elements. In these cases, atomic hydrogen forms a relatively strong chemical bond (ionic and/or covalent) with the elements, and hydrogenation occurs at higher temperatures (100–800 °C) and different pressure ranges, depending on the hydride. The mechanism of formation of hydrides, for both intermetallic and chemical, consists of the formation of a solid solution followed by the hydrogenation reaction [15,16]. Hydrogenation and dehydrogenation of hydride-forming compounds are exothermic and 4 endothermic reactions, respectively. These reactions require efficient heat transfer for efficient hydrogen uptake and release, as shown in Fig. 3. If heat cannot be dissipated or supplied quickly enough, reaction kinetics slow down, temperature gradients form, and system efficiency decreases [9]. Figure 3. Reaction of metal and hydrogen gas [17]. A significant limitation of hydrides is their low effective thermal conductivity (ETC), especially in powder form. The ETC is the apparent macroscopic heat conductivity of a composite, such as packed hydride powder with interstitial gas, under specific conditions. It accounts for heat transport through the solid matrix, the gas phase, contact resistance, and porosity [10,18,19]. When scaling up a metal hydride tank for practical applications, heat transfer via conduction is the primary rate-limiting mechanism for the [18]. Typical values of the ETC range from 0.1 to 0.5 W/m K [20]. For efficient system performance, values above 5 W/m K are desirable [20]. To improve the effective thermal conductivity of the metal hydride bed, conductive additives such as expanded natural graphite (ENG), carbon foams, or metal meshes are used to enhance thermal conductivity [13,21,22]. Warfsmann et al. demonstrated that adding 10 wt% ENG and 10 % EVA to Hydralloy C5 reduced swelling-induced stress, but the thermal performance was not significantly improved due to the presence of the non-conducting EVA elastomer [7]. It has been reported that significant improvements in storage properties were observed with the addition of ENG [13,21,22]. The addition of ENG creates a percolating conductive network within the powder matrix, improving thermal transport across the hydride bed without significantly affecting hydrogen storage capacity [13,21]. ENG is particularly attractive due to its high intrinsic thermal conductivity (above 100 W/m K), chemical inertness, and compatibility with hydride materials. Studies by Yasuda et al. and Atalmis et al. have shown that adding 5–15 wt% ENG to metal hydrides can increase ETC values up to tenfold, depending on the packing density and operating conditions [21,22]. Moreover, ENG can help reduce mechanical degradation caused by volume changes during cycling, thus contributing to better structural stability [7,21]. Other additive materials—such as carbon nanotubes, graphene nanoplatelets, and metal foams—have also been tested; however, ENG remains the most widely applied ETC enhancer due to its performance, cost-effectiveness, and ease of processing [13,21,22]. 5 The determination of the ETC is a crucial parameter for designing hydrogen storage and compression vessels [10]. Various methods are available for determining ETC, including steadystate methods (such as radial heat flow and guarded hot plate) and transient methods (like hotwire, laser flash, and transient plane source) techniques [20]. Among them, the Transient Plane Source (TPS) method is notable for its non-destructive approach, versatility, and suitability for powder and pellet samples. TPS sensors—such as those in the C-Therm Trident system—use a flat spiral that functions as both a heater and a thermometer. The response over time and temperature allows for the extraction of both thermal conductivity and diffusivity [7,23]. Along with the inherent benefits of metal hydrides for hydrogen storage, their practical use is limited by both kinetic and thermodynamic factors. Hydrogen absorption in metal hydrides depends not only on equilibrium aspects but also on the thermal nature of the chemical reactions involved. These characteristics have important implications for system and reactor design. During absorption, the heat produced must be efficiently removed to prevent temperature-induced shifts in equilibrium that could slow the reaction. During desorption, enough external heat must be supplied to maintain hydrogen release [9,15]. Poor thermal management can cause localized overheating or insufficient activation energy, both of which impair performance and reversibility. This thermal behavior underscores the importance of accurately measuring the effective thermal conductivity (ETC) of hydride beds, particularly under dynamic hydrogen cycling conditions. From a thermodynamic standpoint, hydrogen absorption/desorption occurs only when the applied pressure diverges from the material's equilibrium pressure. The equilibrium pressure is defined as the point where the forward (hydrogenation) and reverse (dehydrogenation) reaction rates are equal. The van't Hoff equation describes this equilibrium behavior as: ln(peq) = −ΔH RT +ΔS R [24,25]. Where ΔH is the enthalpy of formation (which denotes the strength of the bond between the metal and hydrogen), ΔS is the entropy change (for hydrogen from the gas to solid state and vice versa, which theoretical value is 130 J/ mol K), R is the universal gas constant, and T is the absolute temperature in Kelvin degrees [24,25]. This logarithmic relation helps predict the pressure– temperature conditions needed for reversible hydrogen storage and is commonly used in thermodynamic modeling of hydride systems. Furthermore, kinetic effects significantly influence the effective performance of these materials during cycling. The initial hydrogenation phase typically exhibits a higher hydrogen uptake compared to subsequent cycles. First, the extended absorption times used during activation allow hydrogen to penetrate more deeply into the material. Second, initial exposure to hydrogen causes irreversible microstructural changes, such as particle cracking, dislocation formation, and the 12 uniformity, and the absence of reliable capacity monitoring. As a result, absorption times were lengthened, and in some cases, the hydrogen pressure was increased to ensure complete activation. In particular, during initial measurements, it was not always clear whether a material had fully activated within the pressure chamber setup. After activation, repeated cycling experiments were performed under constant conditions to assess kinetic reversibility and capacity retention. The hydrogen capacity during the activation cycle was consistently higher than during subsequent cycling. 2.2.3 Thermodynamic consideration To determine suitable operating conditions for each material, van't Hoff plots of equilibrium pressure versus temperature were prepared, based on literature enthalpy and entropy values. To illustrate this thermodynamic relationship, Fig. 6 shows van't Hoff plots of the equilibrium pressure 𝑝𝑒𝑞 versus inverse temperature T for Hydralloy C5 and HPM3.1, respectively. These diagrams are critical for evaluating and comparing the temperature ranges in which hydrogenation or dehydrogenation is feasible. For example, the low equilibrium pressure of HPM3.1 at 5°C requires applied pressures of up to 80 bar during absorption and near-vacuum conditions during desorption. If the equilibrium condition is not reached, the material may show sluggish kinetics or incomplete sorption [9,33]. In contrast, Hydralloy C5 reaches equilibrium at significantly lower pressures under the same conditions. To initiate absorption, the applied pressure must be greater than the equilibrium pressure; conversely, desorption requires a pressure below the equilibrium pressure. Deviating from this balance can result in sluggish kinetics, incomplete sorption, or irreversible degradation of the hydride's performance [18,40]. Figure 6. van't Hoff plots of equilibrium pressure during absorption/desorption versus temperature for Hydralloy C5 [30] and HPM3 [internal report, confidential]. 13 2.3 ETC measurements In hydrogen storage systems, heat management is vital, especially during absorption and desorption cycles. As explained in Chapter 2.2, these processes are exothermic and endothermic, respectively, making thermal conductivity a crucial factor in optimizing performance. To address this, the effective thermal conductivity (ETC) of all studied metal hydrides was examined using transient plane source (TPS) measurement techniques. This chapter explains how ETC was measured using the C-Therm Trident system under both in situ and ex-situ conditions. These complementary methods offer insights into the thermal behavior of metal hydrides after treatment and throughout active hydrogenation cycles. 2.3.1 Overview of the Measurement Setup The effective thermal conductivity of all examined samples was measured using the C-Therm Trident Thermal Conductivity Analyzer, a commercial device based on the transient plane source (TPS) method [23]. In this approach, a flat sensor with a spiral-shaped heating element embedded between two Kapton layers acts as both a heat source and a temperature detector [23]. When a current flows through the element, it heats the surrounding sample, and the temperature increase is monitored over time [23]. This time-dependent temperature profile is then analyzed to determine thermal conductivity and thermal diffusivity, assuming a finite sample geometry [9,20,23]. In the current study, the Trident system was combined with a stainless-steel pressure chamber and connected to a hydrogen and argon loading station. This enabled temperatureand pressurecontrolled measurements under in-situ or ex-situ conditions. The pressure chamber houses the sample holder, sensor, and the sample and is designed to withstand hydrogen pressures of up to 100 bar. The setup also included safety valves, gas flow control lines, thermocouple inputs, and electrical feedthroughs. An overview image of the entire system is shown in Fig. 7. For all measurements, the High-Temp-Flex TPS sensor was placed between two identical portions of the sample material. For powder samples, the materials were gently compressed in the sample holder to create a flat surface. Meanwhile, TiFeMn pellets were cut to match the sample holder and sensor diameter requirements of 18-19.5 mm in diameter and over 6 mm in height [23]. The sensor and sample assembly were secured with a fixed mechanical clamping system that ensures consistent thermal contact throughout multiple cycles, as shown in Fig. 8. 14 Figure 7. System setup for ETC measurements. Figure 8. Sample holder and TPS sensor for ETC measurements. Before an ETC measurement, the system was purged and filled with hydrogen or argon as needed, and the sample was allowed to reach the desired temperature. Temperature was controlled using external heating elements integrated into the chamber wall and monitored with a thermocouple placed close to the sensor plane. All parameters, including measurement time, power input, sample properties, and environmental conditions, were set in the Trident software. A detailed list of all experimental parameters for the ETC measurements of the investigated materials is provided in Appendix A. For each measurement, a 30-minute stabilization period was maintained following any pressure or temperature adjustment. This duration also served as the necessary cool-down time for the sensor [23]. 15 2.3.2 In-situ vs. Ex-situ Measurements The measurements were carried out in two different operational modes: ex-situ and in-situ. Exsitu measurements involved samples that had been activated and cycled in the pressure chamber before the experiment. These were performed without a hydrogen atmosphere, reflecting the stable post-cycling state of the material. This method enables a rapid assessment of the material's thermal state after treatment, but does not capture dynamic changes in ETC under actual reaction conditions [9,20]. In-situ measurements, in contrast to ex-situ tests, were conducted directly during hydrogenation processes within the sealed measurement chamber. In this approach, the sample remained under operating conditions throughout the experiment, and hydrogen was introduced stepwise using a calibrated flowmeter. After each pressure adjustment, the system was allowed to thermally stabilize, ensuring that the sample had completed its hydrogenation response before the ETC measurement was initiated. This procedure enabled the determination of thermal conductivity as a function of hydrogen pressure and temperature under quasi-equilibrium conditions. For each ETC measurement series, a target temperature was chosen. However, the actual temperature inside the pressure chamber, as monitored by a thermocouple near the sensor, consistently varied by 2–6 °C from the set point due to thermal losses and the limited insulation of the system. The deviations are shown in Table 2. Depending on the material, two experimental strategies were used: in some cases, desorption occurred after each absorption step before increasing the pressure again; in others, the pressure was gradually increased without intermediate desorption. This method enabled the observation of both reversible and cumulative effects of hydrogenation on the material's thermal transport behavior [20,23]. A comprehensive summary of the measurement parameters, including sample mass, target temperature, target pressure steps, flowmeter configuration, and chosen hydrogenation strategy, is provided in Table 2. This dual-mode strategy provides a comprehensive overview of the thermal behavior of metal hydrides, helping to differentiate between irreversible changes (such as microstructural modifications during activation) and reversible effects (such as pressureor temperature-induced shifts in thermal transport properties) [20,23]. Both modes offer distinct advantages and disadvantages. While ex-situ tests are quicker and more consistent, due to stable ambient conditions, in-situ measurements provide more realistic and time-resolved insights, demonstrating how the hydride bed performs in practical systems [9,20,23]. They are, however, more difficult regarding thermal stabilization, baseline correction, and pressure-tight sensor mounting [23]. 16 Sample Mass [g] Target Temperatures [°C] (Hydride-Bed Temperatures [°C]) Target Pressures [bar] Flowmeter [l/min] Absorption Strategy TiFeMn 26.5 - - - - Hydralloy C5 + 5 wt% ENG 17.626 5 (11) 10 (14) 20 (22) 30 (32) 40 (42) 192040 6080 180 10 stepwise without desorption in between Hydralloy C5 pure 14.6324 30 (32) 1, 9, 20, 40, 60, 80 1 desorption after every step HPM3.1 + 5 wt% ENG 11.0838 -5 (-1.5) 30 (32) 60 (62) 192040 608090 190 1 stepwise without desorption in between HPM3.1 pure 20.219 5 (7.5) 30 (28.5) 1, 9, 20, 40, 60, 80, 90 1 desorption after every step Table 2. Overview of in-situ ETC-measurement parameters for each sample. 2.4 XRD measurements and crystalline phase analysis X-ray diffraction (XRD) was used to analyze the crystalline structure and microstructural properties of selected metal hydride samples after activation and hydrogen cycling. As a nondestructive method, XRD is commonly employed to evaluate phase composition, crystallinity, and grain size by examining the shape and width of diffraction peaks [41,42]. The underlying principle of XRD is the constructive interference of monochromatic X-rays scattered by regularly spaced atomic planes in a crystalline material. Bragg's law describes this phenomenon: nλ=2 d sinθ [41]. Where n is the order of reflection, λ is the X-ray wavelength, d is the spacing between lattice planes, and θ is the angle of incidence. By analyzing diffraction patterns—specifically, peak positions and intensities—valuable information can be extracted regarding crystal symmetry, lattice constants, and preferred orientations (texture) [41,42]. 17 In this study, XRD was conducted to identify potential phase transformations, structural degradation, or crystalline reordering that may occur during hydrogenation cycles. The tested materials, Hydralloy C5 and HPM3 (with and without ENG), are classified as AB₂-type intermetallic compounds, where atoms from group A (typically rare earths, such as La or mischmetal) combine with two atoms from group B (commonly Ni, Mn, or Al). These AB₂ materials typically form hexagonal Laves phases (C14 or C15), which have three axes of equal length in one plane and a fourth axis perpendicular to that plane, differing in length. This hexagonal anisotropy affects lattice expansion and hydrogen diffusion pathways during sorption reactions [41,43,44]. XRD measurements were conducted using a Bruker D8 discovery diffractometer with the "MEasSrv" software and "Powder Diffraction" application. A Cu Kα radiation source (λ = 1.5406 Å), operated at 50 kV and 1000 mW, was used. Scans were carried out in Bragg–Brentano geometry (Scan mode: Step), covering a 2θ range of 15° to 85°, with step increments of 8.75°. A time per step of 7200 seconds with 9 steps resulted in a total measurement time of 64800 seconds. To reduce noise and improve peak resolution, especially in fine powders and ENGmodified samples, longer measurement durations were necessary [42]. All samples were measured after activation and hydrogen cycling, with no exposure to ambient air between treatment and scanning, as seen in Fig. 9. Since the goal was not complete phase identification, pattern matching with ICDD or Rietveld refinement was not performed. Instead, a comparative analysis of crystallite size was conducted based on the peak broadening of selected peaks [41]. Crystallite size (also called "grain size") was estimated using the Scherrer equation: 𝐷 = 𝐾∗λ β∗cosθ⁡ [41]. Where D is the average crystallite size, K is the shape factor (assumed to be 0.9 for near-spherical particles), λ is the X-ray wavelength (1.5405 Å), β is the full width at half maximum (FWHM) of the peak in radians, and θ is the Bragg angle [41,45]. For consistent comparison, a dominant peak in the low-angle region, with 2θ < 40°, was selected. Peaks in this angular range were preferred because the impact of the Cu-Kα₂ component, which causes artificial peak broadening and peak splitting, increases at higher angles and can distort the analysis [34,41]. A narrow and intense peak indicates a higher degree of crystallinity and a larger coherent domain size, while broader and flatter peaks suggest reduced crystallinity or smaller crystallites [41,45]. This comparative approach provides a semi-quantitative evaluation of the effect of ENG addition on crystallite size and structure after activation. The ENG particles likely cause mechanical disruption and hinder crystal domain growth during hydrogen cycling, resulting in increased grain boundaries and enhanced interfacial effects [22,43]. 18 Figure 9. X-ray diffraction (XRD) device (left) with close-up of the mounting (bottom right) and sample on the dome sample holder (upper right). 2.5 Manipulation Handling metal hydride samples safely and reproducibly requires strict environmental control, as many of these materials are highly reactive with atmospheric oxygen and moisture. This is especially important for activated hydrides, which—due to their increased surface area—are more prone to oxidation, hydrolysis, and, in some cases, even spontaneous ignition when exposed to air [11,43]. Therefore, all samples—regardless of their initial air stability—were transferred into argon-filled gloveboxes immediately after activation and remained under inert conditions during all subsequent handling procedures. This approach ensured both experimental reproducibility and the safety of personnel and laboratory infrastructure when working with pyrophoric powders and composite materials [34,43,44]. A glovebox is a sealed, enclosed workstation designed to enable the handling of air-sensitive substances under a controlled, inert gas atmosphere, typically argon or nitrogen. The system 19 features gas-tight gloves integrated into transparent front panels, allowing users to manipulate materials inside safely without direct contact. Access to the interior is through an airlock or transfer chamber, which is evacuated and flushed with inert gas multiple times to prevent air entry. Oxygen and moisture levels are continuously monitored and maintained below critical thresholds, using purification units and sensor systems [43,44]. This setup is crucial when handling fine powders, metal–graphite composites, or hydrides that quickly degrade or ignite in air. In this study, two dedicated gloveboxes were utilized for the various stages of the sample process. Both are shown in Fig. 10. The first glovebox ("GB-Tank"), equipped with a microbalance and storage ports, was primarily used to prepare samples for volumetric measurements in Sievertstype titration instruments. Tasks included weighing, transferring, and sealing powder samples into stainless steel crucibles or reaction cells. Its compact design enabled efficient sample handling under consistently low O₂ and H₂O levels, making it ideal for routine preparation of small amounts of air-sensitive materials. The second glovebox, a larger system built in-house, was used for sample integration into the high-pressure measurement chamber. Due to the significant weight (~21 kg) and size of the pressure vessel, this glovebox was equipped with a wide front access port and an internal crane system to facilitate safe and ergonomic handling. The entire sensor module, pressure chamber, and connected loading station had to be assembled and sealed under inert conditions to prevent contamination of activated powders before measurement. Throughout all handling steps—both before and after ETC measurements—samples were either stored inside the glovebox or transferred in gas-tight containers. This was especially important for the HPM3-based materials, which showed increased sensitivity due to their finely divided microstructure and high chemical reactivity toward hydrogen and oxygen [11,43]. Despite some limitations, such as reduced dexterity caused by glove resistance, electrostatic charging of fine powders like ENG, and slow transfer through airlocks, gloveboxes remain essential tools in hydrogen storage research. Their ability to maintain extremely low levels of oxygen and moisture makes them crucial for working with pyrophoric or composite hydrides that would otherwise degrade irreversibly under ambient conditions [34,43]. 20 Figure 10. Glovebox "GB-Tank" (orange) and in-house-built (blue) with airlocks. 21 3. Results The following chapter presents the experimental results of all measurements, including the effective thermal conductivity (ETC), both ex-situ and in-situ, as well as their hydrogen capacity and grain size of the proposed hydride-forming materials. 3.1 Activation and cycling The hydrogen storage properties of the investigated materials were characterized before effective thermal conductivity measurements to confirm activation, assess cyclic stability, and establish capacity reference values. For Hydralloy® C5 (with and without ENG), hydrogen absorption and desorption measurements were performed using a Sieverts apparatus. For HPM3 (with and without ENG), a volumetric titration device was used. These methods provided a precise assessment of hydrogen uptake under specified pressure and temperature conditions. The results for the AB-type alloy TiFeMn (HyCare®) are presented separately in Appendix B and discussed in Section 3.3. 3.1.1 Hydralloy® C5 with and without ENG The hydrogen storage behaviour of Hydralloy® C5 was investigated in both its pure form and with the addition of 5 wt% expanded natural graphite. Both variants were tested under identical pressure and temperature conditions to enable a direct comparison of their absorption and desorption performance during activation and cycling. As shown in Fig. 11, Hydralloy® C5 achieved an absorption capacity of 1.54 wt% during activation and stabilized between 0.91 and 0.98 wt% in subsequent cycles. The corresponding desorption capacity was 1.34 wt% during activation and ranged from 1.00 to 1.33 wt% during cycling. The detailed values are listed in Table 3. 28 Figure 17. XRD measurement of Hydralloy® C5 pure after cycling. Figure 18. XRD measurement of Hydralloy® C5 +5 wt% ENG after cycling. 29 Figure 19. XRD measurement of HPM3 pure after cycling. Figure 20. XRD measurement of HPM3 + 5 wt% ENG after cycling. 30 3.3 Ex-situ ETC-measurements Ex-situ ETC measurements of Hydralloy C5 pure, Hydralloy C5 + 5 wt% ENG, HPM3 pure, and HPM3 + 5 wt% ENG were performed on four powder samples under vacuum conditions after prior activation and cycling. The measurements reflect the effective thermal conductivity of the materials in a desorbed state, without the influence of hydrogen gas during measurement. During preliminary tests, the TiFeMn pellet caused mechanical damage to the sensor due to substantial volumetric expansion during hydrogenation. The resulting damage is shown in Fig. 21. TiFeMn was excluded from further ETC analysis, and the results of the titration device are in Appendix B. Figure 21. Sensor damage caused by TiFeMn pellet expansion during hydrogenation. For Hydralloy® C5 pure, sensor deformation was also observed after in-situ cycling, requiring manual removal and remeasurement of the sample under ex-situ conditions. The effective thermal conductivities of all four tested materials are summarized in Table 8. The measurement uncertainty is estimated to be ±5 % based on repeated tests and manufacturer specifications. 31 Material Ex-situ pressure (vakuum) [bar] Hydride-bed temperature [°C] ETC [W/mK] Hydralloy C5 pure 0.02 29 0.22 Hydralloy C5 + 5 wt% ENG 0.03 32 0.38 HPM3 pure 0.03 8 0.60 HPM3 + 5 wt% ENG 0.027 27 0.42 Table 8. ETC values under vacuum conditions (ex-situ) for all powder samples. 3.4 In-situ ETC-measurements This section presents the in-situ measurements of the effective thermal conductivity of Hydralloy C5 pure, Hydralloy C5 + 5 wt% ENG, HPM3 pure, and HPM3 + 5 wt% ENG hydride-forming materials under specific hydrogenation and dehydrogenation conditions. The ETC measurements were performed inside the sealed pressure chamber of the C-Therm Trident system, which allows simultaneous control of gas atmosphere, pressure, and temperature. In contrast, the corresponding hydrogen absorption and desorption capacities were measured using external titration devices and a Sieverts-type apparatus (see also Section 3.1). Combining both methods provides a comprehensive assessment of how thermal conductivity and hydrogen capacity change during dynamic cycling. 3.4.1 Hydralloy C5 pure For the in-situ ETC measurements, Hydralloy® C5 pure was placed into the pressure chamber and activated before testing. After each absorption step, a complete desorption cycle was conducted before proceeding to the next pressure level. Fig. 22 shows the sensor temperature inside the bed, hydrogen flow, and pressure during this procedure. The temperature in the hydride bed during these measurements was approximately 29 °C. Under ~ 8 bar, the first pressure ramp, the temperature increase was the smallest, i.e., 4 °C. From 20 bar onwards, the temperature increase became more pronounced, ~ 10 °C, reaching its highest temperature peak under 60 bar at ~13 °C. This temperature behavior above 20 bar indicates that, at 29 °C and with an operative pressure exceeding the equilibrium pressure, the hydrogenation reaction is occurring. 32 The measured ETC values at each stabilized hydrogenation state are shown in Fig. 23. The values were recorded after thermal and pressure equilibrium had been reached in the system. Figure 22. Absorption and desorption behavior of Hydralloy® C5 pure via Loading Station 1 for ETC measurements. Figure 23. In-situ ETC measurements (initial ex-situ vacuum point) using the C-Therm High-Temp-Flex sensor on Hydralloy® C5 pure. Following the ETC measurements, the hydrogen content was determined using the Sieverts apparatus under similar temperature conditions (32 °C), as shown in Fig. 24, with the summarized results in Table 9. For most pressure levels, a sample mass of 1.028 g was used; however, for the 60 bar point, a sample mass of 0.9559 g was used due to the prior removal of a sample. This 33 enabled the correlation of hydrogen capacity with the previously measured ETC values. The results of this correlation, along with their relation to the equilibrium pressure, are displayed in Fig. 25. It is important to mention that the saturation capacity of about 1.6 wt% is reached upon activation. However, due to a device artifact, the capacity is reduced to a maximum of 1.2 wt% upon hydrogenation, which is considered equivalent to the capacity reached during activation. For this reason, the capacity from dehydrogenation is taken as a reference for correlating the capacity with the ETC. Figure 24. Pressure-dependent hydrogen capacity of Hydralloy® C5 pure from Sieverts apparatus measurements at 32 °C. Pressure [bar] Capacity max. absorption [wt%] Capacity max. desorption [wt%] 9 0.15 0.13 22 0.89 1.09 40 1.02 1.38 60 (1.11) (1.62) 80 1.29 1.43 Table 9. Pressure-dependent hydrogen capacity maximum of Hydralloy® C5 pure from Sieverts apparatus measurements at 32 °C. 34 Figure 25. Correlation of hydrogen capacity to ETC for Hydralloy® C5 pure (left) and the relation to the equilibrium pressure (right). 3.4.2 Hydralloy C5 + 5 wt% ENG For the in-situ ETC measurements, Hydralloy® C5 + 5 wt% ENG was placed into the pressure chamber, activated in situ, and subsequently subjected to a stepwise increase in hydrogen pressure without intermediate desorption. The corresponding pressure and temperature profiles for two temperature examples (32 °C and 14 °C) are shown in Fig. 26. In the 32 °C series, the most considerable temperature rise during hydrogenation was 17 °C (from 9 to 22 bar), while the smallest was 2 °C (from 60 to 80 bar). A single direct pressure step from vacuum to 80 bar, carried out outside the main series, resulted in a temperature increase of 40 °C. In the 14 °C series, temperature peaks ranged from 2 °C (60 to 80 bar) to 26 °C (8 to 22 bar). 35 Figure 26. Stepwise absorption behaviour of Hydralloy® C5 + 5 wt% ENG via Loading Station 1 for ETC measurements. The measured ETC values at each stabilized hydrogenation state are shown in Fig. 27. The values were recorded after thermal and pressure equilibrium had been reached in the system. After completing the ETC measurements, the hydrogen content was determined using the Sieverts apparatus at 32 °C. This allows assignment of the corresponding hydrogen capacities to each previously measured ETC value. The pressure-dependent capacity trend is illustrated in Fig. 28, with the corresponding data presented in Table 10. A constant sample mass of 1.463 g was used. Due to a brief interruption in the hydrogen supply before the 80 bar measurement, the capacity at this point may be slightly underestimated. 36 Figure 27. In-situ ETC measurements (initial ex-situ vacuum point) using the C-Therm High-Temp-Flex sensor on Hydralloy® C5 +5 wt% ENG. Figure 28. Pressure-dependent hydrogen capacity of Hydralloy® C5 pure from Sieverts apparatus measurements at 32 °C. 37 Pressure [bar] Capacity max. absorption [wt%] Capacity max. desorption [wt%] 9 0.1 0.17 22 0.8 0.91 40 1.16 1.46 60 1.26 1.48 80 (1.24) 1.74 Table 10. Pressure-dependent hydrogen capacity maximum of Hydralloy® C5 + 5 wt% ENG from Sieverts apparatus measurements at 32 °C. This enabled the correlation of hydrogen capacity with the previously measured ETC values. The results of this correlation, along with their relation to the equilibrium pressure, are displayed in Fig. 29. Figure 29. Correlation of hydrogen capacity to ETC for Hydralloy® C5 + 5 wt% ENG (left) and the relation to the equilibrium pressure (right). 3.4.3 HPM3 pure In the in-situ ETC measurements, HPM3 pure was activated in the pressure chamber and then subjected to alternating absorption and desorption steps at defined pressure levels. Measurements were carried out at two different temperature series: one at 29 °C and one at 8 °C, as shown in Fig. 30. After each hydrogenation step, a complete desorption cycle was performed before proceeding to the next absorption point. The highest temperature peak overall was only at 2 °C. 44 allowed in the in-situ setup were approximately 1-90 bar due to technical limitations. As a result, the low-pressure part of the curve, where a quick ETC increase is expected, was not accessible. 4.1.2 The influence of temperature Unlike pressure, temperature had only a minimal effect within the tested range of approximately -1.5°C to 60°C. From Figs. 27 (C5 + 5 wt.% ENG) and 34 (HPM3 + 5 wt.% ENG), the dependence of ETC on temperature for the materials with ENG was subtracted under specific pressure conditions. Figures 36 and 37 show the results. The materials without ENG behave similarly. 10 15 20 25 30 35 40 45 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 ETC (W/m K) Temperature (ºC) ETC C5+5 wt% ENG 1.0 bar ETC C5+5 wt% ENG 40.2 bar ETC C5+5 wt% ENG 78.3 bar Figure 36. Dependence of ETC on temperature for Hydralloy® C5 + 5 wt% ENG (From Fig. 27). -10 0 10 20 30 40 50 60 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 ETC (W/m K) Temperature (ºC) ETC HPM3+5 wt% ENG 1.0 bar ETC HPM3+5 wt% ENG 60.5 bar ETC HPM3+5 wt% ENG 91.2 bar Figure 37. Dependence of ETC on temperature for HPM3 + 5 wt% ENG (From Fig. 34). 45 ETC remains nearly constant with temperature changes for HPM3 and Hydralloy® C5, both with and without ENG. This can be explained by the fact that the ETC of hydride powders is typically dominated by contact resistance and gas-phase conduction, both of which exhibit limited sensitivity to moderate temperature variations. Additionally, the heat conductivity of hydrogen gas itself increases only slightly within this range, while phonon-based transport in the solid matrix remains mainly unaffected. A significant temperature dependence is more likely to occur at higher temperatures (above ~100 °C), where material-specific effects such as phase transitions, sintering, or increased phonon scattering become significant [9,49,50]. The finding of the independence of the ETC on temperature agrees with the theoretical calculations from ETC models published by Scarpati et al. [51]. 4.1.3 The influence of material composition The role of composition, especially the addition of expanded natural graphite (ENG), was more complex. Fig. 38 displays the in situ ETC measurements of Hydralloy C5 with and without 5 wt% ENG at 32 °C. The pressure-dependent curves originate from the individual measurements previously shown in Figs. 23 and 27. Fig. 39 presents the corresponding ETC data for HPM3, comparing the pure material (measured at 8 °C) and the sample with 5 wt% ENG (measured at – 1.5 °C). The curves are derived from the results presented earlier in Figs. 31 and 34. These combined graphs enable a direct visual comparison of the ETC performance with and without ENG under similar or representative conditions. In the case of Hydralloy® C5, ENG consistently enhanced ETC (Fig. 36). Values increased both under vacuum (from 0.22 to 0.38 W/m K) and across all pressure levels in in-situ measurements. This improvement aligns with the formation of a continuous conductive network, where graphite particles bridge the gaps between hydride grains, enabling lateral heat transfer through their high intrinsic conductivity (>100 W/m K). According to Warfsmann et al. [7], graphite also helps stabilize the powder bed mechanically and reduces structural degradation during cycling, thereby supporting the long-term stability of thermal performance. Other studies, such as those by Yasuda et al. and Ye et al. [21,52], confirm these findings across various compositions and additive loadings. It has been demonstrated in porous silicon, metal oxides, and sand structures that smaller crystallite sizes are associated with larger pore sizes [53]. Hence, the ETC can be affected by larger pore sizes, as they preclude contact among particles. However, the addition of ENG to C5 did not affect the crystallite size, as shown in Table 7. However, the expected positive trend was not fully observed in the ex-situ measurements of HPM3 (Fig. 37). While adding 5 wt% ENG consistently improved the ETC in Hydralloy® C5, the ex-situ ETC of HPM3 with ENG (0.42 W/m K) was lower than that of the pure sample (0.60 W/m K). This difference is probably due to variations in sample packing within the fixed-volume sample holder and/or incomplete activation. For HPM3, a lower initial mass was used to accommodate 46 expected volume expansion during activation and to prevent sensor damage. However, predicting the extent of expansion during hydrogen cycling is difficult, and the resulting packing density may have decreased significantly. Bellosta von Colbe et al. [10] emphasize that packing density and physical arrangement are crucial for accurate ETC measurements and must be carefully controlled in both experimental and practical systems. In this particular case, another hypothesis for the lower value of ETC in vacuum for the HPM3+5 wt% ENG could also be attributed to the reduction in crystallite size from 58 nm (pure HPM3) to 29 nm for HPM3+5 wt% ENG, as the smaller crystallite size increases porosity. Therefore, the effective distance between solid particles increases, resulting in a lower ETC value for the material with ENG [53]. In contrast, the in-situ ETC values of HPM3 with and without ENG followed the expected trend, with ENG still demonstrating a noticeable enhancing effect, although with a slightly flatter curve compared to Hydralloy® C5. Figure 38. Comparison of in-situ ETC of Hydralloy® C5 with and without 5 wt% ENG at 32 °C (data from Fig. 23 and Fig. 27). 47 Figure 39. Comparison of in-situ ETC of HPM3 with and without 5 wt% ENG at 8 °C and –1.5 °C (data from Fig. 31 and Fig. 34). A design improvement of the sample holder is proposed in Chapter 5 to accommodate expansion better while ensuring consistent packing. As discussed by Zhao et al. [20], differences in experimental configuration, such as sample holder geometry, compaction technique, or expansion allowance, can cause significant variation between in-situ and ex-situ ETC values, even for the same material composition [20]. 4.1.4 The influence of hydrogen capacity In addition to pressure, temperature, and composition, another key factor in evaluating thermal behavior is the hydrogen storage capacity of the material, which refers to the amount of hydrogen absorbed during a specific measurement step. In this context, it was hypothesized that higher hydrogen absorption could impact the ETC, affecting particle surface interactions or changing phase compositions. However, the ETC results for HPM3 showed that samples measured under sub-equilibrium conditions—meaning at pressures below the equilibrium pressure where only partial hydrogen uptake occurred—still displayed ETC values within the same range as fully hydrogenated samples (Figs. 31 and 34). Fig. 40 summarizes, using HPM3 + 5 wt.% ENG, the values of ETC in the hydrogenated and dehydrogenated states under 91.2 bar according to the equilibrium pressure shown in Fig. 35. This suggests that the capacity's direct influence on ETC is less significant than that of pressure [9,18]. 48 1.37 1.44 1.47 Hydrogenated at -1.5 ºC Dehydrogented at 32 ºC Dehydrogenated at 60 ºC 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 ETC (W/m K) Status ETC HPM3+5 wt% ENG under 91.2 bar Figure 40. Effect of the hydrogen capacity under 91.2 bar on ETC for HPM3 + 5 wt% ENG at -1.5, 32, and 60°C (data from Fig. 34). Although higher capacity generally improves hydrogen-metal contact and affects mechanical stress, its direct impact on thermal conductivity appears to be minimal. This may be because pressure effects dominate both the gas phase and particle bed compaction, overshadowing secondary effects of hydrogen content. However, the data from the HPM3 series should be interpreted carefully. The instrument used for ETC measurements operated at fixed intervals, and the actual hydrogen content was not independently verified through a mass balance or Sievertstype measurement at each step. Additional studies combining thermal and sorption analysis are necessary to determine if ETC truly remains unaffected by capacity for specific materials or conditions. For alloys with phase transitions or two-step hydrogenation behavior, more complex interactions between hydrogen content and thermal properties could occur [9,47]. Overall, the combination of in-situ and ex-situ results confirms that the effective thermal conductivity of hydride materials is a multifactorial property influenced by external conditions (pressure, temperature) and intrinsic material characteristics (composition, structure, packing, and hydrogen capacity). While pressure emerged as the most influential external factor, composition—especially the use of conductive additives like ENG—also plays a significant role when properly integrated. Temperature effects were limited within the studied range, and capacity effects were not evident under the chosen measurement protocol. These findings provide a solid experimental foundation for further modeling of ETC behavior in hydride beds, highlighting the importance of controlled sample preparation and testing conditions. 49 Based on the analysis of the dependence of ETC on pressure, temperature, and hydrogen capacity, it is possible to conclude that pressure is the primary parameter to consider for further investigation and modeling of ETC. 4.2 Evaluation of the obtained results based on the literature review To evaluate the plausibility of the measured effective thermal conductivities (ETC), selected literature values were compiled for comparison (see Table 11). Reported ETCs for hydrideforming materials vary widely depending on material composition, hydrogenation state, measurement setup, and the presence of additives. For Hydralloy® C5, the in-situ measured ETC values in this study ranged from 0.22 to 1.35 W/m K for the additive-free sample and from 0.38 to 1.81 W/m K with 5 wt% expanded natural graphite (ENG), across a pressure range of 1–80 bar. These values fall within the lower to middle range of those reported in the literature [7,49,54]. Hahne et al. [55] reported values between 0.05 and 1.05 W/m K for Hydralloy® C5 under various gases and pressures using a transient hot-wire setup [52]. The observed pressure-dependent increase in ETC, as shown in Fig. 18, is consistent with previous findings, reflecting enhanced particle contact and gas-phase conduction at higher hydrogen pressures. The ex-situ values for Hydralloy® C5 were slightly lower, ranging from 0.22 to 0.38 W/m K, especially for the additive-free sample, due to the absence of gas-phase conduction and hydrogen-induced structural effects. Warfsmann et al. reported values ranging from 0.3 to 0.7 W/m K for similar materials containing 10 wt% ENG and 10 wt% EVA under an air atmosphere [7]. The trend of higher ETC with ENG was maintained but became less pronounced. These results highlight the significant influence of gas pressure and additive-based conduction networks. Notably, even without ENG, the ETC of Hydralloy® C5 increased under pressure, indicating densification and particle contact effects discussed in Chapter 4.1. These comparisons indicate that the values for Hydralloy® C5 in this study fall within the middle range of reported ETCs, which is reasonable given the relatively low additive content (5 wt%) and limited compaction. Future research could explore higher ENG concentrations (10–15 wt%) or alternative compaction methods to improve ETC values further. For HPM3, in the case of in-situ ETC measurements, the values ranged from 0.6 to 1.24 W/m K without ENG and from 0.42 to 1.5 W/m K with 5 wt% ENG. These values are within the range reported by Pasquini et al. for MgH₂-based systems (0.2 to 1.1 W/m K) and by Zhao et al., who observed up to 2.0 W/m K in Ti-doped Mg alloys under optimal cycling and compaction [16,20]. The results for HPM3 demonstrate its strong intrinsic thermal performance, further improved by ENG. 50 In the ex-situ state, HPM3 samples exhibited values ranging from 0.42 to 0.6 W/m K, both with and without ENG. Once again, this trend aligns qualitatively with the in-situ results but at a lower absolute level, due to the measurement conditions under vacuum. Notably, even without gas, the ETC remained above 0.2 W/m K, indicating a compact and well-connected powder bed structure. Overall, the literature comparison confirms a wide range of reported ETC values for similar materials, which depend strongly on the hydrogenation state, pressure, and additive formulation. The in-situ results of this study are within or near expected ranges for both Hydralloy® C5 and HPM3. The substantial impact of pressure and the complex role of ENG are consistent with previous findings, and the measured trends are robust across materials and testing protocols. These findings reinforce the validity and reproducibility of the present measurement methodology, underscoring the critical role of hydrogen pressure and composite design in optimizing heat transfer behavior in metal hydride beds. Reference Material Technique to measure the ETC Conditions under which ETC was measured ETC Range [W/m K] Warfsmann et al. [7] Hydralloy® C5 + ENG Transient Plane Source method with a Hot Disk TPS Powder, RT, air atmosphere 0.2973 (no ENG)-0.7106 (10 wt% ENG) Yoshida et al. [56] LaNi5 Hot-wire method Pellet, 60 °C, 1-10 bar H₂ 0.4-1.1 Hahne et al. [55] Hydralloy® C5 (HWT 5800) Transient hot wire method Powder, 10 mbar – 60 bar, different gases (incl. H2), - 80-140 °C 0.051.05 Hahne et al. [55] LaNi4.7Al0.3Hx Transient hot wire method Powder, 10 mbar – 60 bar, different gases (incl. H2), - 80-140 °C <1.1 Pasquini et al. [16] Zr/Ti-based AB2 C14-Laves alloy + 10 wt% ENG Steady-state radial heat flow method Powder, 25 °C, 80 bar H₂ 8 Zhao et al. [20] MmNi4FeH5.2 Steady-state radial heat flow method 0 °C, 40 bar H₂ 0.8-1.05 Pohlmann et al. [49] Hydralloy® + ENG Laser flash method Pellets (axial + radial cut), RT-300 °C, 1-40 bar H₂ 2.4-62.8 (radial) 2-8 (axial) Flueckiger et al. [47] Ti1.1CrMn Transient plan source method Powder, RT, 3-253 bar H₂ 0.3–0.7 51 Anil Kumar et al. [57] Mg + 50 wt% LaNi4.6Al0.4 + additives Radial heat conduction method Powder and pellets, 125-200 °C, 110 bar H₂ 0.5-1.5 (powder) 2-8 (pellet with additives) Kumar et al. [46] MmNi4.5Al0.5 Hydride Onedimensional steady-state axial heat transfer comparative method. Powder, 0-100 °C, 0-50 bar H₂ 0.1–1.2 Suda et al. [50] MmNi-hydrides + additives Static technique Powder, 10-40 °C, 0.5-50 bar H₂ 0.2–1.2 Suda et al. [50] TiMn-hydride Static technique Powder,10-40 °C, 0.5-50 bar H₂ 0.5-1.2 Table 11. Experimental ETC values from the literature for comparison. 4.3 Limitations and Uncertainties While the measured ETC values fall within the expected literature ranges and exhibit consistent trends with respect to pressure and composition, several sources of uncertainty should be acknowledged. The most significant limitation is the compaction state of the powder samples, particularly in ex-situ measurements. For HPM3 specifically, the deviation seen in the ENGcontaining sample is probably due to uncontrolled packing density caused by activation-induced volume expansion (see Section 4.2). The amount of swelling during activation was not precisely predictable, and the initial filling was deliberately reduced to avoid sensor damage. Consequently, contact resistances and internal voids may have impacted the measurement results. In the in-situ setup, pressure settings and temperature stabilization were reliably reproducible; however, due to hardware limitations, only a limited number of discrete pressure steps could be recorded. This limitation reduces the resolution of potential nonlinear effects, especially in the transition zone between low and high hydrogen densities. Another source of uncertainty comes from the thermal equilibrium condition needed before measurement. Although ETC values were only recorded once temperature and pressure remained stable (constant for 30 minutes), internal gradients or residual reactions could still have subtly influenced the measured values. Finally, all thermal conductivity measurements were taken in the radial direction within the sample chamber. Possible anisotropic effects in thermal transport, mainly caused by additive alignment (e.g., graphite flakes), were not considered in this study but could be significant in real-world systems or layered bed designs. 52 4.4 Modeling the ETC To enable a quantitative assessment of the effective thermal conductivity (ETC), this section introduces a mathematical model based on the previously discussed experimental data. Based on the findings from Section 4.1, which showed that hydrogen capacity had a relatively minor effect on the ETC, the modeling approach focused on the two main variables: hydrogen pressure and material composition. Consequently, a two-dimensional mathematical model was created for both Hydralloy® C5 and HPM3, with and without ENG. In addition to the mathematical models, a physical model was also used on Hydralloy® C5 to better understand its thermal transport behavior under hydrogenation conditions. This physical method provides a baseline for assessing the validity of the measured and fitted data and will be detailed in a dedicated subsection. 4.4.1 Mathematical model The primary objective of this modeling step was to derive analytical expressions for the effective thermal conductivity (ETC) as a function of hydrogen pressure. Based on the results in Section 3 and the discussion in Section 4.1, temperature and hydrogen composition had minimal experimental impact on the ETC during hydrogenation. Therefore, it is reasonable to assume that ETC during hydrogenation can be modeled (or predicted) primarily by changes in hydrogen pressure as the main variable. 𝐸𝑇𝐶 = 𝑓(𝑝). The expression proposed by Pons and Dantzer [58] is applied [56]. This modeling has been broadly used in several publications [59–62] 𝐸𝑇𝐶 = 𝐶1𝑝𝐶2 1 𝐶0+𝑝𝐶2. This equation provided greater flexibility in reproducing the experimental data and yielded a significantly improved fit across all datasets. The corresponding fit parameters and curves are shown in the following subsection for each material. 4.4.1.1 Hydralloy® C5 with and without ENG For Hydralloy® C5 (both with and without ENG), the available data points were limited; however, the overall trend appeared smooth enough to justify interpolation. Therefore, Akima spline interpolation was used to create a more continuous data representation, reducing artificial oscillations and preserving local monotonicity. The Akima spline-interpolated curves and both fits for Hydralloy® C with and without ENG are shown in Figs. 38 and 39, along with the corresponding functions. 53 Figure 41. Akima-spline interpolated ETC and hydrogen pressure with fitting functions for Hydralloy® C5. Figure 42. Akima-spline interpolated ETC and hydrogen pressure with fitting functions for Hydralloy® C5 with 5 wt% ENG. 60 Figure 47. Influences of different terms for ETC in ZBS-modeling of Hydralloy® C5. It should be noted that these results may vary considerably with pelletized materials, where external pressure improves particle–particle contact and increases the importance of the solid pathway in heat conduction. In such cases, the contact term and even the solid-phase contribution may become more significant. In conclusion, although the ZBS model offers a valid approximation for visualizing pressuredependent trends in ETC, particularly in the mid-to-high pressure range, it cannot fully reproduce the complex behavior of real metal hydride beds. The model's simplicity, while helpful for understanding, limits its ability to capture phenomena such as microstructural changes, hysteresis, or non-linear pressure effects at the gas–solids interface. This first overview does not allow for the application of the model to obtain the best representation and to analyze the influence of the intrinsic parameters. Therefore, in the next section, this point is addressed. 4.4.2.2 Comprehensive analysis on the application of the ZBS model for the ETC dependence on the pressure All equations, parameters, and calculations are presented in Appendix E. As seen in the equation of the model, the kh depends on the thermal conductivity of the hydrogen gas as a function of 61 temperature and pressure, as well as non-dimensional numbers such as the Nusselt (Nu) and the Knudsen (Kn) numbers. The kbp also depends on the non-dimensional number, as well as the thermal conductivity of the gas and the solid phase. The most relevant parameter for the kbp is the shape factor B, which includes the contact between particles and the biphasic cavity. The solid thermal conductivity, ks, is taken as constant, and the parameters influencing its contribution are the porosity and the flattening factor (). As already shown in Section 4.4.2.1, on the one hand, the terms relating to the kh and ks do not significantly influence the ETC. On the other hand, kbp was identified as the most important factor. To achieve the best model fit, it was determined that B (shape factor) is the parameter that the model allows to tune for optimal results. The B factor depends on porosity, which has already been calculated and cannot be changed, as well as parameters C and m, as shown in the equations in Appendix E. The best model fit was achieved with C = 0.25 and m = 4.85 (with no constraints). Fig. 48a, b, and c show the contribution of the different factors, i.e., (1−√1−ε)𝑘ℎ, √1−ε⁡⁡((1−φ)𝑘𝑏𝑝), and √1−ε⁡⁡(𝜑𝑘𝑠), where it is evident that the thermal conductivity of the biphasic region has the most significant contribution to the ETC. Fig. 48d exposes the experimental and calculated curves. The model exhibits relatively good agreement at high pressures. It suggests that more parameters, such as the effect of the volumetric expansion of the hydride upon hydrogenation, should be considered, as this would increase the contact among particles and the change in shape of the particles. This is addressed in the Zehner-SchlünderBauer extended model [9]. Moreover, the change in thermal conductivity from the alloy to the hydride should also be considered. Both the swelling of the hydride and the change in thermal conductivity of the solid during the metal-to-metal hydride transition influence the kbp and could contribute to representing the experimental behavior better. 62 Figure 8. Contribution of the a. effective gas conductivity, b. effective biphasic conductivity and c. effective solid conductivity on the ETC, and d. calculated ETC. Application of ZBS-modeling for Hydralloy® C5. ETC Experimental [W/m K] 0.41 0.53 0.84 1.14 1.27 1.33 1.35 Pressure [bar] 0.69 1 9 22.1 40.5 59.5 80.3 ETC - Calculated ZBS [W/m K] 0.37 0.38 0.46 0.94 1.35 1.35 1.35 )) 63 5. Conclusions and prospects This thesis investigated the effective thermal conductivity (ETC) of hydride-forming materials through both in-situ and ex-situ measurements across various temperatures and pressures, complemented by mathematical and physical modeling. The study focused on two AB₂-type alloys, Hydralloy® C5 and HPM3, tested in their pure form and with 5 wt% expanded natural graphite (ENG) as a conductive additive. All experiments used powder samples to simulate the thermal management of the hydride bed under operational conditions. The conclusions and future prospects of this thesis are outlined as follows. 5.1 Conclusions The addition of ENG increased ETC values in both materials. However, the measured ETC values remain below the desired target range for efficient thermal management in metal hydride systems, indicating ongoing limitations due to structural factors such as particle morphology, contact resistance, and limited homogeneous distribution of additives (ENG). Hydralloy® C5 generally exhibited higher baseline thermal conductivity than HPM3, which may be attributed to differences in intrinsic microstructure and oxidation sensitivity. These findings align with earlier reports summarized in Scarpati et al. [9], confirming that particle morphology and additive dispersion are crucial for optimizing thermal transport. In this study, pressure was found to be the primary factor influencing ETC, suggesting that densifying the powder bed and increasing the gas-phase thermal conductivity could significantly enhance overall heat transfer. However, this insight should be interpreted cautiously. The strong link between hydrogen pressure and ETC may be specific to the test conditions, particularly regarding powder morphology and packing density. See Section 5.2 for potential future experiments that may be needed to verify this. To support the interpretation of these trends, a simplified mathematical model was developed that empirically describes ETC as a function of pressure and temperature. The model reproduces the pressure dependence of the observed in-situ data quite well and provides a concise framework for applications in metal hydride vessel design through FEM simulations. The Zehner–Bauer–Schlünder (ZBS) model was applied to gain more insight into the parameters influencing the ETC. This model considers conduction through both solid and gas phases and treats porosity as a key parameter. In the ZBS model, increasing pressure reduces the mean free path of gas molecules, thereby increasing the gas-phase contribution to thermal conductivity. Additionally, higher pressure improves particle contact by decreasing interstitial voids, further enhancing the solid conduction pathway. This combined effect was reflected in the measurement data, confirming that ETC in metal hydride powders is highly pressure-dependent. Moreover, it 64 has been demonstrated that the shape factor, related to the morphological characteristics of the particles, influences the thermal conductivity in the biphasic region, which is the primary contributor to the ETC value. Although a relatively good agreement was reached at the time to apply the ZBS, it is necessary to account for two main substantial effects: the swelling of the particles and the change in solid thermal conductivity during the hydrogenation process. Such effects can be considered by applying more complex ETC models. However, this approach falls outside the scope of this thesis. Practically, the findings of this work highlight the importance of incorporating ETC as a dynamic parameter in the design of hydrogen storage and compression systems. Poor heat transfer remains a significant obstacle to the rapid and efficient cycling of hydrogen, especially in largescale applications. Understanding how ETC changes under real operating conditions—affected by pressure, temperature, and material composition—enables more accurate system simulations and targeted material improvements. The in-situ methodology and modeling strategies described in this thesis contribute to this goal, providing a foundation for the future development of thermally optimized hydride-based energy technologies. In summary, this work confirms the essential role of ETC in influencing hydride performance and emphasizes the benefits of in-situ characterization for realistic material assessment. It also provides a valuable dataset and methodological framework for future development and modeling efforts in hydrogen storage and compression systems. 5.2 Prospects The findings of this thesis offer several starting points for further development, both experimentally and through modeling. To better understand the pressure dependence of ETC, additional TPS measurements should be performed with more pressure points to provide curves with better resolution, especially in regions where nonlinear behavior is expected. The in-situ measurements on HPM3 need to be repeated, as the results obtained via the loading station were unusual: ETC remained nearly constant across different hydrogen pressures, even though measurements were taken under the equilibrium pressure. A possible explanation is that hydrogen content could not be accurately determined during TPS measurements due to the small powder quantity. For future measurements, the sample mass should be increased to at least 100 g to enable a reliable determination of hydrogen content inside the loading station while simultaneously performing ETC measurements. Another sample holder that still fits the pressure chamber would be needed. The problems with the sample holder regarding pellets could be solved in the future by using a different sample holder that allows for greater volumetric expansion; however, this still needs to be tested. Future research should aim to extend the measurable pressure range to determine if the trends continue or level off at lower or higher gas densities. 65 On the modeling side, the existing empirical and physical models should be further developed into hybrid models that combine thermal conductivity evolution with ab/desorption kinetics and thermodynamics. This would enable a better description of dynamic behavior under real operating conditions and should be supported by in-situ data. The models could also benefit from structural input parameters obtained through advanced characterization techniques. Furthermore, the in-situ method used here could be adapted for larger or application-specific systems. Integrating ETC monitoring into operating hydrogen storage or compression units would enable real-time thermal management and improved control strategies. Finally, future work should examine the long-term stability of additive-containing hydrides under repeated cycling. This includes the degradation of thermal pathways, changes in microstructure, and the mechanical and chemical stability of the additive itself. Altogether, this work lays the groundwork for further studies, with numerous promising prospects remaining to be explored. iii Acknowledgements First and foremost, I would like to express my sincere gratitude to Prof. J. Jepsen for giving me the opportunity to carry out my Master’s thesis at Helmholtz-Zentrum Hereon. It was a privilege to gain hands-on research experience in such a renowned scientific institution, and I am deeply thankful for the trust placed in me. I am also very grateful to the entire team at Hereon for the warm welcome, the friendly working atmosphere, and the continuous support throughout my time in the laboratory. Their openness, availability, and willingness to help made a significant difference and contributed greatly to the success of this work. My deepest thanks go to my supervisor, Dr. J. A. Puszkiel, whose patient guidance, thorough explanations, and tireless support were invaluable to me during every stage of the project. His expertise, encouragement, and feedback have not only enriched this thesis but also shaped my scientific thinking far beyond. Finally, I would like to thank all those who supported me during this time — academically, technically, and personally. iv Declaration of Authorship I, Sarah Kretschmann (Student ID 894770, Wirtschaftsingenieurwesen 2021), declare that this Master’s thesis is the result of my own work and that it has not been submitted, either in whole or in part, for a degree or other academic qualification at any other university or institution. All sources and materials used have been acknowledged and properly referenced. Any assistance received during the research and writing process has been clearly stated. I confirm that I have read and understood the relevant institutional regulations regarding plagiarism and academic misconduct, and I affirm that this thesis complies fully with those guidelines. Date, Signature v References [1] Executive summary – World Energy Outlook 2023 – Analysis - IEA n.d. https://www.iea.org/reports/world-energy-outlook-2023/executive-summary (accessed July 1, 2025). 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Reaction behavior modeling of metal hydride based on FeTiMn using numerical simulations 2021. https://doi.org/10.31224/OSF.IO/AK8J3. xiii Appendix A Material Temperature [°C] Pressure [bar] TPS Power [W] TPS Time [s] ETC [W/ mK] Hydralloy® C5 + 5 wt% ENG 14 1.000 0.04 80 0.4993 Hydralloy® C5 + 5 wt% ENG 14 8.136 8.04 60 0.9304 Hydralloy® C5 + 5 wt% ENG 14 22.585 0.04 50 1.3745 Hydralloy® C5 + 5 wt% ENG 10 40.000 0.05 40 1.5724 Hydralloy® C5 + 5 wt% ENG 14 60.000 0.05 40 1.757 Hydralloy® C5 + 5 wt% ENG 14 80.000 0.06 40 1.8459 Hydralloy® C5 + 5 wt% ENG 22 1.000 0.04 80 0.8845 Hydralloy® C5 + 5 wt% ENG 22 9.500 0.04 60 1.0148 Hydralloy® C5 + 5 wt% ENG 22 23.600 0.04 50 1.3533 Hydralloy® C5 + 5 wt% ENG 22 41.300 0.05 40 1.5689 Hydralloy® C5 + 5 wt% ENG 22 60.400 0.05 40 1.6932 Hydralloy® C5 + 5 wt% ENG 22 79.800 0.06 40 1.1782 Hydralloy® C5 + 5 wt% ENG 11 1.020 0.04 70 0.5219 Hydralloy® C5 + 5 wt% ENG 11 1.020 0.04 70 0.5279 Hydralloy® C5 + 5 wt% ENG 11 9.880 0.04 50 1.2282 Hydralloy® C5 + 5 wt% ENG 11 21.900 0.04 40 1.3725 Hydralloy® C5 + 5 wt% ENG 11 40.690 0.05 35 1.5933 Hydralloy® C5 + 5 wt% ENG 11 59.380 0.05 35 1.7005 Hydralloy® C5 + 5 wt% ENG 11 78.250 0.06 35 1.7909 Hydralloy® C5 + 5 wt% ENG 32 1.020 0.04 70 0.5357 Hydralloy® C5 + 5 wt% ENG 32 8.820 0.05 50 0.9695 Hydralloy® C5 + 5 wt% ENG 32 22.170 0.05 50 1.3194 Hydralloy® C5 + 5 wt% ENG 32 40.370 0.06 40 1.5304 xiv Hydralloy® C5 + 5 wt% ENG 32 59.680 0.06 40 1.6793 Hydralloy® C5 + 5 wt% ENG 32 79.300 0.06 35 1.7701 Hydralloy® C5 + 5 wt% ENG 32 80.410 0.06 35 1.8185 Hydralloy® C5 + 5 wt% ENG 32 80.360 0.07 25 1.8158 Hydralloy® C5 + 5 wt% ENG 42 1.030 0.04 70 0.6347 Hydralloy® C5 + 5 wt% ENG 42 8.460 0.04 50 0.9533 Hydralloy® C5 + 5 wt% ENG 42 21.840 0.05 50 1.3208 Hydralloy® C5 + 5 wt% ENG 42 41.060 0.06 40 1.5193 Hydralloy® C5 + 5 wt% ENG 42 60.740 0.06 40 1.6686 Hydralloy® C5 + 5 wt% ENG 42 80.050 0.07 35 1.7969 HPM3 + 5 wt% ENG -1.5 1.019 0.04 50 0.6845 HPM3 + 5 wt% ENG -1.5 88.470 0.06 50 1.39 HPM3 + 5 wt% ENG -1.5 9.477 0.04 50 1.1195 HPM3 + 5 wt% ENG -1.5 21.862 0.05 40 1.2299 HPM3 + 5 wt% ENG -1.5 41.110 0.06 40 1.3031 HPM3 + 5 wt% ENG -1.5 60.527 0.06 40 1.3218 HPM3 + 5 wt% ENG -1.5 79.345 0.06 40 1.396 HPM3 + 5 wt% ENG -1.5 91.223 0.07 40 1.3658 HPM3 + 5 wt% ENG 60 1.028 0.04 50 0.6781 HPM3 + 5 wt% ENG 60 9.289 0.04 50 1.1282 HPM3 + 5 wt% ENG 60 22.267 0.05 50 1.2574 HPM3 + 5 wt% ENG 60 40.556 0.06 50 1.3544 HPM3 + 5 wt% ENG 60 60.292 0.06 40 1.3751 HPM3 + 5 wt% ENG 60 79.683 0.07 40 1.4177 HPM3 + 5 wt% ENG 60 91.502 0.07 40 1.4728 HPM3 + 5 wt% ENG 60 1.018 0.04 40 0.6568 HPM3 + 5 wt% ENG 60 92.453 0.07 40 1.4906 HPM3 + 5 wt% ENG 27 0.027 0.04 50 0.4203 HPM3 + 5 wt% ENG 32 1.050 0.04 50 0.6489 HPM3 + 5 wt% ENG 32 10.310 0.04 50 1.1331 HPM3 + 5 wt% ENG 32 21.607 0.05 50 1.2521 HPM3 + 5 wt% ENG 32 41.498 0.06 40 1.329 HPM3 + 5 wt% ENG 32 60.930 0.06 40 1.4017 HPM3 + 5 wt% ENG 32 79.845 0.07 40 1.3856 HPM3 + 5 wt% ENG 32 91.977 0.07 40 1.4412 HPM3 + 5 wt% ENG 32 1.014 0.04 40 0.6466 HPM3 + 5 wt% ENG 32 29.344 0.07 40 1.4492 Hydralloy® C5 29 1.012 0.04 60 0.4609 Hydralloy® C5 29 1.014 0.04 50 0.4351 Hydralloy® C5 29 8.482 0.04 50 0.9288 xv Hydralloy® C5 29 21.459 0.05 40 1.2394 Hydralloy® C5 29 1.014 0.04 40 0.5417 Hydralloy® C5 29 40.600 0.05 40 1.3369 Hydralloy® C5 29 1.013 0.04 40 0.5284 Hydralloy® C5 29 59.525 0.06 40 1.3307 Hydralloy® C5 29 80.342 0.07 40 1.3513 Hydralloy® C5 29 40.521 0.05 40 1.2668 Hydralloy® C5 29 22.069 0.05 40 1.14 Hydralloy® C5 29 9.013 0.05 40 0.8416 Hydralloy® C5 29 0.020 0.04 50 0.2205 Hydralloy® C5 29 8.968 0.04 40 0.8415 Hydralloy® C5 29 0.688 0.04 40 0.4145 HPM3 29 1.014 0.04 60 0.6605 HPM3 29 10.106 0.05 50 1.0732 HPM3 29 22.631 0.05 50 1.1674 HPM3 29 40.240 0.05 50 1.2048 HPM3 29 60.795 0.05 50 1.2167 HPM3 29 91.230 0.06 50 1.24 HPM3 8 1.151 0.04 50 0.72 HPM3 8 91.382 0.06 40 1.2297 HPM3 8 0.030 0.04 60 0.6001 HPM3 8 10.470 0.05 40 1.0683 HPM3 8 22.087 0.05 40 1.1327 HPM3 8 5.321 0.05 40 0.9907 Table 12. Detailed experimental parameters for ETC measurements with C-Therm TPS. xvi Appendix B Figure 48. TiFeMn activation in Sieverts apparatus, 13. cycle. Figure 49. TiFeMn after activation during cycling in Sieverts apparatus, 17. cycle. xvii Figure 50. TiFeMn after activation and cycling in Sieverts apparatus, 18. cycle. xviii Appendix C xix Appendix D Parameters and Equations Material Hydralloy® C5 T [°C] 29 ks [W/m K] 10.1 kg [W/m K] formula 𝑘𝑔= 0.004748329+5.881455∗10−4𝑇+7.320371∗10−7𝑇2−3.871176 ∗10−9𝑇3+5.367395∗10−12𝑇4−2.444096∗10−17𝑇5 kg [W/m K] 0.18101395 dc/d Variable (1/1000) 𝛗 formula φ = 23(𝑑𝑐 𝑑)2 1+22(𝑑𝑐 𝑑)4 3 𝛗 2.29495E-05 𝟏−𝛗 0.999977050 ETC [W/m K] 𝑘𝑒𝑓𝑓 =(1−√1−ε)𝑘ℎ+√1−ε((1−φ)𝑘𝑏𝑝 +𝜑𝑘𝑠) kbp/kh Variable (9) 𝜹𝒑 [kg/𝒎𝟑] 0.16 𝛆 formula ε = ε⁡0 1− 1 ε⁡0𝑋𝛿𝑝 1−𝑋𝛿𝑝 𝒌𝒉 formula 𝑘ℎ= 𝑘𝑔/{1+2[2−𝛼 𝛼](𝜆0𝑃0) 𝑙𝑃 } α 0,15 λ formula 𝜆 = 3.7206∗10−10𝑇 𝑃 l [m] 𝑙 = 𝑑𝑝10−6 𝒅𝒑[µm] formula 𝑑𝑝= 𝑑𝑝,0(1−𝑋𝛿𝑝)−1/3 𝒅𝒑,𝟎 [µm] 23 Calculations p [bar] 0.69 1 9 22.1 40.5 59.5 80.3 ETC [W/m K] 0.41 0.53 0.84 1.14 1.27 1.33 1.35 X normalised 0 0 0.0709 22 0.7517 73 0.9645 39 1 1 l [m] 2.00E05 2.00E05 2.01E05 2.09E05 2.12E05 2.12E05 2.12E05 𝛆 0.61 0.61 0.6 0.55 0.53 0.53 0.53 𝒌𝒉 [W/m K] 0.1507 39 0.1589 82 0.1782 79 0.1799 33 0.1804 3 0.1806 16 0.1807 19 (𝟏−√𝟏−𝛆)𝒌𝒉 [W/m K] 0.0566 02525 0.0596 97773 0.0655 2546 0.0592 30274 0.0567 33424 0.0567 91909 0.0568 24296 𝒌𝒃𝒑 [W/m K] 1.3566 51 1.4308 38 1.6045 11 1.6193 97 1.6238 7 1.6255 44 1.6264 71 xx √𝟏−𝛆((𝟏−𝛗)𝒌𝒃𝒑 + 𝝋𝒌𝒔) [W/m K] 0.8473 53587 0.8936 82291 1.0149 05166 1.0864 55091 1.1134 02542 1.1145 50152 1.1151 85657 √𝟏−𝛆((𝟏−𝛗)𝒌𝒃𝒑) [W/m K] 0.8472 08834 0.8935 37538 1.0147 58569 1.0862 99602 1.1132 43635 1.1143 91245 1.1150 26749 √𝟏−𝛆(𝝋𝒌𝒔) [W/m K] 0.0001 44753 0.0001 44753 0.0001 46597 0.0001 5549 0.0001 58907 0.0001 58907 0.0001 58907 ETC [W/m K] 0.9039 56112 0.9533 80064 1.0804 30627 1.1456 85365 1.1701 35966 1.1713 42061 1.1720 09952 Deviation ETC (experimental + model) 0.4939 56112 0.4233 80064 0.2404 30627 0.0056 85365 0.0998 64034 0.1586 57939 0.1779 90048 xxi Appendix E Equations Parameters Calculations