Review of metallic phase change materials for high heat flux transient thermal management applications

Applied Energy 258 (2020) 113955

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Review of metallic phase change materials for high heat flux transient thermal management applications

T

Patrick J. Shambergera, , Nickolaus M. Brunob ⁎

a b

Department of Materials Science and Engineering, Texas A&M University, College Station, TX 77843, USA Department of Mechanical Engineering, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA

HIGHLIGHTS

physical properties and melting behavior in metallic phase change materials. • Review > 130 metallic phases with melting temperatures < 1000 °C from 7 chemical families. • Highest energy density, thermal conductivity phase change materials. • Identifiedvolumetric promising directions for near-term materials development. • ARTICLE INFO

ABSTRACT

Keywords: Phase change material Latent heat energy storage Alloys Electronics thermal management

Metallic phase change materials offer an approach to rapidly transport heat away from a critical device, and to store that heat using the latent heat of fusion, buffering the temperature of a device during periods of transient high-power operation. Despite this interest, thermophysical properties and details of melting behavior of metallic alloys and compounds are scattered across the literature. Here, we critically review metallic phase change materials, and introduce quantitative comparative metrics to evaluate the relative performance of different compounds. This review focuses on (1) discussion of advanced prototype systems based on metallic phase change materials which rapidly absorb heat and buffer temperature rise in different devices and components, (2) historical development and focused applications of these materials by different communities, (3) identification of chemical alloy families with desirable melting characteristics, (4) critically evaluated thermophysical properties of different chemical alloy families, and (5) description of characteristic melting behavior in metallic systems. We focus here on describing different chemical classes of metallic phase change materials with melting points, Tfus, from near room temperature to < 1000 °C. The objective of this review is to assess the state of knowledge of metallic phase change materials, and to identify promising opportunities for further development. We conclude by identifying three critical areas for further development of metallic phase change materials.

1. Introduction Phase change materials (PCMs) are substances which reversibly absorb and release heat over a narrow range of temperature due to the enthalpy of a reversible phase transition. In the context of thermal energy storage materials, the phase transition is generally a transition between two condensed phases (e.g., liquid-solid, or solid-solid), allowing heat to be absorbed and released over many cycles, with minimal change in volume each cycle. While PCMs have found use commercially to regulate building temperatures [1–3], to allow for offpeak demand use of HVAC systems [4,5], and to regulate body temperature for personal comfort [6–8], they have traditionally been

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limited to transient thermal management applications operating at low frequencies due to slow rates of heat transfer into the PCM. In contrast, current and future demands in the area of high-power electronic systems and devices, require faster rates of heat absorption to manage brief (< 1 s) and high-power (> 100 W·cm−2) thermal transients. These needs are not met by traditional organic or inorganic salt PCMs, but require materials with high thermal conductivity, motivating the recent interest in metallic PCMs. In the context of heat transfer rates, metallic PCMs offer advantages for transient thermal management due to their relatively high thermal conductivities (~1 to 2 orders of magnitude greater than other chemical classes of PCMs), and relatively high volumetric energy storage

Corresponding author. E-mail addresses: [email protected] (P.J. Shamberger), [email protected] (N.M. Bruno).

https://doi.org/10.1016/j.apenergy.2019.113955 Received 18 March 2019; Received in revised form 21 September 2019; Accepted 30 September 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

Applied Energy 258 (2020) 113955

P.J. Shamberger and N.M. Bruno

densities. Together, these qualities make metallic PCMs of interest for certain stationary or small length-scale problems, where the rate of heat absorption and rejection is the principal metric of concern. Of particular relevance in this domain are power electronics (e.g., inverters, rectifiers, converters) [9,10], laser components (e.g., pump diodes, optical gain media) [11–13], RF amplifiers [14,15], and processing units [16–18], all of which can be found to operate in transient pulsed modes, and their use is generally limited by some critical threshold temperature, which must not be exceeded during operation of the component. Use of metallic PCMs for these applications requires a detailed understanding of thermophysical properties of different candidate materials, as well as an understanding of the nature of melting phenomena in these materials, in order to adequately integrate them into a packaging solution. PCMs can be classified based on their chemical nature. Broad chemical classes of PCMs investigated previously include organic compounds (paraffins, sugar alcohols, etc.), salt hydrates, anhydrous salts, and metallic alloys, where each class of PCM generally has some advantages and disadvantages. As an example, paraffins are one of the most common classes of PCMs due to their repeatable solidification characteristics, and their stability at atmospheric conditions. However, paraffins have only moderate energy storage densities, relatively low thermal conductivities, and are flammable. A number of extensive reviews have been published previously which review PCMs and their integration into heat exchangers [19,20], review known classifications of PCMs with insights into different applications which utilize PCMs [21,22], or focus on specific temperature ranges of PCMs, e.g., PCMs applicable for solar heating [23,24]. Furthermore, previous reviews have focused on specific classes of PCMs (e.g., organic compounds [25]), and have focused on techniques to improve the thermal conductivity of PCMs [26]. Similarly, a number of reviews focus on the use of PCMs for specific applications, including automotive [27], battery [28], or aerospace applications [29,30]. Of particular interest in describing the fundamental materials science underlying PCM materials is the outstanding series of volumes edited by Lane, which describes the development of latent energy storage materials for storage of solar heat [31]. Given equivalent external forcing, metallic PCMs absorb heat from an interface ≈1 to 2 orders of magnitude faster than other classes of PCMs [32], and at rates competitive against steady-state convective cooling approaches for short periods of time. To quantify this comparison, we illustrate the heat flux, q'', across an interface in different PCMs as a function of time, and compare this against q'' observed due to convective cooling approaches caused by an abrupt temperature rise in an interface of ΔT = 10 °C (Fig. 1). Heat flux into PCMs decays over time due to the propagation of a melt front away from the interface. However, the large thermal conductivity and volumetric heat of fusion cause metallic PCMs to out-perform other PCMs (Fig. 1). Furthermore, free or forced convective heat transfer from a heat exchanger (heat sink) to some heat transfer fluid (air, oil, water, etc.), allows for continuous operation, but at relatively low rates of heat transfer. Thus, to accommodate periods of high-power output, a system would need to be sized to reject heat at the maximum operation power of a device, which typically results in an oversized heat exchanger for most operational conditions. Spray, jet, and boiling heat transfer modes offer approaches to achieve either steady-state or pulsed high-heat flux transfer rates. However, these approaches can produce design challenges, and can result in surface fouling, and dry out, which can degrade the ability to regulate component temperatures over time. Given these considerations, metallic PCMs offer a compact and passive approach to mitigate brief thermal transients in a system caused by periodic pulses of heat. From this standpoint, selecting metallic PCMs with appropriate thermophysical properties can result in extending the period of pulse that can be mitigated before exceeding an allowable q'' (Fig. 1).

Fig. 1. Heat flux across an interface into various classes of PCMs upon melting as a function of time (paraffins, blue; salt hydrates, green; alloy PCMs, orange), for the case of a constant temperature boundary condition due to conduction. In all cases, PCMs are initially solid at their melting temperature, Tfus, and the wall temperature is abruptly raised (ΔT = 10 °C). For comparison, convective heat flux due to convection of air, oil, or water, under different conditions: free convection, forced convection (FC), boiling (B), and evaporative spray cooling (Sp), where the temperature difference between the wall and the fluid is also ΔT = 10 °C. Grey region illustrates the time longer than which heat flux into water (forced convection) exceeds heat flux into different PCMs.

Multiple proof-of-concept experiments have demonstrated the promise of metallic PCMs for high heat flux thermal management applications. These include both numerical [33] and coupled numerical/ experimental investigations of temperature rise in electronic chips at the die level [34,35], experimental investigations of thermal management for smartphones [36], or numerical [37,38] or experimental [39,40] investigation of heat absorption within thermal energy storage modules. Despite the promise of metallic PCMs, the literature on the relevant low melting point alloys and metallic compounds is fragmented across a number of fields, which limits application of these materials, and further development of additional compounds of interest. For this reason, we have endeavored to critically review the state of alloy PCM development, including the properties of congruently melting metals and alloys that were developed for alternative applications (e.g., as solder alloys, or as metallic heat transfer fluids), a general description of characteristic melting behavior in alloy systems, and a review of initial experiments demonstrating the capabilities of metallic PCMs to buffer temperature at a component surface. This review attempts to describe systematic variations in material properties within different classes of metals, to provide bounds on currently known and described systems, and to evaluate and resolve contradictory data in the literature, whenever possible. The physical properties reviewed herein are critical for accurate computational investigations of melting processes in metallic PCM systems, and for design of thermal energy storage components. Furthermore, we aim to identify areas still in need of detailed investigation. The goal of this review is to assess the state of known metallic PCM compounds to allow for comparisons of existing known materials and selection of a particular compound based on relevant parameters of interest. We are particularly motivated by the observation that much of the previous work is distributed across different technical communities, and in some cases, lacks cross-validation with well-established libraries of phase equilibria data. This review starts by briefly describing the major technological development efforts over the past few decades which have contributed to the current state of knowledge of metallic PCMs, as well as a discussion of their current and potential uses. This is

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Table 1 Experimental and numerical thermal buffering capacity (stall time) and temperature rise (ΔTpk) of metallic PCMs in a cavity under constant heat flux loading from an adjacent surface. PCM

Cavity Geometry

Heat Flux W·cm−2

Pulse Length s

Pulse Period s

Stall Time s

Tpk °C

Type

Ref.

n-eicosene 49Bi-21In-18Pb-12Sn Ga N-eicosane Na2SO4·10H2O Paraffin 49Bi-21In-18Pb-12Sn

rect. rect. rect. rect. rect. rect. rect. rect.

49Bi-21In-18Pb-12Sn Ga 50Bi-27Pb-13Sn-10Cd

rect. channels finned cavity finned cavity

52In-48Sn

rect. channels

0.44 0.44 0.22 0.66 0.66 0.66 0.66 0.26 1.04 11 100 18,000 12,000 6,000 500,000

3000 3000 3000 1800 1800 1800 1800 1250 1250 0.6 1 0.2·10-3 0.2·10-3 0.2·10-3 2·10-6

– – – – – – – – – 6.6 – 3.2·10-3 3.2·10-3 3.2·10-3 100·10-6

0 ≈400 ≈1000 550 300 300 200 ≈60 ≈250 0.28 – – – – –

– – – – – – – – – 10 to 15 25 24.5 20.5 13 21

Numer. Numer. Numer. Exp. Exp. Exp. Exp. Exp. Exp. Exp. Numer. Numer. Numer. Numer. Numer.

[37] [37] [37] [36] [36] [36] [36] [39] [39] [18,35] [38] [34] [34] [34] [33]

cavity cavity cavity cavity cavity cavity cavity cavity

followed with a brief description of known chemical families of metallic PCMs with melting points Tfus < 1000 °C, classifying these on the basis of chemical behavior. Next, we include a critical review of thermophysical properties of these alloys, including densities, melting and crystallization temperatures, enthalpies of fusion, as well as conductive transport properties, allowing for comparison between different materials on both energy and power density basis. This section includes detailed tables, cross-referenced against thermophysical data available in the literature. Finally, we review numerical and experimental investigations of melting behavior, including the role of convective heat transfer in such systems, and their effectiveness in buffering temperature rise during heating. It is the shared hope of the authors that this review will unify the current understanding of various classes of metallic PCMs, and also motivate further development of metallic PCMs in promising but underdeveloped directions.

volumes of PCM involved, but require finned structures [43,44] or pinfins [45] to effectively transport heat into that volume. More sophisticated hybrid designs seek to incorporate PCM directly into a heat sink, which is simultaneously optimized to reject heat by natural or forced convection to an external heat transfer fluid [46,47]. One common feature of the studies mentioned above, however, is the design of heat sink fins and channels that encapsulate the non-metallic PCM, to increase the surface area and enhance thermal conduction. For non-metallic PCM heat sinks, the thermal transfer from the die packaging to the PCM is the limiting factor on performance due to their relatively low thermal conductivity and high thermal resistivity. Recent efforts have investigated the use of metallic PCMs to buffer temperature deviations in pulsed electronics systems, in many cases in direct comparison against organic or other PCMs. The first investigations of electronics thermal management using low melting point alloy PCMs were reported in the 1990s, motivated by increasing power demands and electronics module complexities [39,48]. These were followed shortly by the work of Joshi and others who performed computational heat transfer studies on power electronic modules comprised of metallic and non-metallic heat exchangers [37]. Since these earlier studies, numerical and experimental studies have investigated the relative performance of incorporating metallic PCMs in specific power electronics packages [34,49], or for power electronics at the die level [33], in USB flash memory devices [50], in portable electronics (phones, tablets, etc.) [36,51], and in processors which operate in pulsed transient modes [16,18,52]. More recently, comparative studies of different non-metallic and metallic PCMs incorporated into different heat sink designs have been investigated by multiple groups [38,40,53]. No matter the cavity or fined geometry in heat spreaders, metallic PCMs outperform non-metallic PCMs for TES in electronic devices under most conditions (Table 1), as they exhibit a longer temperature stall period and higher temperature peak shaving ability. Under the range of conditions investigated, metallic PCMs tend to exhibit longer pinning durations and larger ΔTpk when compared against organic PCMs due to their favorable thermophysical properties. Moreover, metallic PCMs can offer the same, if not greater, temperature shaving ability and stall times for heat fluxes orders of magnitude larger than those applied to non-metallic PCMs.

2. Current and potential applications of phase change materials 2.1. Pulsed High-Power electronics Over the last two decades, PCMs have been the subject of numerous numerical and experimental studies aimed at understanding heat storage in high heat-flux electronics. Studies describing thermal energy storage (TES) of electronics typically consist of a PCM-filled cavity surrounding a microprocessor or equivalent thin film heater, operated under a constant heat flux conditions for some hold period. Pulsed experiments consist of cycles of pulses followed by a repose period with the heat source turned off, operating at some overall duty factor. As the principal motivation for inclusion of PCMs within an electronics package is reducing the temperature of the electronic device for some operational period of time, the relevant questions in these experiments are: (1) how does the peak surface temperature decrease due to the presence of the PCM (i.e., what is the magnitude of peak shaving, ΔTpk)? (2) what is the duration of temperature buffering? and (3) How are these performance metrics dependent on the intrinsic properties of the investigated PCM? Non-metallic PCMs have been investigated as an approach to absorb transient pulses of heat both at the level of the electronics packaging, and integrated into a heat sink module. PCM microvolumes embedded within a substrate [41], or at the interface between a substrate and an electronics package [42] tend to have very quick response times, but limited overall capacitance, due to the small allowable PCM volumes. In contrast, PCMs incorporated into volumes external to the electronics package, can generally buffer heat for longer periods, due to the larger

2.2. Solar thermal systems Solar thermal energy (STE) systems convert solar radiation directly to heat which can then be used as process heat (e.g., for heating water), or can be converted to electrical power by steam or gas-driven turbine

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generators, Stirling engines, or thermoelectric generators. In all cases, introducing thermal storage elements tends to counterbalance the inherent variability associated with solar power. Use of STE systems for solar water heating has a long history, and various classes of PCMs have been evaluated for the purpose of accumulating and storing heat in a compact volume, to be extracted for water heating at a later point [23]. Recent investigations of solar water heating application focus on organic and salt hydrate PCMs, primarily due to their low overall cost [54]. However, more effective heat transfer within the TES media tends to decrease system losses associated with internal thermal gradients, therefore directly increasing overall system efficiency. Thus, metallic PCMs, and in particular, low-cost alloy compositions, have the potential to result in a cost-effective system when the cost is levelized over the lifespan of the hot water system. STE generators tend to operate at higher temperatures (generally ≈300 to 500 °C) to maximize the thermodynamic efficiency of the energy conversion process. Within this temperature range, anhydrous salts (chlorides, nitrates, fluorides, etc.) are the most common PCMs considered, due to their low cost and reasonable energy storage densities [55]. While metallic PCMs have been considered as candidate materials, due to their high thermal conductivity [25], their higher relative cost tends to make them uncompetitive against other TES approaches [56]. Despite this limitation, distributed < 100 kW concentrated STE systems could potentially benefit from the high cooling powers associated with metallic PCMs, leading to work on intermediate melting point aluminum [57] and copper-silicon-magnesium [58] alloys.

device for cooling the breathing air in firefighter facial masks for up to 20 min during search and rescue missions [67]. Again, the high volumetric energy density and thermal conductivity of metallic PCMs could be reasonably anticipated to perform well for this application. Finally, Wang and others have demonstrated that PCMs are capable of direct energy conversion, rather than storage [68]. In this work, temperature fluctuations in the ocean change the phase of the PCM resulting in either expansion (melting) or contraction (solidification). The volume change of the PCM is used as potential mechanical energy, which is then converted to kinetic energy, and ultimately to electric power. In addition to these enumerated use cases, it is likely that metallic PCMs could enable other technologies which have not yet been envisioned. The key rational which runs consistently through all of these examples is a need for high power energy storage, or to manage very short heat pulses, which are transient in nature. 3. Technological development of liquid metals and metallic phase change materials Our current state of knowledge of alloy PCMs derives from historical development of these systems for four distinct applications: (1) metallic heat transfer fluids, (2) liquid metal electronics, (3) solder alloys, and (4) metallic PCMs. The current known alloy systems strongly reflect the properties of interest for these applications. Here, we describe these applications, and identify related properties of interest, as well as the principle alloy groups developed under these efforts. 3.1. Metallic heat transfer fluids

2.3. Photovoltaic cooling

Metallic heat transfer fluids serve a niche role in the thermal management of liquid metal cooled fast neutron reactors (LMFR) developed for either power generation, or for naval propulsion [69]. In this role, liquid metals are of interest due to their ability to rapidly transfer heat that is generated from small volume reactors. A number of experimental reactors have been developed based on liquid metals, predominantly using liquid sodium as a heat transfer fluid (despite the reactivity of liquid sodium with oxygen and water, which has led to multiple reactor shut-downs) [70,71]. Due to this interest, a number of efforts focused on characterizing thermophysical properties of liquid metals have been conducted over the past 50 years [72–74]. Key among these thermophysical properties of interest are low Tfus, low vapor pressures, and high thermal conductivities, allowing for effective use of metallic heat transfer fluids over the temperature range of interest. In addition, to serve as a heat transfer fluid in a reactor environment, it is imperative that liquid metals have low neutron cross sections (so as not to degrade under radiation environments), and not corrode structural materials used in pumps, heat exchangers, and vessel and pipe walls and linings. Certain pure metals (Hg, Na, Pb, and Sn) and binary eutectics (Na-K, Pb-Bi) have attracted the vast majority of interest in test reactors, as well as for Gen IV reactor designs, due to their favorable characteristics [70,71].

As PV cells heat, their energy conversion efficiency and life to failure decreases. Thus, passive cooling via PCM TES could introduce an affordable approach to maintain high efficiencies and long operational life. A number of experimental studies have investigated the effect of incorporating PCMs on the backside of PV panels, generally observing improvements in PV conversion efficiency from 2 to 6% based on the PV module considered, and the details of PCM integration [59–61]. Specifically, the inclusion of conductive particles to favor heat transfer into the PCM layer [62], and the selection of optimal PCM thickness [63] were observed to impact the overall efficiency of the PV module. This is particularly relevant for concentrated PV, in which a large solar flux is focused on a relatively small area, resulting in higher heat fluxes [64]. While these studies generally employ non-metallic PCMs such as paraffin wax and fatty acids, initial results have shown problems with temperature gradients and non-uniform melting of the PCM caused by convective effects [64], and limitations in regulating temperature for long periods due to low thermal conductivity of organic PCMs [59]. From this perspective, passive PV thermal management offers one additional potential use of metallic PCMs. 2.4. Novel applications In addition to the use cases described above, metallic PCMs are also potentially advantageous for a number of unique TES applications, although in most cases, metallic PCMs have not been directly tested yet. PCMs have been used to regulate the temperature of lithium-ion batteries during periods of charging and discharging [65,66]. Due to the importance of the Biot Number and thermal resistance of the PCM in transferring and storing heat at rates commensurate with heat generation during charging and discharging, Alipanah and co-authors in particular evaluated both metallic PCMs and paraffin-filled aluminum foams and found both of these systems more effective at mitigating temperature rise within the battery than pure paraffin PCMs [65]. In a different application, paraffin wax has also been employed in a novel

3.2. Liquid metal electronics Electrically conductive metallic liquids offer novel electrical applications, including stretchable and deformable wiring, self-healing wiring, and adaptive antennae, that are not possible in typical solid metal wiring [75–77]. While mercury-based systems have been utilized as electrically conducting liquids for the greater part of the 20th century (e.g., as an element in a bimetallic thermostat switch), the toxicity of mercury has limited broader applications. Current laboratory investigations in a number of research groups focus on Ga-based eutectics, driven by the low melting point of these eutectics which allows for room-temperature 3D printing [78], and room-temperature

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operation in the liquid phase [79]. The most relevant properties of interest for liquid metal electronics include: electrical transport properties, melting/solidification temperatures, stability (especially the tendency of many of these systems to oxidize), and compatibility with different electrode materials. The current Ga-based eutectics tend to strongly corrode many metallic electrodes [80–82]. Thus, Ga-free deep eutectics may offer the advantage of enabling liquid electronics interfacing directly with other standard electrical conductors (Al- or Cu-based alloys). Relevant to the goals of this review, identifying different metallic systems with different solidification temperatures could potentially allow multiple operation regimes in which different elements were either liquid or solid.

focused on chloride salts [90], and other inorganic salts as PCMs and heat transfer fluids, resulting in a number of compendia of thermophysical properties of inorganic salts and salt eutectics compounds [91–93], and critically evaluated correlations for density, surface tension, electrical conductance, and viscosity [94]. Unfortunately, inorganic salts tend to suffer from low thermal conductivity, which limits the rate of thermal energy storage and discharge. To counter this limitation, high-thermal conductivity metallic PCMs could be directly integrated into thermal energy storage systems [55]. Furthermore, increasing energy storage and conversion temperatures of concentrated solar thermal plants directly increases the efficiency of energy conversion. Metallic PCMs have the advantage of operating over relatively large temperature ranges with relatively low vapor pressures. Continued development of metal PCMs over the past few decades have increasingly been driven by thermal management demands in electronic components, which require very rapid response times (< 1 ms) to brief periods of increased power output. This general class of thermal management challenges occurs both in power electronics, which generally dissipate power in a transient intermittent fashion, as well directly in silicon-based processors, which are known to currently operate under thermally limited conditions [95–97]. As with earlier PCM applications, potential low-melting point alloys have principally been identified from existing known alloys, as opposed to purposedriven design of ideal alloy systems. Initial studies have focused principally on Bi-In-Pb-Sn alloys, and are outlined in greater detail in §4.3.

3.3. Solder alloys Plumbing and electronic solders represent the largest commercial application driving development of low-melting point alloys. In both cases, desirable solders generally melt at Tfus ≈ 200 °C, allowing for easy workability of these alloys, while maintaining a sufficiently large working temperature range for the solid alloy. In addition to temperature considerations, solder alloys must remain ductile, avoiding brittle fracture under mechanical loads, while also maintaining good resistance to thermal or mechanical fatigue. Furthermore, plumbing solders must be resistant to leaching toxic elements or galvanic corrosion when exposed to potable water. Similarly, electronic solders must resist electro-migration, or long-term growth of metallic whiskers, which can lead to short-circuits in electronic systems [83,84]. Due to their favorable thermophysical characteristics and long history of use, Pb-based solder alloys (especially Pb-Sn alloys) have dominated the commercial markets for both plumbing and electronic solders. Because of long-running concerns over Pb toxicity, Pb-based solders were prohibited from use in potable water plumbing in the mid 1980′s, and were slowly phased out as electronic solders around the beginning of the 21st century. In both cases, extensive development of Pb-free solders that maintained the favorable workable characteristics, as well as mechanical properties of Pb-Sn solders resulted in a large number of different solder alloy systems of potential interest as metallic PCMs [85,86]. Current commercial plumbing solders are generally derived from Sn-Sb alloys, in some cases containing minor amounts of Ag, Ni, or Cu to improve mechanical properties of the solder. Current electronic solders are generally derived from the Sn-Ag-Cu (SAC) alloy system which was selected due to the ability to introduce these alloys directly into most existing industrial soldering assemblies [87].

4. Chemical classifications Metal PCMs can be classified chemically based on their major components. Compositions of interest must avoid chemical segregation, necessitating the identification of either congruently melting or eutectic melting behavior. Due to the difficulty of identifying congruently melting compositions in multivariate compositional space, many such efforts focus on related families of alloys based around a single component (e.g., Ga), or a family of related components (e.g., Bi/In/Pb/Sn). In considering the known coverage of potential alloy systems (i.e., compositions and melting points of eutectic points and congruently melting compounds), it is worth acknowledging the remarkable wealth of data on binary alloy systems [98], while simultaneously acknowledging the paucity of data on ternary and higher order (4 or more major components) systems. As an example, at the time of preparation of this manuscript, while phase diagrams exist for 75 binary Al-X systems, ternary phase diagrams cover only ≈27% of the potential combinations of those systems (while ternary Ga and Bi phase diagrams cover only ≈18% and ≈11% of their respective available combinations) [98]. Thus, it is fair to claim that while this review attempts to capture the current known metallic PCM systems, there are a substantial population of ternary and higher order alloy PCMs that remain unexplored. Here, we will consistently use the convention “66.5 Ga-20.5In13.0Sn” to refer to alloy composition in mass percent, while we reserve the convention “In2Bi” for intermetallic compounds, given in terms of stoichiometric atomic concentrations.

3.4. Metallic phase change materials The potential use of metals as PCMs has a long history of development, starting in the space age, with the need to develop compact lowmass approaches to regulate temperature in manned and un-manned space vehicles [29,30,88]. These early efforts identified a number of potential systems of interest, primarily focusing on elemental metals (e.g., Sn, In, etc.), or previously developed commercial low melting point alloys (e.g., the Cerro family of alloys developed in the 1940s for use as solders). Due to critical constraints on component mass and volume, metallic PCMs for space applications were considered when they displaced other bulkier components (e.g., additional thermal radiator elements), and only when high heat fluxes required the high thermal conductivity of metallic PCMs, as other materials (e.g., organic waxes) generally offer greater specific energy storage density than metallic PCMs. Early development of concentrated solar thermal plants led to interest in developing high-temperature PCMs as a means of thermal energy storage to enable continued extraction of power overnight and during periods of low solar irradiance [89]. Significant effort has

4.1. Melting behavior The melting behavior of a particular alloy limits its functional utility as a PCM. Univariant melting reactions (e.g., melting of alloys in a binary isomorphous phase diagram) generally occur over a wide range of temperatures, which is not considered desirable behavior for a PCM. Furthermore, in the case of invariant melting reactions, which have a single well-defined melting temperature, certain classes of reactions result in poor PCM performance. Substances that melt incongruently, where the composition of the liquid produced is different from the bulk composition of solid phases tend to be susceptible to chemical

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among the first metals worked, and were alloyed with Cu to make bronzes, the hallmark of the Bronze Age. Development of these metals initiated in the Near East circa 3500 BC, and propagated through Europe over the next few millennia [107]. In modern times, this family of alloys has been explored extensively for use as liquid metal coolants [74] and solder alloys [101,108], due to their favorable working temperatures, malleable nature, and relative resistance to oxidation. Furthermore, the abundance of eutectics in this system results in available melting point depressions, which have favorable thermal characteristics [109]. Common minor alloying elements include Cd, Zn, Cu, and Ag, which allow for further refinement of melting points and physical properties. In extreme cases, deep eutectics (containing 4 or 5 components) have melting points as low as Tfus = 47 °C (Appendix A). Examples of well-known eutectic alloys in this family include Wood’s metal (50.0Bi-26.7Pb-13.3Sn-10.0Cd), and Field’s metal (51.0In16.5Sn-32.5Bi) [101]. Common Pb-containing solders (e.g., 60Sn-40Pb, or the eutectic alloy 63Sn-37Pb) are being phased out in commercial electronics in many markets and replaced with Pb-free alloys. Among the leading contenders are the family of Sn-Ag alloys, with > 90 wt. % Sn, containing minor amounts of third or fourth alloying elements (e.g., Bi, Cu) to control physical properties of the alloy. Such high-Sn content alloys are potentially susceptible to Sn pest, a material degradation phenomenon associated with transformation from high-temperature β-Sn (white tin) to low-temperature α-Sn (grey tin), and to the formation of Sn-whiskers, a phenomenon associated with residual stress in Sn alloys [83,84]. This has spurred significant research into the role of minor elements in limiting Sn pest and Sn-whisker growth. As metallic PCMs are restricted under RoHS regulations in the European Union and similar regulations in other regions, Pb- and Cd-containing PCMs are not anticipated to serve as viable candidates in most commercial applications, but are included here for completeness.

Fig. 2. Generic phase diagram, illustrating examples of melting along a univariant melting curve (pt U: L ), as well as invariant congruent melting (pt + ), and incongruent melting from a C: L ), eutectic melting (pt E: L + L 2 ) or from a peritectic (pt P: L + ). monotectic (pt M: L1

segregation over repeated melting [24,31]. In these cases, a liquid phase can spatially separate from solid phases during the melting or solidification processes, due to density differences between the two phases, resulting in chemical segregation, and irreproducible melting behavior. This represents a known problem for many classes of PCMs, most notably Glauber’s salt, NaSO4·10H2O, which requires significant engineering steps to avoid degradation of energy storage performance over the lifetime of the PCM [31,99]. Thus, monotectic reactions (which take the general form L1 S + L2), and peritectic reactions S2), are both examples of in(which take the general form: L + S1 congruent invariant reactions (Fig. 2). In contrast, congruent melting reactions, which only involve a single liquid and a single solid phase (L S) do not lead to phase segregation [24,31]. Similarly, eutectic reactions (L S1 + S2) involve two simultaneously solidifying, physically inseparable solid phases, and therefore also do not tend to lead to chemical segregation over time (Fig. 2). Thus, preference in this work is given to congruent melting and eutectic reactions. The nature of the melting reaction, including the specific solid phases involved have been cross-referenced against available phase diagrams in the literature [98], and are specified in Appendix A. Enthalpy of fusion, ΔfusH, entropy of fusion, ΔfusS, and available data on undercooling, ΔT, are described in Appendix B.

4.4. Au alloys Au (Tfus = 1064.2 °C) [100] is a well-known noble metal, which form intermetallics and eutectics with depressed Tfus (to < 500 °C) with many post-transition metals (e.g., Au-In, Au-Sn systems) [108]. However, the thermal properties, including ΔfusH, of such alloys have not been thoroughly investigated. Thus, only a few values of ΔfusH are reported here (Appendix B). As a noble-metal, gold and its alloys are particular resistant to oxidation. Despite this, such alloys tend to be prohibitively costly, limiting their potential for commercial application.

4.2. Ga Alloys Pure gallium (Ga) melts at 29.8 °C [100], whereas Ga eutectics span the temperature range (10 to 25) °C [101,102], representing the only known class of metallic PCMs, other than Hg-based alloys, which can store heat at and below room temperature (Appendix A). Ga is commonly alloyed with other post-transition metals, including In, Zn, Sn, and Cd. Of these, only Cd is controlled by Restriction of Hazardous Substances (RoHS) regulations. Low melting point gallium alloys, including the gallium eutectic 66.5 Ga-20.5In-13.0Sn (composition reported in mass %[101]) referred to by the trade name ‘Galinstan,’ have attracted the most interest recently as liquid conductors for reconfigurable antenna and self-healing wires, due to their stability as liquid metals at room temperature [75,76]. Ga is considered to be fairly corrosive, dissolving into many other metals (e.g., aluminum alloys, copper alloys, steels, etc.) [80–82], and therefore generally requires diffusion barriers to limit degradation of container materials [103,104].

4.5. Al-Mg-Zn alloys The low density metals Al (Tfus = 660.3 °C) [100] and Mg (Tfus = 649.9 °C) [110] are especially of interest due to their relatively low melting points, and their low densities (ρAl,liq = 2.38 g·cm−3, ρMg,liq = 1.59 g·cm−3 at their respective Tfus; Appendix D) [111]. Thus, eutectics containing these major components have potential as high specific energy density PCMs, while maintaining the high thermal conductivity associated with other metal PCMs. Al and Mg are commonly found alloyed with Zn (Tfus = 419.5 °C) [112], as well as Ca, Cu, and Si [102,113–115]. Eutectics with Tfus as low as 340 °C have been experimentally observed [102,112,114,115], while eutectics as low as 134 °C have been predicted using thermodynamic databases, but have not been experimentally validated [116]. Al-Mg-Zn alloys generally represent a chemically distinct subset of alloys from Bi-In-Pb-Sn alloys. As an example, Al-X binaries (X = Bi, In, Sn, or Pb) do not lead to eutectics with melting point depressions significantly below the Tfus of pure endmember X [98]. A similar case is observed for Mg-X binaries, however some minor depression of Tfus is observed in Mg-Pb and Mg-Sn systems [98]. In contrast, Zn tends to serve as a eutectic-forming

4.3. Bi-In-Pb-Sn alloys Bi (Tfus = 271.4 °C) [105], In (Tfus = 156.6 °C) [100], Pb (Tfus = 327.4 °C) [106], and Sn (Tfus = 231.9 °C) [100] are a family of post-transition metals commonly alloyed with each other and with other minor elements. Low melting point metals Sn, Zn, and Pb were

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element in both of these two systems. Al-Mg-Zn alloys have principally been investigated for higher-temperature thermal management applications, especially related to spacecraft thermal management [113]. Despite such potential, oxidation of both aluminum and magnesium are highly exothermic, and both metals can serve as oxidizers for thermite reactions [117]. Thus, maintaining an oxygen-free environment is considered to be of paramount importance for Al-Mg-Zn PCMs.

perspective, and from an applied perspective, due to use of these materials as heat transfer media in power plants and industrial settings [123,124]. Temperature dependence of liquid densities are generally well described by simple linear relationships, which are valid for ranges of (500 to 1000) K over the melting point of substances: L 3 i /kg·m

=A

(1)

B × T /K

Values for A and B are aggregated and reported in Appendix D for alkali metals [74,125], alkaline earth metals [125,126], transition metals [125,127–130], post-transition metals [127–129,131], metalloids [125,127,128], and a few non-metals [125,132,133]. From this data, liquid metals are observed to have volumetric thermal expansion coefficients, , in the range (60 to 200) ×10-6 K−1. While complete coverage of elemental metals and semiconductors exists, measured densities of liquid alloys are not universally available. Thus, liquid densities are calculated at Tfus for each alloy from temperature-dependent densities of elemental liquids using Vegard’s law, which predicts a linear relationship between molar volume and the molar fraction of constituent elements:

4.6. Cu alloys Cu (Tfus = 1084.6 °C) [100] has among the highest thermal conductivities of metals, and is commonly used in various thermal management applications where high heat transfer rates are important. In general, Cu tends to form low Tfus eutectics with Mg, Al, and Ag; Cu-X (X = Sn, In, Pb, Zn) forms intermetallic phases but eutectics in these systems tend to have high Tfus relative to endmember X. ΔfusH for only a few Cu eutectic systems are reported, which have Tfus (570 to 840) °C (Appendix B) [102,111,113,115]. These systems predominantly feature alloying with Al, Zn, Si, and other minor elements.

VµL =

4.7. Si alloys

L

Si (Tfus = 1411.9 °C) [110] is a widely-used semiconductor (bandgap 1.1 eV), which behaves as a conductive metal in the liquid state [118]. Si, along with many silicide intermetallic phases, have anomalous high ΔfusH due to contributions from changes in the electronic entropy of these systems upon melting [119–121]. Si forms many intermetallic phases with depressed Tfus with alloy families listed previously (Al, Mg, Cu). In this sense, Al-Mg-Zn, Cu, and Si alloys can all be considered to be subsets of a broader family of alloys. In contrast, Bi, In, Pb, Sn, and Zn do not tend to form low Tfus eutectics with Si. ΔfusH for only a few Si eutectic systems are reported, which have Tfus > 850 °C (Appendix B) [113–115].

=

(

i

(

i

x i (Mi/

)(

x i Mi /

)

L 1/3 i )

i

3

x i (Mi/

(2a)

)

L 1/3 i )

3

(2b)

L i ,

and xi are the molar mass, liquid density, and the molar where Mi, fraction of the ith component in the liquid [74]. VµL is the molar volume L = Mi/ iL , is the molar volume of the ith component of the liquid, and Vµ,i in the liquid. Liquid densities of metallic PCMs at their respective Tfus are reported in Appendix A. Calculated densities are within 3% for those liquid alloys which have been previously measured experimentally [109]. 5.2. Melting temperature Equilibrium melting or fusion temperatures, Tfus, are generally attained from calorimetric techniques (predominantly differential scanning calorimetry, DSC; Appendix B). Chemical families of PCMs discussed in §4 occupy different ranges of Tfus with moderate overlap (especially at higher temperatures). Ga alloys (11 to 25 °C), Ba-In-Pb-Sn alloys (47 to 199 °C), Au alloys (495 to 541 °C), Al-Mg-Zn alloys (134 to 800 °C), Cu alloys (571 to 840 °C), Si alloys (865 to 946 °C), and binary semiconductors (312 to > 1000 °C) all include phases melting < 1000 °C, the temperature regime considered in this review. To the extent possible, Tfus have been validated by cross-referencing eutectic temperatures and congruent Tfus of compounds with available phase diagrams [86,98,134], which generally represent assessment of thermodynamic stability based upon multiple experimental studies over some compositional range (Appendix A). Tfus reported in studies of PCMs are generally within (2 to 3) °C of available data from phase diagrams of alloy systems.

4.8. Binary semiconductors Also considered in this review are binary semiconductors with Tfus < 1000 °C (Appendix A, B) [110,122]. These are composed principally of chalcogenide compounds (containing an element from group VI of the periodic table: S, Se, Te) together with a few III-V semiconductors (e.g., InSb, GaSb, InAs). Most of these phases represent semiconducting solids, but are metallic in the liquid state (reflected by relatively large electrical and thermal conductivity in the liquid state). While these compounds traditionally have not been considered as potential PCMs, they offer interesting attributes, namely the potential for a large ΔfusH due to electronic contributions to the entropy of fusion [109,120]. Furthermore, they are chemically closely related to many of the intermetallic compounds that exist within the Bi-In-Pb-Sn alloy system. All of the compounds included here are congruently melting intermetallic phases. In many cases, these phases form low Tfus eutectics with elemental end-members and other intermetallic phase, the ΔfusH of which compounds have not been previously reported. Further investigation of phase space combining chalcogenide semiconductors and post-transition metals (e.g., Bi-In-Pb-Sn) is anticipated to be a rich area for exploration of new PCMs. Members of this family have Tfus (312 to > 1000) °C (Appendix A).

5.3. Crystallization temperature Undercooling represents the tendency for a material to retain a metastable liquid state for some temperature range below the equilibrium melting point of the alloy [31]. Undercooling is a consequence of the first-order solidification transformation, which requires a nucleus to grow larger than some critical radius, r*, defined by the energy balance between volumetric and surface energy terms, before the nucleus spontaneously grows. Thus, some temperature difference, referred to as undercooling or supercooling, ΔT, is generally observed before a material spontaneously solidifies. Because nucleation is a stochastic process, ΔT depends on the potency of available heterogeneous nucleation

5. Thermophysical properties 5.1. Density Thermophysical properties of liquid metals, including density and viscosity, have long been of interest from both a fundamental scientific

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Fig. 3. (a) Specific and (b) volumetric ΔfusH of elemental metals, and (c) specific and (d) volumetric ΔfusH of congruently melting intermetallic alloys and eutectics. In (a) and (b) BCC metals, FCC metals, and HCP metals illustrated by blue diamonds, green squares, and orange triangles, respectively (Appendix B). Post-transition metals and semiconductors illustrated by black circles. In (c) and (d), fields for alloys and eutectics as labelled; fields for other classes of PCMs are included for reference. Black x’s represent Si alloys.

sites, the volume of material solidifying, and the solidification rate. Due to the tendency for pre-melting to occur at free surfaces and interfaces (Tfus, surface < Tfus, bulk), which serves to nucleate the liquid phase, a symmetric superheating on melting is generally not observed in bulk metallic systems [135]. Undercooling reported for metal PCMs in this review is observed using scanning calorimetry techniques, in commercially pure alloys [109,114]. Undercooling is infrequently reported in solder alloys and potential PCM phases. When steps are taken to reduce the tendency for nucleation to occur at surfaces and interfaces (e.g., through levitation of droplets, suspension of droplets in a liquid, or encapsulation of droplets in a different alloy shell), ΔT of (90 to 240) °C is attainable in pure metals [136,137], suggesting that observations of smaller ΔT are indicative of heterogeneous nucleation off container surfaces, or impurity phases. The magnitude of undercooling depends on the relative potencies of such defects to nucleate some particular solid phase, which do not necessarily vary systematically based on composition. Thus, in the absence of a complete consideration of surface energies of different crystallographic planes of solid phases, undercooling is a difficult property to anticipate without direct experimental observation. The magnitude of undercooling in select alloy compositions is qualitatively reported in Appendix B, based on experiments with solidifying mg-scale alloys in Al DSC pans [109], and in unspecified pans [114]. 5.4. Enthalpy and entropy of fusion Fig. 4. Molar ΔfusH of (a) elemental metals, and (b) congruently melting intermetallic alloys and eutectics (Appendix B). Slope of linear fits fus H = fus S × T result in fus SBCC = 0.91R , fus SHCP = 1.00R , fus SFCC = 1.15R , and for semiconductors and post-transition metals, fus SSC = 2.76R , where R is the ideal gas constant (8.314 J·mol−1·K−1). Lines from elemental metals and semiconductors included in part b for reference. Symbols as described in Fig. 3 caption.

Specific enthalpy of fusion, ΔfusH, is characterized for alloys using calorimetry techniques, principally DSC (Appendix B). Adiabatic calorimetry is used for high accuracy measurements of elemental solids for use as calorimetry standards [105,138,139] Molar ΔfusH is calculated from known alloy compositions. Volumetric ΔfusHsol, ΔfusHliq are included, as reported in original studies, and complete volumetric ΔfusHliq are also calculated from densities calculated as described in

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Fig. 5. Cooling power figure of merit, ηq for (a, b) low-Tfus metals, and (c, d) high-Tfus metals (Appendix C), calculated for ΔT = 10 K. Symbols for elemental BCC, FCC, and HCP metals, as well as semiconductors labelled as in Fig. 3. Fields for low-Tfus alloys (a, b), and high-Tfus alloys (c, d) as labelled. For those metals with estimated thermal conductivities, upper and lower bounds on ηq are connected by a tie line. For comparisons, fields representing other classes of PCMs are illustrated as labelled. Properties of water (empty triangle) and erythritol (filled triangle) are also illustrated.

§5.1 (Appendix B). Molar entropy of fusion, ΔfusS, are calculated as fus S = fus H /T . Specific ΔfusH of Ga alloys and Bi-In-Pb-Sn alloys are both < 100 J·g−1, significantly lower than paraffins and inorganic salt hydrates with similar melting temperatures (Fig. 3c). In contrast, the volumetric ΔfusH of Bi-In-Pb-Sn alloys are in the range of (200 to 500 J·cm−3), exceeding paraffins and comparable to inorganic salt hydrates with similar melting temperatures, while Ga alloys are in the range of (400 to 500 J·cm−3), higher than all other inorganic or organic PCMs with comparable melting temperatures (Fig. 3d). Higher melting temperature alloys, including Al-Mg-Zn alloys, Cu alloys, silicides, and binary chalcogenides span a fairly wide range of specific and volumetric ΔfusH, but are generally comparable to ranges observed in carbonates, nitrates, chlorides, and other inorganic anhydrous salts (Fig. 3c,d). Due to the low densities of Al and Mg, alloys based on these principal components have especially high specific ΔfusH (up to 600 J·g−1), which is competitive against other PCMs in the range < 600 °C. Specific and volumetric ΔfusH (Fig. 3) and molar ΔfusH (Fig. 4) are strongly dependent on Tfus, with the largest ΔfusH only available for Tfus > 500 °C. However, trends of specific and volumetric ΔfusH are complicated by the variable molar masses and molar volumes of the investigated alloys. As an example, Ga-based alloys have significantly larger specific and volumetric ΔfusH than Bi-In-Pb-Sn alloys (Fig. 3), whereas the molar ΔfusH of the two families of alloys are comparable (Fig. 4), due in part to the lesser molar mass and volume of Ga. Elemental molar ΔfusH increase linearly with temperature, following the relationship fus H = fus S × T . ΔfusS for different metals and semiconductors are indicative of a combination of contributing entropic terms: fus S = config S + vol S + rot S + mix S + elec S + , including changes in the configurational, volumetric, rotational, mixing, and

electronic degrees of freedom in the solid associated with the melting process [109,114]. Thus, metals with FCC, HCP, and BCC structures tend to have differences in config S and vol S , whereas semiconductors can have significant contributions from elec S associated with transitioning from strongly localized semiconducting solids to metallic liquids with electron density at the Fermi energy [119,120]. In alloys, these various effects combine, causing ΔfusS of alloys to represent complex combinations of multiple factors which, in general, are difficult to predict with much accuracy. As an example, it has previously been demonstrated that accurate prediction of mix S , for eutectics in the Bi-In-Pb-Sn system, resulting from interatomic mixing in a multi-component liquid, requires pre-knowledge of both the equilibrium solid solution composition of different solid phases [114], as well as the magnitude of excess entropy of mixing terms associated with residual order in the liquid [109]. Both of these aspects are generally predictable only in the case of extensive thermodynamic observations on a given system (see Fig. 5). 5.5. Thermal conductivity Thermal transport of crystalline solids is generally composed of two contributions, an electronic contribution, k elec , and a lattice vibration contribution, klat , resulting in a total thermal conductivity: k tot = k elec + klat . In liquids, mobile atoms are no longer restricted to a lattice, and rather introduce a conductivity term related to diffusive atomic or molecular conduction, k diff : k tot = k elec + kdiff [140,141]. In conductive metals, k elec tends to play the dominant role. Thus, a decrease in thermal conductivity is observed upon melting of the solid, associated with a decrease in electrical conductivity by a factor of 1.5 to 2.3 associated with an increase in the disorder of the liquid state [142]. Near the melting point, the electronic contribution of thermal

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conductivity in both liquid and solid metals and alloys are well described by the Wiedemann-Franz relationship, relating electronic thermal conductivity to electronic conductivity, :

where c1 is a scaling factor to account for those cases where alloy thermal conductivities are depressed below elemental endmembers [153]. Here, we adopt c1 = 0.5, as a conservative empirical estimate which covers the extremes of experimental observations [74,153,154]. Liquid thermal conductivities of metallic PCMs at their respective Tfus are reported in Appendix C. These bounds are observed to hold in the general case for the limited observations of thermal conductivities in liquid alloys [74,153,154]. It is clear from this review that accurate observations on thermal transport measurements do not exist for many metallic PCM systems. This systematic absence represents a major limitation for prediction of thermal responses in metallic PCM systems.

(3a)

k elec = L T

where L is the Lorentz ratio, which has a theoretical value of L0 = 2.445·10-8 W·Ω·K−2., and T is the absolute temperature. Experimentally observed values of L /L 0 are ≈ 1, and generally within 0.9 < L/ L 0 < 1.2 [140]. Ewing and co-workers introduced a generalized expression for k tot of liquid metals of the form:

k tot = A T [1

B ( T / Cp

L )]

+ C (Cp ( L ) 2/ MT )

(3b)

where M is the average atomic mass for an alloy. The first term describes the electronic contribution, the second term represents a correction factor for highly electronically conductive liquids, and the final term represents the diffusive contribution, and is proportional to the energy difference across a volume, and the number of atoms per volume, and is inversely proportional to the absolute temperature [141]. Eq. (3b) was fit to 140 metals and alloys (A = 2.61·10-8; B = 2·10-17; C = 97), resulting in an overall average deviation of 5% [141]. Thermal conductivities of liquid metals vary approximately linearly with temperature over a range Tfus toTfus + 100 K, and are tabulated as:

k iL/W·m 1·K

1

=A

B × T /K.

5.6. Cooling power figure of merit For thermal management applications, PCMs are evaluated on their capacity to either absorb heat at a constant temperature boundary condition, or to minimize a temperature excursion at an interface at a constant power boundary condition [9,32,155]. Both of these aspects require the capacity of a PCM to rapidly transfer heat away from an interface into the material. Momentarily neglecting convective processes, conductive heat transfer away from an interface favors materials which are both highly thermally conductive (which can conduct heat into the PCM), and which are highly thermally capacitive (which can store heat within some volume of PCM). Thus, for applications which involve rapid thermal transients, it is favorable for both the thermal conductivity of the liquid, kL , and for the volumetric heat of fusion, fus Hvol , to be large. In the case of planar geometries, it is possible to define a cooling power figure of merit, ηq, from the exact analytical solution to the Stefan melting problem which in the case of one-dimensional heat transfer (into a semi-infinite medium, constant temperature boundary condition), is directly proportional to the heat flux across the interface:

(4)

Values for A and B are aggregated and reported in Appendix E for alkali metals [74,118,143,144], alkaline earth metals [123,143,145], transition metals [142,143,146], post-transition metals [74,118,143,144,147,148], and for metalloids [123,142,143]. In some cases, temperature dependence is not well established (e.g., Cs, Cu), and only kL (Tfus) is reported (B = 0). In a few cases (e.g., Ba, Ca), thermal conductivities of the liquid have not been reported, and values are estimated from Eq. (3a). Finally, reliable data for both electrical and thermal conductivity of semiconducting liquids (e.g., As, P, S) are not available, and thus are not reported. Thermal conductivities of liquid metallic elements at their respective Tfus range from (8 to 30) W·m−1·K−1 for high atomic mass metalloids (Hg, Pb, Bi, Sn, Sb) to (100 to 175) W·m−1·K−1 for highly electrically conductive metals (Al, Cu, Ag, Au). Thus, metallic PCMs have thermal conductivities nearly 1 to 2 orders of magnitude greater than liquid salt hydrate PCMs (≈0.5 W·m−1·K−1) and nearly 1 to 3 orders of magnitude greater than liquid paraffins (≈0.2 W·m−1·K−1) [29,149,150]. Highly conductive elements (kL (Tfus) > 20 W·m−1·K−1) tend to express metallic behavior, where kL decreases with temperature (B > 0), whereas poorly conductive elements (e.g., Bi, Ga, Pb) express semiconducting behavior, where kL increases with temperature (B < 0, Appendix E). Unlike density calculations, simple linear mixing relationships relating an alloy thermal conductivity to the thermal conductivity of its constituent elemental components do not hold, due to the non-linear contribution of alloying elements to modifying carrier concentration densities, as well as mean free path in the liquid state. As in the solid state, observations of thermal conductivities of liquid alloys generally show thermal conductivities depressed below weighted rule-of-mixtures assumptions, calculated on the basis of thermal conductivities of pure end-member elemental liquids [151–153]. For the purpose of establishing approximate liquid thermal conductivities for those compositions which have not previously been measured, we have established approximations for upper (UB) and lower (LB) bounds as follows:

kL,UB =

i

x i ki

kL,LB = c1 × min(k i )

q =

q

=

Tw

Tfus × t

(6)

q

kL erf( l 2)

(7a)

where 2 is the solution to the transcendental for the two-region problem [32]. When the magnitude of latent heat terms are large relative to sensible heat terms (i.e., when the Stefan number, StL CpL (Tw Tfus)/ fus H is < 0.5), erf( 2) StL , and thus: fus Hvol

q

× kL

(7b)

A similar relationship is observed for approximate solutions to onedimensional melting of a slab under a constant heating power boundary condition [9], suggesting the underlying importance of this relationship in the general case (where neither boundary condition is strictly met). Recently, this concept has been extended to define an effective effusivity of a material, qeff , which incorporates a thermal capacitance term associated with sensible heating:[156] eff q

=

(

fus Hvol

+ CpL

L (T w

Tfus)) × kL

(7c)

We calculate upper and lower bounds for ηq as given by Eq. (7a), using fus Hvol for liquids (§5.4), and upper and lower bounds for kL (§5.5), and assuming a value of (Tw Tfus) = 10 K (Appendix C). Compared against other low-Tfus PCMs (salt hydrates, paraffins, inorganic salts), metal PCMs have approximately an order of magnitude higher value for q , and comparable fus Hvol (Fig. 4). This attribute is principally due to the relatively high value of kL in metallic liquids.

(5a) (5b)

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While further observations on liquid thermal conductivities are needed to refine these actual values of q , the upper and lower bounds presented here are sufficient to demonstrate the relative advantage of these compounds over other classes of PCMs. Thus, q , which is a property of PCMs for a particular boundary condition, indicates that metallic alloy PCMs will generally demonstrate greater relative cooling power compared against other classes of PCMs, regardless of boundary condition, or geometric configuration. Numerical and experimental observations of transient heat transfer under different geometries and boundary conditions are discussed in §6.

the PCM cavity perpendicular to the applied heat source [159]. In thermal transport problems involving a phase change, the product of the Fourier number and the Stefan number (Fo·St) serves as a dimensionless time as it accounts for both transient heat conduction and latent heat due to melting [159]. This product represents the ratio of heat conduction to heat storage through solid–liquid transformation latent heat and is defined as:[161]

= Fo·St =

6. Numerical and experimental studies of melting behavior

fus H

W

,

(9a) (9b)

where q0 is the heat flux at the wall and is the mass density in the liquid PCM. In paraffin PCMs, it has been shown that Fo·St is insufficient to capture geometry effects that dictate convective heat transfer [158,159]. Thus, non-dimensional time is scaled by the Rayleigh number (Ra, discussed below) as a means to generalize thermal transfer in systems where convection is important [159]. In contrast, melt fraction in metallic PCM systems does not appear to scale with Ra to the same extent [161], due to the fact that conductive heat transfer is comparatively large with respect to convection in metallic PCMs. Fluid flow in free convection problems originates due to some thermal instability indicated by the physical separation of hot and cold fluids resulting in the uneven PCM melt profiles. The Rayleigh number, Ra, relates buoyancy and viscous forces to thermal and physical diffusivities in a fluid and can be used to predict whether flow will be laminar or turbulent and ultimately the effectiveness of a proposed PCM to transfer and store heat energy. Ra is defined as the product of the Grashof number, Gr, and the Prandtl number, Pr [160]:

6.1. Melting physics in phase change material systems PCMs for thermal management applications are typically encased in a sealed cavity and are positioned in close proximity to some thermal source, i.e. a constant heat flux or temperature boundary [157]. As the PCM begins to melt, a flow pattern develops dictated by convection and buoyancy forces. How quickly the PCM system stores thermal energy in the un-melted PCM is strongly dependent on how evenly the heat is spread by the liquid PCM. Furthermore, as the solid–liquid interface moves away from the heated boundary, it is expected that natural convection plays a larger role in net heat transfer from the boundary at higher melt fractions. It is important to note that convection will generally increase thermal transport from a heated boundary into a PCM. Furthermore, while convective heat transfer is relatively important in non-metallic PCMs [158,159], conductive heat transfer in metallic PCMs is orders of magnitude larger than that convective heat transfer in these systems (particularly for smaller volumes and at lower heat fluxes), causing convection to play a relatively less important role in these systems.

(10)

Ra = Gr·Pr

In the above equation, Gr defines the ratio of buoyancy to viscous forces of a flowing PCM and is defined as [160]:

Gr =

Gr =

6.2. Dimensionless analysis of phase change material systems

T 2W 3 , or µ2

g

g q0

2W

(11a)

4

(11b)

kµ2

where g is gravitational acceleration, is the volume expansivity of a liquid PCM (see discussion related to Eq. (1)), and μ is dynamic viscosity. Pr is a temperature dependent intrinsic material property defined by the ratio of momentum diffusivity ( µ ) and thermal diffusivities ( k )

Typically, dimensional analysis is employed to generalize the melt behavior in a PCM system, thereby allowing accurate predictions of heat and mass transfer between dissimilar PCM thermophysical properties and scaling relationships across different power densities. Successful dimensional analysis results in a convergence of thermal response in different systems with dissimilar boundary conditions against a non-dimensional form of time. Below, we qualitatively discuss a few physical behaviors of PCM systems and explain why each of these dimensionless parameters play a pivotal role in understanding the thermal transfer behavior of engineered PCM systems. The Fourier number (Fo) generally serves as a dimensionless time for heat conduction problems in a single-phase system (i.e., with no phase change present). Fo represents the ratio of heat conduction rate, T T kA W , to the rate of thermal energy storage, VCp t , in a medium:[160]

t W2

q0 t

= Fo·St =

PCM thermophysical properties and heat absorber geometry influence the critical dimensionless parameters used to generalize a PCM system’s heat absorption efficiency. In this section, we describe observations on melting in metallic and non-metallic PCM systems, and in particular, the role dimensionless parameters play on describing convective heat transfer.

Fo =

t Cp T , or W 2 fus H

Cp

in a liquid:

Pr =

Cp µ

(12)

k

Together, Pr and Gr dictate the melt profile geometry (through free convection) that develops in the melted PCM. Dimensionless heat transfer across solid–liquid boundaries is qualitatively described using the Nusselt number, Nu, where Nu is defined as the ratio between the rate of convective heat transfer to conductive heat transfer across a solid–liquid interface [161].

Nu =

(8)

q

convection

q

conduction

=

h T hW = k T /W k

(13a)

Nu serves as an indication of the enhancement of heat transfer by q convection. Alternatively, substituting h = T from Newton’s law of cooling, Nu can be defined as [158]:

where is thermal diffusivity, t is time, and W is a characteristic length. In studies of melting from a vertical wall, where convection plays a large role on interface geometry, W is typically defined as the width of

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Fig. 6. Melt profiles, temperature gradients, and melt velocity profiles for a) eicosane, and b) gallium at different melt fractions (0.3, 0.6, 0.9) resulting from melting at a constant temperature wall boundary condition with a wall over-temperature of 15 K [161]. Figure has been duplicated with the permission of the copyright holder.

Nu =

Wq k T

[144]. Non-uniform melt fronts in non-metallic PCM systems, as depicted in Fig. 6, are responsible for trapped vortices and locally constricted PCM liquid flow that leads to unprecedented fluctuations in Nu at the heated boundary. Liquid fractions, temperature gradients, and PCM flow patterns for non-metallic and metallic PCM filled cavities are depicted in Fig. 6 to clearly show the melt physics in vertical wallconstant flux experiments [161]. In non-metallic PCM systems (particularly paraffins), Nu is comparatively large during melting for a given heat flux, relative to metallic PCMs [162,163]. As an example, eicosane encased in an enclosure of 5 mm wide and 20 mm tall subjected to a constant vertical wall temperature of 25 K above Tfus (≈309 K) exhibited a Nu of approximately 12 at Fo·St = 0.01 [161]. Conversely, gallium, in the same enclosure exposed to a vertical wall temperature 25 K above Tfus (≈302 K) exhibited a Nu of approximately 9 at the onset of melting [161]. As Fo·St (dimensionless time) progressed, Nu for gallium rapidly decreased to nearly 2 at Fo·St = 0.11, yet for eicosane, Nu was found to be greater than 4. Nu decreases as the melted PCM widens and increases when the geometry of the liquid favors convection. Melt physics are depicted in Fig. 6 for the aforementioned study at melt fractions (or Fo·St ) of 0.3, 0.6, and 0.9 clearly showing flow velocity and temperature gradients as a function of melt fraction and melt front geometry.

(13b)

where T is the temperature difference across the boundary. In PCM studies with a constant flux boundary condition, all the variables in Eq. (13b) remain independent of time except for T . Over time, T will increase as a consequence of a higher thermal resistance to heat flow in the PCM as the solid–liquid interface moves further away from the heated boundary. In contrast, the heat flux, as driven by the thermal gradient, is expected to decrease in time in PCM systems exposed to constant wall temperature. In both cases, Nu is expected to decrease in time as the melt front propagates and the system reaches a thermal equilibrium, and the rate at which this decrease occurs depends on the thermophysical properties of the PCM. 6.3. Characteristics of Nusselt number in metallic phase change materials Nu is the ratio of convective to conductive heat transfer across a solid-liquid interface. At the initiation of melting, Nu is expected to be high in both metallic and non-metallic PCM systems as a result of the small liquid layer experiencing high velocity convective flow with buoyancy forces in the narrow liquid boundary. As time progresses, Nu decreases, indicating convection plays a lower role on heat transfer at the interface due to the widening of a liquid layer between the heated boundary and the remaining solid PCM. It has been shown that for paraffin (eicosane), Nu may increase and decrease with Fo·St > 0 depending on flow geometry, whereas in metallic systems Nu exhibits nearly an exponential decay with dimensionless time [161] due primarily to the much larger thermal conductivity in the metallic PCM

6.4. Role of convection in metallic phase change materials Highly buoyant and turbulent flow within a PCM cavity tends to unevenly transfer heat to any remaining un-melted PCM, thus resulting in a non-uniform melt front, and delaying bulk energy transfer relative to the laminar flow case. Increases in Ra tend to result in uneven melt

12

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P.J. Shamberger and N.M. Bruno

Fig. 7. The temperature rise (T Tm ) versus = Fo ·St under constant flux boundary conditions for 49Bi-21In-18Pb-12Sn [167] (a) and versus = Fo ·St for pure gallium at different constant flux boundaries computed from Ref. [161] (b). In (a), the applied heat flux was reported to be 1.61 W·cm−2, 4.84 W·cm−2, and 11.29 W·cm−2, respectively, for the heater dimensions [167]. Dimensional analysis was performed by computing with corrected heat fluxes using the PCM enclosure surface area rather than the heater area, resulting in heat fluxes of 0.083 W·cm−2, 0.25 W·cm−2, and 0.58 W·cm−2 that correspond to for complete melting of 1.14, 1.6, and 1.07, respectively. T Tm was computed using the quasi-steady melting approximation (assuming a pure conduction model) in (b) for 0 1 as represented by data points, but was omitted in (a) due to the somewhat more complicated geometry considered in that study.

profiles along a vertical wall, although the Ra number is generally not directly reported [164–166]. The common feature of increased Ra in metallic PCMs is greater circular velocity profiles [161], a higher melt fraction in the PCM at the upper end of the enclosure due to buoyancy forces and greater overall surface temperature at the flux boundary throughout the duration of melting. For identical geometries, Ra is significantly greater in paraffin PCMs than in metallic PCMs. As an example, for a PCM in an enclosure 20 mm tall × 5 mm wide, subjected to 10.0 W·cm−2 along a vertical wall (width represents direction perpendicular to the heated wall), Ra for eicosane was computed to be 8.9 × 106 whereas for gallium, Ra was reported to be 547 [161]. This is apparently the result of a significantly lower Pr number in gallium driven by its high thermal conductivity, and lower Gr number, i.e. low volume expansivity and high dynamic viscosity within the same enclosure. Both PCMs exhibited laminar flow, yet the non-metallic PCM generated melt profile asymmetries due to higher circular velocity and larger buoyancy forces relative to viscous forces. In Fig. 7a and b, surface temperature profiles show linear rise with non-dimensional time, as predicted by purely conductive heat transfer across a wide range of heat fluxes and a three order of magnitude range of Ra. Surface temperature rise was measured while melting 49Bi-21In18Pb-12Sn in a 60 mm long × 20 mm wide × 10 mm tall enclosure (0.083 to 0.58 W·cm−2; Ra 1719 to 12,043) [167] from the base (height represents direction perpendicular to the heated wall), and through numerical simulations in gallium in a 20 mm tall × 5 mm wide enclosure (3.0 to 10.0 W·cm−2; Ra 164 to 547) along a vertical wall (width represents direction perpendicular to the heated wall) [161]. While it is expected that laminar flow existed within both studies, increasing Ra would tend to promote higher velocity profiles and more asymmetric melting profile. Despite this, the temperature rise across the melt transition from Tfus was linear and proportional to q'', as anticipated from a pure conduction melting model overlaid on digitized data in Fig. 7b. Pure conduction behavior was numerically predicted using a quasi-steady state one-dimensional heat transfer model that neglects convective effects, i.e. T (t ) = (q0 ) 2t /(kl LV ) , where LV is volumetric heat of fusion in units of J·m−3 of the PCM. As shown in Fig. 7b, Ga exhibits minimal convective heat transfer with Ra below 547 as the

data is nearly identical to the pure conduction model. At Ra of 547, convection plays a small role in temperature pinning for greater than 0.8. Thus, over the regime typically investigated experimentally, melting behavior of metallic PCMs is predicted fairly accurately using simple conduction models, and neglecting convection. However, this does not preclude an important role for convection in larger container geometries and at larger heat fluxes. 6.5. Prandtl and Rayleigh numbers in metallic phase change materials The Ra and Pr numbers were determined for select metallic PCMs using Eqs. (10)–(12), and plotted in Fig. 8, adopting a uniform characteristic length of 5 mm and a constant heat flux of q'' = 3.0 W·cm−2. The volumetric thermal expansion coefficient ( ) for metals, i.e. those employed for computing Gr, were determined using Vegard’s Law for for non-metallic PCMs was compounds with data in Appendix D. approximated as 0.001 for the data in Fig. 8 [159]. Dynamic viscosity ( µ ) was approximated to be 1.75 g·m−1·s−1 for Ga alloys [161], and that of the elemental metal with the highest molar fraction in other compounds [168]. Dynamic viscosity for non-metals was computed using an approximation [169],

µ /g·m 1·s

1

= exp A +

B T /K

(14)

where A = 4.25 and B = 1790 [159,161]. Molar fractions and compound thermal-fluid properties for computing Pr and Ra can be found in Appendix F. As described previously, Pr is a material property that does not depend on the boundary conditions of the PCM system, but Ra depends also on Gr, which includes the characteristic length of the PCM channel, and heat flux or wall temperature. Interestingly, the selected metallic PCMs cover a large range of Ra between 100 to over 10,000 around their melting points. Bismuth alloys exhibit near the maximum Ra in their subclass of metallic compounds which can be attributed to their relatively high mass densities and low dynamic viscosity and thermal conductivities.

13

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P.J. Shamberger and N.M. Bruno

Fig. 8. (a) Rayleigh number for various metallic PCMs as a function of melting point, Tfus, and (b) corresponding Pr number. Rayleigh numbers were computed with Eqs. (10)–(13), using a characteristic length of 5 mm, a constant wall flux of 3.0 W·cm−2. Volume expansivity was computed using Vegard’s Law, described in the text and the temperature factor, B, for the given compounds in Appendix D. Liquid metal compound viscosities were approximated as that of the element with the largest molar fraction using data provided in Ref. [168]. Error bars indicate the possible range for a given compound from the upper and lower bound thermal conductivity in Appendix C. Non-metal Tfus, k, and ρ were found in Ref. [21] and viscosities were computed using an approximation described in Refs. [159,161,169]. Volume expansivities of non-metals were approximated to be 0.001 m3·K−1 [159].

Fig. 8b contains Pr for paraffins, fatty acids, hydrated salts, and metals [21]. Metals have been reported to exhibit Pr 0.1 which aligns with our computed values [72]. Viscosities and volume expansivities were approximated as explained, above, for computing Pr in metallic and non-metallic PCMs. Dynamic viscosities were computed for nonmetallic PCMs as described, above, at Tfus. Zn and Cu-based alloys exhibited some of the smallest Pr as also evidenced by their lower Ra numbers. In Bi-based compounds, although Pr is very low, Ra is among the highest in the metal compounds listed, here. This demonstrates the importance and need for further studies in characterizing the viscosity and volumetric thermal expansion coefficients in metallic PCM compounds.

dramatically non-uniform melt fronts determined largely by buoyancydriven convection along the heated surface. It should be noted that these observations hold for low to moderate heat fluxes or boundary super-heating temperatures (q" < 20 W·cm−2, or ΔT < 15 K). Under larger thermal loads, it is reasonable to expect convective heat transfer will play a larger role within metal phase change materials. While there is much known about metallic phase change material systems, we identify three key opportunities for short-term advancement in this field. First, thermal transport properties are largely absent for many of the systems of interest, in both liquid and solid states. While we present an approximation that enables investigators to bracket a likely range of thermal conductivity, these numbers are exceedingly course. For systems of interest, it is important to experimentally measure thermal conductivity, due to the lack of quantitative models in multi-component liquid and solid phases. Second, while some of the potential chemical space of low melting point alloys has been investigated, many ternary, quaternary, or higher order eutectic systems remain unexplored. Particularly, systems based on high thermal conductivity base metals (e.g., Cu, Al, Mg) bear further scrutiny. Finally, post-transition metal intermetallics offer an approach to leverage both configurational entropy and electronic entropy effects at the melting transformation. This class of materials offers a promising approach to identify new metallic material systems which have even higher volumetric enthalpies of fusion.

7. Conclusions and outlook Metallic phase change materials offer an approach to rapidly transport heat away from a critical device or component, thereby buffering the temperature of that device during periods of transient high power operation. These compounds are of increasing interest to both electronics packaging thermal management and solar thermal communities. Despite this interest, thermophysical properties and details of melting behavior of metallic alloys and compounds are scattered across the literature. Here, we critically review metallic phase change materials, evaluating the thermophysical properties of different chemical alloy families. Where possible, these are compared against other available thermodynamic data sets describing melting multi-component metallic systems. The objective of this review is to assess the state of knowledge of metallic phase change materials, to further our understanding of heat transfer in these systems, and to identify promising opportunities for further development. Effective phase change material systems for thermal energy storage evenly transfer the heat from a hot boundary to the un-melted phase change material within a cavity. The intrinsic high thermal conductivity of metallic phase change material systems results in relatively uniform melting along the melt front, and heat transfer that can be well described by simple conduction models, largely neglecting convection. This sharply contrasts lower thermal conductivity phase change material phases (e.g., paraffins), where low thermal conductivity results in

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors would like to acknowledge support of this work from the Office of Naval Research (ONR) grant N00014-17-1-2802. We also acknowledge Dr. Bamdad Lessani for fruitful discussions on heat transfer and dimensional analysis.

14

15

Ga Alloys 67Ga-20.5In-12.5Zn 78.6Ga-21.4In

Binary Semiconductors As2S3 As2Te3 As2Se3 InSb Sb2S3 B2S3 GeS GeSe InS GaSb GeTe Bi2S3 SnTe HgS Ag2S GeS2 SnS InAs

Elements Hg Cs Ga Rb K Na S In Li Se Sn Bi Tl Cd Pb Zn Te P Sb Mg Al Ba Sr As Ca Ge Ag Au Cu

PCM

a

a

a

a

a

a

a

a

a

a

Alloy # b

Eutectic Comp. c

78.2Ga-21.8In

Arsenic Sulfide Arsenic Telluride Arsenic Selenide Indium Antimonide Antimony Sulfide Boron Sulfide Germanium Sulfide Germanium Selenide Indium Sulfide Gallium Antimonide Germanium Telluride Bismuth Sulfide Tin Telluride Mercury Sulfide Silver Sulfide Germanium Sulfide Tin Sulfide Indium Arsenide

Mercury Cesium Gallium Rubidium Potassium Sodium Sulfur Indium Lithium Selenium Tin Bismuth Thallium Cadmium Lead Zinc Tellurium Phosphorous Antimony Magnesium Aluminum Barium Strontium Arsenic Calcium Germanium Silver Gold Copper

Name

E e

congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr.

congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr. congr.

Type d

⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺

⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ As2S3 As2Te3 As2Se3 InSb Sb2S3 B2S3 GeS GeSe InS GaSb GeTe Bi2S3 SnTe HgS Ag2S GeS2 SnS InAs

Hg Cs Ga Rb K Na S In Li Se Sn Bi Tl Cd Pb Zn Te P Sb Mg Al Ba Sr As Ca Ge Ag Au Cu

L ⟺ Ga + In + Zn L ⟺ Ga + In

L L L L L L L L L L L L L L L L L L

L L L L L L L L L L L L L L L L L L L L L L L L L L L L L

Reaction

Appendix A. Composition, common alloy name, previously assessed composition, reaction of phases of interest.

75.15 76.14

49.21 106.53 77.34 118.29 67.94 23.56 52.35 75.80 73.44 95.74 100.12 102.83 123.16 116.33 82.60 45.59 75.39 94.87

200.59 132.91 69.72 85.47 39.10 22.99 32.07 114.82 6.94 78.96 118.71 208.98 204.38 112.41 207.20 65.38 127.60 30.97 121.76 24.31 26.98 137.33 87.62 74.92 40.08 72.64 107.87 196.97 63.55

M.W. /mol atoms g·mol-1

6.423 6.316

2.850 4.375 3.444 6.213 5.746 4.048 6.039 5.168 5.103 1.988 3.178 5.874

2.862 5.845 4.368 6.635 3.184

13.686 1.837 6.077 1.463 0.829 0.927 1.807 7.022 0.515 5.998 6.979 10.028 11.232 8.008 10.656 6.559 5.820 1.263 6.464 1.589 2.377 3.257 2.258 5.220 2.350 5.485 9.294 17.400 7.997

ρliq calc. g·cm-3

10.7 15.7

312 375 377 524 550 563 658 675 692 712 724 777 806 820 836 840 881 942

-38.86 28.4 29.765 39.5 63.2 97.83 115.21 156.599 180.54 220.81 231.928 271.416 304.01 321.079 327.43 419.527 449.52 596.85 630.638 649.85 660.3 726.85 776.85 817.01 841.85 938.26 961.79 1064.19 1084.63

Tfus reported C

o

15.3

Tfus valid.e o C

10] 10] 10] 10] 10], 10] 10] 10] 10] 10] 10] 10], 10] 10] 10], 10] 10], 10]

10], 10], 10], 10], 10], 10], 10], 10], 10], 10] 10], 10], 10] 10] 10], 10], 10] 10], 10] 10], 10], 10], 10], 10] 10], 10] 10], 10], 10],

[Ga 00] [Ga 00]

[Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li

[Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li

Refs

98] 98] 98], [SAD 08], [Pr 90] 98] 98] 98] 98] 98], [SAD 08], [Pr 90] 98]

98] 98], [SAD 08] 98] 98]

[Ja 88]

[Ja 88]

[Ja 88]

[Ja 88]

[SAD 08] [SAD 08] [Ch 98]

[Ch 98]

[Ch [Ch [Ch [Ch

[Ch 98]

[Ch 98], [SAD 08] [Ch 98], [SAD 08]

[Ch 98], [SAD 08], [Pr 90] [SAD 08]

[Ch [Ch [Ch [Ch [Ch [Ch [Ch [Ch [Ch

P.J. Shamberger and N.M. Bruno

Applied Energy 258 (2020) 113955

176

Cerrobase Cerrotru

Cerroshield

Wood's Met., Cerrobend

16 95Zn-5Al 95Zn-5Al 65.4Al-34.6Mg 65.4Al-34.6Mg -

53.1Zn-46.9Mg 53.1Zn-46.9Mg

66.7In-33.3Bi 53.6Bi-30.3In-16.1Sn In2Bi 51.6Bi-32.6Pb-15.8Sn 51.6Bi-32.6Pb-15.8Sn 67.4Bi-32.6In InBi 50.9In-49.1Sn 74.6In-25.4Cd 56Bi-44Pb 57Bi-43Sn 61.9Sn-38.1Pb 91.2Sn-8.8Zn

Bi + InBi + Pb0.7Bi0.3 In2Bi + εIn0.9Bi0.1 Bi + InBi + γIn0.2Sn0.8 In2Bi Bi + εPb + βSn Bi + εPb + βSn Bi + InBi InBi βIn0.75Sn0.25 + γIn0.2Sn0.8 Cd3In + αCd0.1In0.9 Bi + εPb0.7Bi0.3 Bi + βSn Pb + βSn Sn + Zn

L L L L L L L L L L L

⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺

Al + Zn + θMg2Zn11 Al + Zn Al + Zn Mg + τCaMg2 + βCaMg2Zn Al + τMg3Zn3Al2 + βMg2Al3 Al + βAl3Mg2 Al + βAl3Mg2 Mg2Cu + Mg + Mg(Cu,Zn)2 Mg + Mg2Cu + CaMg2 Al + Al2Cu + Al2CuMg Al + Al2Cu + Al2CuMg

L ⟺ Mg + τMg3Zn3Al2 + εMgZn L ⟺ MgZn + Mg7Zn4 L ⟺ MgZn + Mg7Zn4

⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺

E E E E E E E E E E E E e e E E E E e e E E e e E E E E

a

a

a

a

a

a

a

⟺ In2Bi + βIn0.75Sn0.25 + γIn0.2Sn0.8

⟺ Ga + Zn

⟺ Ga + βSn

⟺ Ga + In ⟺ Ga + Sn + Zn

Zn/Al/Mg Alloys Mg-Sn-Li (not spec.) Mg-Zn-Sn (not spec.) Mg-Sn-Cu (not spec.) Mg-Al-Sn (not spec.) Zn-Al-Sn (not spec.) Zn-Cu-Sn (not spec.) Mg-Zn-Cu (not spec.) Mg-Zn-Cu (not spec.) Mg-Zn-Ni (not spec.) Mg-Zn-Al (not spec.) Mg-Zn-Li (not spec.) 49Mg-47Zn-4Al 52Zn-48Mg 53.7Zn-46.3Mg Mg-Zn-Zr (not spec.) Mg-Zn-C (not spec.) Mg-Zn-Ir (not spec.) 93.9Zn-3.7Al-2.4Mg 95Zn-5Al 96Zn-4Al 55Mg-28Ca-17Zn 59.0Al-35.0Mg-6.0Zn 64.9Al-35.1Mg 65.4Al-34.7Mg 60Mg-25Cu-15Zn 60Mg-25Cu-15Ca 55Al-33Cu-12Mg 60.8Al-33.2Cu-6Mg

L L L L

L ⟺ AuIn L ⟺ AuIn2

Field's Met.

E E E E E

e E E e E e

congr. congr.

158

a

a

162 27 38/203 39 53 1E 253 255 281 106 201

117 136 19

a

a

51.4In-17.2Sn-31.4Bi -

78.2Ga-21.8In 86.5Ga-13.5Sn 96.2Ga-3.8Zn

E e E/U congr. E E e congr. e e e e e e

60

L L L L L L L L L L L L L L L

a

a

Bi/In/Pb/Sn Alloys 44.7Bi-22.6Pb-19.1In-8.3Sn-5.3Cd 49Bi-21In-18Pb-12Sn 51.0In-16.5Sn-32.5Bi 51In-16Cd-33Bi 50.0Bi-26.7Pb-13.3Sn-10.0Cd 50.0Bi-26.7Pb-13.3Sn-10.0Cd 52Bi-26Pb-22In 66.3In-33.7Bi 54Bi-29.7In-16.3Sn In2Bi 52.5Bi-32Pb-15.5Sn 52Bi-30Pb-18Sn 67Bi-33In InBi 52In-48Sn 74In-26Cd 55.5Bi-44.5Pb 58Bi-42Sn 63Sn-37Pb 91Sn-9Zn Au Alloys AuIn AuIn2

75.5Ga-24.5In 82Ga-12Sn-6Zn 74Ga-22Sn-4Cd 86.5Ga-13.5Sn 93Ga-5Zn-2Cd 96.5Ga-3.5Zn

59.78 61.04 61.86 31.04 26.89 25.98 25.99 32.35 30.90 32.76 33.08

34.69 36.10 36.68

155.92 142.21

164.91 165.20 135.37 134.33 175.71 175.71 176.70 135.37 152.82 146.20 186.49 183.40 164.47 161.90 116.65 114.18 208.18 158.39 140.99 110.59

77.15 73.05 77.99 73.84 70.02 69.56

5.862 6.085 6.181 1.963 2.174 2.100 2.104 2.432 2.121 2.983 3.091

2.654 2.761 2.821

11.414 9.621

9.523 7.938 8.535 8.331 9.782 9.667 8.945 8.858 7.053 7.341 10.511 8.605 8.072 7.057

9.233 9.079 7.913 8.166 9.697

6.349 6.267 6.398 6.230 6.155 6.108

134.4 191.8 200.6 202.9 214.9 215 285 306 328.9 338 339.9 340 340 340 340.7 340.9 341.0 344 382 381 400 443 450.9 450.9 451.9 453 505.9 506

495.4 540.7

47 58 60 61 70 70 70 72 81 89.9 95 96 109 110.6 118 123 125 138 183 199

16 18.8 20.2 20.55 24.6 25

381 381 450 450 -

340.9 340.9

495.4 540.7

55.3 72.7 80.6 89.5 98 98 109.7 110 120 127.7 127.6 139 183 198.5

15.3 20.5 24.67

[Sh 17] [Wh 92] [Sh 17], [So 11] [Sh 17] [Sh 17]

[Sh 17] [Sh 17] [Sh 17]

[Sh 17] [Sh 17]

[Sh 17]

[Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ri 15] [Bi 80a], [Fa 85] [Ga 00] [Ni 16] [Ni 16] [Ni 16] [Ri 15] [SAD 08] [Ga 00] [Bi 80b], [Fa 85] [Bi 80b], [Fa 85] [Bi 80a], [Fa 85] [Ga 00] [Bi 80b], [Fa 85] [Bi 80b], [Fa 85] [Bi 80a], [Fa 85] [Ga 00]

[Wh 92] [Wh 92]

[SAD 08] [SAD 08] [SAD 08], [Ha 71] [SAD 08] [Ga 00] [Ha 71] [SAD 08], [SAD 08], [Sh 17] [SAD 08], [SAD 08], [SAD 08], [Sh 17] [SAD 08], [SAD 08], [SAD 08], [SAD 08], [SAD 08], [SAD 08]

[SAD 08] [Ga 00] [Ga 00] [Ga 00] [Ga 00] [Ga 00]

P.J. Shamberger and N.M. Bruno

Applied Energy 258 (2020) 113955

17

56.6Si-43.4Mg

Si Alloys 49Si-30Mg-21Ca 56.5Si-43.5Mg E/U e

E/U e E E E e E

E e E E E E E e e E E congr. E e e congr. E congr. E Al + CuAl2 + Si Al + CuAl2 + Si Al + CuAl2 + Si Al + CuAl2 + AlSb Al + CuAl2 Al + CuAl2 Al + Mg2Si + Si Al + Mg2Si + Si Mg2Cu Al + AlSb + Si Al + Si Al + Si MgZn2 βCu0.5Zn0.5 + γCu5Zn8 + Mg(Cu,Zn)2 CaMg2 Mg + Mg2Si + MgZn2

⟺ Si + Cu3Si + Cu0.83Si0.17 ⟺ MgCu2 + Cu3Si + Mg6Cu16Si7 ⟺ Si + Cu19Si6 (η)

⟺ Cu + Cu3P

⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺ ⟺

⟺ Mg + CaMg2

L ⟺ CaSi + CaMgSi + Ca7Mg7.5Si14 L ⟺ Si + Mg2Si

L L L L -

L L L L L L L L L L L L L L L L L

28.55 26.30

1.968 2.033

3.776 5.885 4.808 6.910 3.716 5.888 4.988

3.323 3.257 3.186 3.179 2.392 2.401 3.068 2.729 2.443 2.444 4.418 6.003 1.560 2.168

32.69 34.10 33.38 33.32 26.95 26.98 37.39 31.07 27.11 27.11 51.70 58.67 29.56 28.44 37.70 58.05 55.62 58.67 39.34 50.73 53.24

3.036 1.641 2.741 3.024

32.15 25.94 31.45 31.91

865 946

571 715 720 765 770 803 840

545 547.9 547.9 555 559.9 568 575 578.9 578.9 588 705 716.9 800

507 516.9 520 525 523.9

945.6

714 802 -

517 548.2 548.2 568 577 577 590 711 -

[Fa 85] [Bi 80c] [Fa 85] [Fa 85] [Fa 85] [Fa 85] [Bi 80b], [Fa 85] [Bi 80a], [Fa 85]

[Ga 00] [Bi 80b], [Bi 80b], [Bi 80b], [Bi 80b], [Bi 80b], [Bi 80b],

[Ga 00] [Bi 80a], [Bi 80b], [Fa 85] [Bi 80b], [Fa 85] [Ga 00] [Bi 80b] [Bi 80b], [Fa 85] [Ga 00] [Bi 80a], [Bi 80c], [Fa 85] [Ga 00] [Ga 00] [Bi 80a], [Bi 80c], [Fa 85] [Bi 80b], [Fa 85] [Ga 00] [Ga 00], [Wa 15] [Bi 80a], [Bi 80c], [Fa 85] [Bi 80a], [Fa 85] [Bi 80b], [Fa 85] [Bi 80a] [Bi 80b], [Fa 85]

b

RoHS non-compliant, or Tl/As containing. Indalloy/Bolton/Cerro alloy # c Eutectic composition (from ASM phase diagram database) d Type of melting reaction: congr. = congruent melting, e = binary eutectic, E = higher order eutectic, E/U = eutectic or potentially univariant melting reaction. e Validated eutectic temperature from compiled ASM phase diagram database References [Bi 80a] Birchenall, C. E.; Riechman, A. F., Heat Storage in Eutectic Alloys. Metall. Trans. A 1980, 11, 1415–1420. [Bi 80b] Birchenall, C. E.; Güceri, S. I.; Farkas, D.; Labdon, M. B.; Nagaswami, N.; Pregger, B. Heat Storage in Alloy Transformations; University of Delaware: Newark, DE, 1980; p 163. [Bi 80c] Birchenall, C. E.; Harrison, A. J.; Balart, S. N., Determination of Density Changes During Melting by X-Ray Absorption. Metallurgical and Materials Transactions A 1980, 11, 1213–1218. [Ch 98] Chase, M., Nist-Janaf Thermochemical Tables, Fourth Edition. J. Phys. Chem. Ref. Data 1998, Monograph No. 9. [Fa 85] Farkas, D.; Birchenall, C., New Eutectic Alloys and Their Heats of Transformation. Metallurgical Transactions A 1985, 16, 323–328. [Ga 00] Gasanaliev, A. M.; Gamataeva, B. Y., Heat-Accumulating Properties of Melts. Russian Chemical Reviews 2000, 69, 179–186. [Ha 71] Hale, D.; Hoover, M.; ONeill, M. Phase Change Materials Handbook; Huntsville, AL, 1971; p 232. [Ja 88] Janz, G. J., Thermodynamic and Transport Properties for Molten Salts: Correlation Equations for Critically Evaluated Density, Surface Tension, Electrical Conductance, and Viscosity. Journal of Physical and Chemical Reference Data 1988, 17. [Li 10] Lide, D. R., Crc Handbook of Chemistry and Physics, 90th Ed. ed.; CRC Press: Boca Raton, FL, 2010. [Ni 16] Nieto-Maestre, J.; Iparraguirre-Torres, I.; Velasco, Z. A.; Kaltzakorta, I.; Zubieta, M. M. In Novel Metallic Alloys as Phase Change Materials for Heat Storage in Direct Steam Generation Applications, AIP Conference Proceedings, AIP Publishing: 2016; p 050032. [Pr 90] Preston-Thomas, H., The International Temperature Scale of 1990 (Its-90). Metrologia 1990, 27, 3. [Ri 15] Risueño, E.; Faik, A.; Rodríguez-Aseguinolaza, J.; Blanco-Rodríguez, P.; Gil, A.; Tello, M.; D’Aguanno, B., Mg-Zn-Al Eutectic Alloys as Phase Change Material for Latent Heat Thermal Energy Storage. Energy Procedia 2015, 69, 1006–1013. [SAD 08] Solder Alloy Directory; 97,720 (A4) R3; Indium Corporation: Clinton, NY, 2008; p 15. [Sh 17] Shamberger, P. J.; Mizuno, Y.; Talapatra, A. A., Mixing and Electronic Entropy Contributions to Thermal Energy Storage in Low Melting Point Alloys. Journal of Applied Physics 2017, 122, 025105. [So 11] Sobolev, V. Database of Thermophysical Properties of Liquid Metal Coolants for Gen-Iv; SCK•CEN-BLG-1069; Belgian Nuclear Research Centre: Boeretang, Belgium, 2011. [Wa 15] Wang, Z.; Wang, H.; Li, X.; Wang, D.; Zhang, Q.; Chen, G.; Ren, Z., Aluminum and Silicon Based Phase Change Materials for High Capacity Thermal Energy Storage. Applied Thermal Engineering 2015, 89, 204–208. [Wh 92] White, C. E.; Okamoto, H., Phase Diagrams of Indium Alloys and Their Engineering Applications. Indium Corp. of America: Utica, NY, 1992; Vol. 8.

a

91.7Cu-8.3P 84.0Cu-16.0Si -

188

83.1Mg-16.9Ca 67.3Al-32.7Cu 67.3Al-32.7Cu Mg2Cu 87.4Al-12.6Si 87.4Al-12.6Si MgZn2 CaMg2 -

Cu Alloys 49.1Cu-46.3Al-4.6Si 91Cu-9P 69Cu-17Zn-14P 74Cu-19Zn-7Si 56Cu-27Si-17Mg 80Cu-20Si 83Cu-10P-7Si

64.6Al-28Cu-5.2Si-2.2Mg 84Mg-16Ca 54Al-22Cu-18Mg-6Zn 68.5Al-26.5Cu-5Si 68.5Al-26.5Cu-5Si 65Al-30Cu-5Si 64.3Al-34Cu-1.7Sb 66.7Al-33.3Cu 66.9Al-33.1Cu 83.1Al-11.7Si-5.2Mg 82.4Al-13.1Si-4.6Mg Mg2Cu * 86.4Al-9.4Si-4.2Sb 87.8Al-12.2Si 87.6Al-12.4Si MgZn2 * 49Zn-45Cu-6Mg CaMg2 * 47Mg-38Si-15Zn

P.J. Shamberger and N.M. Bruno

Applied Energy 258 (2020) 113955

18

Ga Alloys 67Ga-20.5In-12.5Zn 78.6Ga-21.4In

Binary Semiconductors As2S3 As2Te3 As2Se3 InSb Sb2S3 B2S3 GeS GeSe InS GaSb GeTe Bi2S3 SnTe HgS Ag2S GeS2 SnS InAs

Elements Hg Cs Ga Rb K Na S In Li Se Sn Bi Tl Cd Pb Zn Te P Sb Mg Al Ba Sr As Ca Ge Ag Au Cu

PCM

a

a

a

a

a

a

a

a

a

a

10.7 15.7

312 375 377 524 550 563 658 675 692 712 724 777 806 820 836 840 881 942

−38.9 28.4 29.76 39.5 63.2 97.8 115.2 156.60 180.5 220.8 231.93 271.4 304.0 321.1 327.4 419.53 449.5 596.9 630.6 649.9 660.3 726.9 776.9 817.0 841.9 938.3 961.8 1064.2 1084.6

o

reported C

Tfus

small

large large

small

ΔT

5.05 5.31

8.00 7.20 6.32 39.10 9.62 4.26 8.15 14.35 23.95 3.95 38.50 4.94 20.40 12.55 15.90 15.77 22.60 23.00

2.30 2.09 5.58 2.19 2.33 2.60 1.72 3.29 3.00 6.69 7.15 11.11 4.14 6.21 4.77 7.32 17.38 18.80 19.79 8.48 10.71 8.01 7.43 24.44 8.54 36.94 11.30 12.55 13.14

/mol atoms kJ·mol−1

67.2 69.7

162.6 67.6 81.7 330.5 141.6 180.8 155.7 189.3 326.1 41.3 384.5 48.0 165.6 107.9 192.5 345.8 299.8 242.4

11.4 15.7 80.1 25.6 59.7 113.2 53.7 28.7 432.2 84.7 60.22 53.15 20.3 55.2 23.0 112.0 136.2 607.0 162.5 348.8 397.0 58.3 84.8 326.2 213.1 508.5 104.8 63.7 206.7

J·g−1

415 432

1100 1230

1015

261

438 521

210

473

sol J·cm−3

ΔfusH

Appendix B. Temperature, relative undercooling (ΔT), enthalpy, and entropy of fusion of metallic PCMs.

1256 267

351 2056

liq J·cm−3

432 440

465 395 357 2193 451 0 444 828 1123 256 2209 194 1000 558 982 688 953 1424

157 28.8 487 37.5 49.5 105 97 201 223 508 420 533 228 442 245 735 793 767 1051 554 944 190 191 1703 501 2789 974 1109 1653

liq (calc.) J·cm−3

2.14 2.21

1.64 1.34 1.17 5.90 1.41 0.61 1.05 1.82 2.98 0.48 4.64 0.57 2.27 1.38 1.72 1.70 2.36 2.28

1.18 0.83 2.22 0.84 0.83 0.84 0.53 0.92 0.80 1.63 1.70 2.45 0.86 1.26 0.95 1.27 2.89 2.60 2.63 1.10 1.38 0.96 0.85 2.70 0.92 3.67 1.10 1.13 1.16

ΔfusS/R

10] 10] 10] 10] 10], 10] 10] 10] 10] 10] 10] 10], 10] 10] 10], 10] 10], 10] [Ga 00] [Ga 00]

[Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li

[Ja 88]

[Ja 88]

[Ja 88]

[Ja 88]

[Li 10], [Ch 98] [Li 10], [Ch 98] [SAD 08],[Li 10], [Li 10], [Ch 98] [Li 10], [Ch 98] [Li 10], [Ch 98] [Li 10], [Ch 98] [SAD 08],[Li 10], [Li 10], [Ch 98] [Li 10] [SAD 08],[Li 10], [SAD 08],[Li 10], [Li 10] [Li 10] [SAD 08],[Li 10], [SAD 08],[Li 10], [Li 10] [Li 10], [Ch 98] [Li 10] [Li 10], [Ch 98] [SAD 08],[Li 10], [Li 10], [Ch 98] [Li 10], [Ch 98] [Li 10] [Li 10], [Ch 98] [Li 10] [SAD 08],[Li 10] [SAD 08],[Li 10] [Li 10], [Ch 98]

Refs

[Ch 98]

[Ch 98], [St 99] [Ch 98], [Pr 90]

[Ch 98], [Pr 90] [Ar 04]

[Ch 98], [Pr 90], [Ar 03]

[Ch 98], [Pr 90], [Ar 02]

P.J. Shamberger and N.M. Bruno

Applied Energy 258 (2020) 113955

47.0 58.0 60.0 61.0 70.0 70.0 70.0 72.0 81.0 89.9 95.0 96.0 109.0 110.6 118.0 123.0 125.0 138.0 183.0 199.0 495.4 540.7 134.35 191.8 200.6 202.9 214.9 215 285 306 328.87 338 339.85 340 340 340 340.7 340.9 340.96 344 382.0 381.0 400 443 451 451 452 453 506 506 507

Au Alloys AuIn AuIn2

Zn/Al/Mg Alloys Mg-Sn-Li (not spec.) Mg-Zn-Sn (not spec.) Mg-Sn-Cu (not spec.) Mg-Al-Sn (not spec.) Zn-Al-Sn (not spec.) Zn-Cu-Sn (not spec.) Mg-Zn-Cu (not spec.) Mg-Zn-Cu (not spec.) Mg-Zn-Ni (not spec.) Mg-Zn-Al (not spec.) Mg-Zn-Li (not spec.) 49Mg-47Zn-4Al 52Zn-48Mg 53.7Zn-46.3Mg Mg-Zn-Zr (not spec.) Mg-Zn-C (not spec.) Mg-Zn-Ir (not spec.) 93.9Zn-3.7Al-2.4Mg 95Zn-5Al 96Zn-4Al 55Mg-28Ca-17Zn 59.0Al-35.0Mg-6.0Zn 64.9Al-35.1Mg 65.4Al-34.7Mg 60Mg-25Cu-15Zn 60Mg-25Cu-15Ca 55Al-33Cu-12Mg 60.8Al-33.2Cu-6Mg 64.6Al-28Cu-5.2Si-2.2Mg

a

a

a

a

a

a

a

a

a

a

Bi/In/Pb/Sn Alloys 44.7Bi-22.6Pb-19.1In-8.3Sn-5.3Cd 49Bi-21In-18Pb-12Sn 51.0In-16.5Sn-32.5Bi 51In-16Cd-33Bi 50.0Bi-26.7Pb-13.3Sn-10.0Cd 50.0Bi-26.7Pb-13.3Sn-10.0Cd 52Bi-26Pb-22In 66.3In-33.7Bi 54Bi-29.7In-16.3Sn In2Bi 52.5Bi-32Pb-15.5Sn 52Bi-30Pb-18Sn 67Bi-33In InBi 52In-48Sn 74In-26Cd 55.5Bi-44.5Pb 58Bi-42Sn 63Sn-37Pb 91Sn-9Zn

a

16.0 18.8 20.2 20.55 24.6 25

75.5Ga-24.5In 82Ga-12Sn-6Zn 74Ga-22Sn-4Cd 86.5Ga-13.5Sn 93Ga-5Zn-2Cd 96.5Ga-3.5Zn

19 med med

med

small

med med large

small large small large large large large small

small

8.54 4.53 8.33 8.05 7.41 8.22 5.69 11.80 12.08 12.02

6.22

5.45 6.50 6.79

7.05 6.60

6.07 4.77 3.70 3.36 6.99 8.05 5.12 2.76 5.80 4.44 6.45 6.70 7.09 7.31 2.83 3.41 4.16 7.49 6.43 7.87

5.31 6.32 5.86 6.05 5.95 6.16

138.0 146 310 310 285 254 184 360 365 374

58.34 61.9 65.2 66 54.9 80.2 168 157 168 158.5 170.7 157 180 185 242 152.6 165 104

45.22 46.41

36.8 28.9 27.4 25.0 39.8 45.8 29.0 20.4 38.0 30.4 34.6 36.5 43.1 45.2 24.2 29.9 20.0 47.3 45.6 71.2

69.7 86.5 75.2 81.9 85.03 88.5

915 330 737 713 614 711 368 1098 1113 1646

644

443 882 851

337 260 221 200 381 411 261 165 327 257 340 355 387 403 178 228 213 406 383 518

443 516 450 482 512 526

853 287 673 651 600 618 390 1074 1128 1136

610

417 497 522

516 447

340 262 216 204 386 444 276 162 324 253 339 353 385 400 171 219 210 407 368 502

440 542 481 510 523 541

1.57 0.81 1.40 1.34 1.23 1.36 0.94 1.82 1.86 1.85

1.21

1.07 1.27 1.33

1.10 0.98

2.28 1.73 1.34 1.21 2.45 2.82 1.80 0.96 1.97 1.47 2.11 2.18 2.23 2.29 0.87 1.04 1.26 2.19 1.70 2.01

2.21 2.60 2.40 2.48 2.41 2.48

[Sh 17] [Wh 92] [Sh 17], [So 11] [Sh 17] [Sh 17]

[Sh 17] [Sh 17] [Sh 17]

[Sh 17] [Sh 17]

[Sh 17]

[Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ri 15] [Bi 80a], [Fa 85] [Ga 00] [Ni 16] [Ni 16] [Ni 16] [Ri 15] [SAD 08] [Ga 00] [Bi 80b], [Fa 85] [Bi 80b], [Fa 85] [Bi 80a], [Fa 85] [Ga 00] [Bi 80b], [Fa 85] [Bi 80b], [Fa 85] [Bi 80a], [Fa 85] [Ga 00] [Ga 00]

[Wh 92] [Wh 92]

[SAD 08] [SAD 08] [SAD 08], [Ha 71] [SAD 08] [Ga 00] [Ha 71] [SAD 08], [SAD 08], [Sh 17] [SAD 08], [SAD 08], [SAD 08], [Sh 17] [SAD 08], [SAD 08], [SAD 08], [SAD 08], [SAD 08], [SAD 08]

[SAD 08] [Ga 00] [Ga 00] [Ga 00] [Ga 00] [Ga 00]

P.J. Shamberger and N.M. Bruno

Applied Energy 258 (2020) 113955

20

571 715 720 765 770 803 840 865 946

Cu Alloys 49.1Cu-46.3Al-4.6Si 91Cu-9P 69Cu-17Zn-14P 74Cu-19Zn-7Si 56Cu-27Si-17Mg 80Cu-20Si 83Cu-10P-7Si

Si Alloys 49Si-30Mg-21Ca 56.5Si-43.5Mg small

small

med

small small

8.71 19.91

15.31 7.78 20.47 7.33 16.60 9.99 4.90

13.79 11.29 11.72 12.40 13.07 14.71 9.08 14.63 13.50 14.07 11.89 10.33 16.37 8.93

7.06 9.59 11.62

305 757

406 134 368 125 422 197 92

272 305 364 423 422 331 351 372 485 545 243 471 498 519 230 176 554 314

686 1438

2257 750 2576 896 1751 1300 633

1272 1265 1325 1196 1526 859

1152 1324 1202 1339 1213 1254

375 958 1069

1272

1155

600 1539

1533 789 1769 864 1568 1160 459

1403 1078 1118 1183 1160 1309 745 1285 1217 1268 1016 1057 864 681

446 836 1101

0.92 1.96

2.18 0.95 2.48 0.85 1.91 1.12 0.53

6.07 1.66 1.72 1.82 1.90 2.12 1.30 2.07 1.91 1.99 1.66 1.27 1.99 1.00

1.07 1.45 1.75

[Fa 85] [Bi 80c] [Fa 85] [Fa 85] [Fa 85] [Fa 85] [Bi 80b], [Fa 85] [Bi 80a], [Fa 85]

[Ga 00] [Bi 80b], [Bi 80b], [Bi 80b], [Bi 80b], [Bi 80b], [Bi 80b],

[Bi 80a], [Bi 80b], [Fa 85] [Bi 80b], [Fa 85] [Ga 00] [Bi 80b] [Bi 80b], [Fa 85] [Ga 00] [Bi 80a], [Bi 80c], [Fa 85] [Ga 00] [Ga 00] [Bi 80a], [Bi 80c], [Fa 85] [Bi 80b], [Fa 85] [Ga 00] [Ga 00], [Wa 15] [Bi 80a], [Bi 80c], [Fa 85] [Bi 80a], [Fa 85] [Bi 80b], [Fa 85] [Bi 80a] [Bi 80b], [Fa 85]

RoHS non-compliant, or Tl/As containing References [Ar 02] Archer, D. G., The Enthalpy of Fusion of Gallium. Journal of Chemical & Engineering Data 2002, 47, 304–309. [Ar 03] Archer, D. G.; Rudtsch, S., Enthalpy of Fusion of Indium: A Certified Reference Material for Differential Scanning Calorimetry. J. Chem. Eng. Data 2003, 48, 1157–1163. [Ar 04] Archer, D. G., Enthalpy of Fusion of Bismuth: A Certified Reference Material for Differential Scanning Calorimetry. J. Chem. Eng. Data 2004, 49, 1364–1367. [Bi 80a] Birchenall, C. E.; Riechman, A. F., Heat Storage in Eutectic Alloys. Metall. Trans. A 1980, 11, 1415–1420. [Bi 80b] Birchenall, C. E.; Güceri, S. I.; Farkas, D.; Labdon, M. B.; Nagaswami, N.; Pregger, B. Heat Storage in Alloy Transformations; University of Delaware: Newark, DE, 1980; p 163. [Bi 80c] Birchenall, C. E.; Harrison, A. J.; Balart, S. N., Determination of Density Changes During Melting by X-Ray Absorption. Metallurgical and Materials Transactions A 1980, 11, 1213–1218. [Ch 98] Chase, M., Nist-Janaf Thermochemical Tables, Fourth Edition. J. Phys. Chem. Ref. Data 1998, Monograph No. 9. [Fa 85] Farkas, D.; Birchenall, C., New Eutectic Alloys and Their Heats of Transformation. Metallurgical Transactions A 1985, 16, 323–328. [Ga 00] Gasanaliev, A. M.; Gamataeva, B. Y., Heat-Accumulating Properties of Melts. Russian Chemical Reviews 2000, 69, 179–186. [Ha 71] Hale, D.; Hoover, M.; ONeill, M. Phase Change Materials Handbook; Huntsville, AL, 1971; p 232. [Ja 88] Janz, G. J., Thermodynamic and Transport Properties for Molten Salts: Correlation Equations for Critically Evaluated Density, Surface Tension, Electrical Conductance, and Viscosity. Journal of Physical and Chemical Reference Data 1988, 17. [Li 10] Lide, D. R., Crc Handbook of Chemistry and Physics, 90th Ed. ed.; CRC Press: Boca Raton, FL, 2010. [Ni 16] Nieto-Maestre, J.; Iparraguirre-Torres, I.; Velasco, Z. A.; Kaltzakorta, I.; Zubieta, M. M. In Novel Metallic Alloys as Phase Change Materials for Heat Storage in Direct Steam Generation Applications, AIP Conference Proceedings, AIP Publishing: 2016; p 050032. [Pr 90] Preston-Thomas, H., The International Temperature Scale of 1990 (Its-90). Metrologia 1990, 27, 3. [Ri 15] Risueño, E.; Faik, A.; Rodríguez-Aseguinolaza, J.; Blanco-Rodríguez, P.; Gil, A.; Tello, M.; D’Aguanno, B., Mg-Zn-Al Eutectic Alloys as Phase Change Material for Latent Heat Thermal Energy Storage. Energy Procedia 2015, 69, 1006–1013. [SAD 08] Solder Alloy Directory; 97,720 (A4) R3; Indium Corporation: Clinton, NY, 2008; p 15. [Sh 17] Shamberger, P. J.; Mizuno, Y.; Talapatra, A. A., Mixing and Electronic Entropy Contributions to Thermal Energy Storage in Low Melting Point Alloys. Journal of Applied Physics 2017, 122, 025105. [So 11] Sobolev, V. Database of Thermophysical Properties of Liquid Metal Coolants for Gen-Iv; SCK•CEN-BLG-1069; Belgian Nuclear Research Centre: Boeretang, Belgium, 2011. [St 99] Stølen, S.; Grønvold, F., Critical Assessment of the Enthalpy of Fusion of Metals Used as Enthalpy Standards at Moderate to High Temperatures. Thermochim. Acta 1999, 327, 1–32. [Wa 15] Wang, Z.; Wang, H.; Li, X.; Wang, D.; Zhang, Q.; Chen, G.; Ren, Z., Aluminum and Silicon Based Phase Change Materials for High Capacity Thermal Energy Storage. Applied Thermal Engineering 2015, 89, 204–208. [Wh 92] White, C. E.; Okamoto, H., Phase Diagrams of Indium Alloys and Their Engineering Applications. Indium Corp. of America: Utica, NY, 1992; Vol. 8.

a

517 520 525 524 524 545 548 548 555 560 568 575 579 579 588 705 717 800

84Mg-16Ca 54Al-22Cu-18Mg-6Zn 68.5Al-26.5Cu-5Si 68.5Al-26.5Cu-5Si 65Al-30Cu-5Si 64.3Al-34Cu-1.7Sb 66.7Al-33.3Cu 66.9Al-33.1Cu 83.1Al-11.7Si-5.2Mg 82.4Al-13.1Si-4.6Mg Mg2Cu * 86.4Al-9.4Si-4.2Sb 87.8Al-12.2Si 87.6Al-12.4Si MgZn2 * 49Zn-45Cu-6Mg CaMg2 * 47Mg-38Si-15Zn

P.J. Shamberger and N.M. Bruno

Applied Energy 258 (2020) 113955

21

Ga Alloys 67Ga-20.5In-12.5Zn 78.6Ga-21.4In

Binary Semiconductors As2S3 As2Te3 As2Se3 InSb Sb2S3 B2S3 GeS GeSe InS GaSb GeTe Bi2S3 SnTe HgS Ag2S GeS2 SnS InAs

Elements Hg Cs Ga Rb K Na S In Li Se Sn Bi Tl Cd Pb Zn Te P Sb Mg Al Ba Sr As Ca Ge Ag Au Cu

PCM

a

a

a

a

a

a

a

a

a

a

10.7 15.7

312 375 377 524 550 563 658 675 692 712 724 777 806 820 836 840 881 942

318

12.7 12.8

10.6

40.8

30.7 25.8

11.2

34.7

118.5 49.4 175.0 105.0 120.0

118.5 49.4 175.0 105.0 120.0

0.13

21.7 79.0 92.9 18.2 29.5

21.7 79.0 92.9 18.2 29.5

35

28.4 12.5 25.0 44.5 15.8 58.2

28.4 12.5 25.0 44.5 15.8 58.2

73

0.222

32.8 46.0

7.9 25.0 26.3 30.0 47.9 86.6

L.B. W·m−1·℃-1

32.8 46.0

7.9 25.0 26.3 30.0 47.9 86.6

U.B. W·m−1·℃-1

solid W·m−1·℃-1

liquid W·m−1·℃-1

kliquid (Calc.)

k

0.243

J·g−1·℃-1

J·g−1·℃-1

℃

−38.9 28.4 29.76 39.5 63.2 97.8 115.2 156.60 180.5 220.8 231.93 271.4 304.0 321.1 327.4 419.53 449.5 596.9 630.6 649.9 660.3 726.9 776.9 817.0 841.9 938.3 961.8 1064.2 1084.6

Cp,liquid

Cp,solid

Tfus

Appendix C. Thermal properties of metallic PCMs.

432 440

465 395 357 2193 451 0 444 828 1123 256 2209 194 1000 558 982 688 953 1424

157 28.8 487 37.5 49.5 105 97 201 223 508 420 533 228 442 245 735 793 767 1051 554 944 190 191 1703 501 2789 974 1109 1653

liq (calc.) J·cm−3

ΔfusHliq

46,945 43,505

41,732

112,646

99,411 151,409 168,427 139,215 181,749

61,668 85,359 120,835 24,027 30,670

44,566 33,322 30,781 57,266 25,398 84,374

33,146 41,288

14,338 10,957 46,152 13,682 19,862 38,882

U.B. W·m−2·℃-1·s−0.5

ηq

30,168 30,617

21,296

63,921

99,411 151,409 168,427 139,215 181,749

61,668 85,359 120,835 24,027 30,670

44,566 33,322 30,781 57,266 25,398 84,374

33,146 41,288

14,338 10,957 46,152 13,682 19,862 38,882

L.B. W·m−2·℃-1·s−0.5

10] 10] 10] 10] 10], 10] 10] 10] 10] 10] 10] 10], 10] 10] 10], 10] 10], 10] [Ga 00] [Ga 00]

[Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li [Li

[Ja 88]

[Ja 88]

[Ja 88]

[Ja 88]

[Li 10], [Ch 98] [Li 10], [Ch 98] [SAD 08],[Li 10], [Li 10], [Ch 98] [Li 10], [Ch 98] [Li 10], [Ch 98] [Li 10], [Ch 98] [SAD 08],[Li 10], [Li 10], [Ch 98] [Li 10] [SAD 08],[Li 10], [SAD 08],[Li 10], [Li 10] [Li 10] [SAD 08],[Li 10], [SAD 08],[Li 10], [Li 10] [Li 10], [Ch 98] [Li 10] [Li 10], [Ch 98] [SAD 08],[Li 10], [Li 10], [Ch 98] [Li 10], [Ch 98] [Li 10] [Li 10], [Ch 98] [Li 10] [SAD 08],[Li 10] [SAD 08],[Li 10] [Li 10], [Ch 98]

Refs

[Ch 98]

[Ch 98], [St 99] [Ch 98], [Pr 90]

[Ch 98], [Pr 90] [Ar 04]

[Ch 98], [Pr 90], [Ar 03]

[Ch 98], [Pr 90], [Ar 02]

P.J. Shamberger and N.M. Bruno

Applied Energy 258 (2020) 113955

134.35 191.8 200.6 202.9 214.9 215 285 306 328.87 338 339.85 340 340 340 340.7 340.9 340.96 344 382.0 381.0 400 443 451 451 452 453 506 506 507

Zn/Al/Mg Alloys Mg-Sn-Li (not spec.) Mg-Zn-Sn (not spec.) Mg-Sn-Cu (not spec.) Mg-Al-Sn (not spec.) Zn-Al-Sn (not spec.) Zn-Cu-Sn (not spec.) Mg-Zn-Cu (not spec.) Mg-Zn-Cu (not spec.) Mg-Zn-Ni (not spec.) Mg-Zn-Al (not spec.) Mg-Zn-Li (not spec.) 49Mg-47Zn-4Al 52Zn-48Mg 53.7Zn-46.3Mg Mg-Zn-Zr (not spec.) Mg-Zn-C (not spec.) Mg-Zn-Ir (not spec.) 93.9Zn-3.7Al-2.4Mg 95Zn-5Al 96Zn-4Al 55Mg-28Ca-17Zn 59.0Al-35.0Mg-6.0Zn 64.9Al-35.1Mg 65.4Al-34.7Mg 60Mg-25Cu-15Zn 60Mg-25Cu-15Ca 55Al-33Cu-12Mg 60.8Al-33.2Cu-6Mg 64.6Al-28Cu-5.2Si-2.2Mg

47.0 58.0 60.0 61.0 70.0 70.0 70.0 72.0 81.0 89.9 95.0 96.0 109.0 110.6 118.0 123.0 125.0 138.0 183.0 199.0

16.0 18.8 20.2 20.55 24.6 25

495.4 540.7

a

a

a

a

a

a

a

a

a

a

a

a

a

Au Alloys AuIn AuIn2

Bi/In/Pb/Sn Alloys 44.7Bi-22.6Pb-19.1In-8.3Sn-5.3Cd 49Bi-21In-18Pb-12Sn 51.0In-16.5Sn-32.5Bi 51In-16Cd-33Bi 50.0Bi-26.7Pb-13.3Sn-10.0Cd 50.0Bi-26.7Pb-13.3Sn-10.0Cd 52Bi-26Pb-22In 66.3In-33.7Bi 54Bi-29.7In-16.3Sn In2Bi 52.5Bi-32Pb-15.5Sn 52Bi-30Pb-18Sn 67Bi-33In InBi 52In-48Sn 74In-26Cd 55.5Bi-44.5Pb 58Bi-42Sn 63Sn-37Pb 91Sn-9Zn

75.5Ga-24.5In 82Ga-12Sn-6Zn 74Ga-22Sn-4Cd 86.5Ga-13.5Sn 93Ga-5Zn-2Cd 96.5Ga-3.5Zn

22 0.53

1.46

0.41

1.63 1.73

1.09

0.83

0.272

0.155 0.201

0.167

0.17

0.184

0.197 0.201 0.25

0.69 1.04

0.126 0.167 0.167 0.239

0.151

0.146

0.163 0.167

115

80

59

47 80

4 19 50 61

34

13

75

50

55

59 50

9.5

18

15 10

62.3 63.3 62.4 74.0 85.3 86.8 86.9 71.9 78.4 96.9 99.3 97.6

60.5 58.2 58.2

75.5 66.9

17.5 25.4 21.1 23.7 14.8 15.3 20.4 21.0 28.4 35.5 12.2 19.3 23.8 32.3

20.1 18.6 24.1 28.6 19.4

25.9 27.8 25.9 25.5 28.2 27.3

29.1 29.2 29.2 29.2 29.0 32.8 32.8 29.0 32.8 34.6 34.6 28.0

29.0 29.0 29.0

23.0 23.9

5.3 5.3 5.4 5.4 5.4 5.4 5.5 5.5 12.6 15.7 5.6 5.6 7.1 13.7

5.2 5.2 5.3 5.3 5.3

12.8 11.1 11.2 11.2 13.0 13.0

610 853 853 287 673 651 600 618 390 1074 1128 1136

417 497 522

516 447

340 262 216 204 386 444 276 162 324 253 339 353 385 400 171 219 210 407 368 502

440 542 481 510 523 541

79,513 94,840 94,151 59,434 97,737 96,972 93,145 86,013 71,360 131,637 136,571 135,826

64,785 69,409 71,127

80,559 70,500

33,735 28,471 29,451 31,179 35,342 0 28,362 26,132 33,716 31,600 28,930 29,976 36,185 37,397 28,413 35,988 20,661 36,208 38,165 52,014

43,549 50,115 45,554 46,569 49,529 49,601

54,390 64,422 64,426 37,310 57,031 59,585 57,183 54,611 46,183 78,664 80,645 72,757

44,865 48,994 50,203

44,460 42,140

17,136 15,134 13,757 13,367 18,454 0 15,611 11,956 16,993 15,070 17,476 17,858 18,761 19,131 18,903 23,972 13,938 19,523 20,872 33,879

30,626 31,703 29,894 30,793 33,673 34,235

[Sh 17] [Wh 92] [Sh 17], [So 11] [Sh 17] [Sh 17]

[Sh 17] [Sh 17] [Sh 17]

[Sh 17] [Sh 17], [Li 13]

[Sh 17], [Li 13]

[Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ni 16] [Ri 15] [Bi 80a], [Fa 85] [Ga 00] [Ni 16] [Ni 16] [Ni 16] [Ri 15] [SAD 08] [Ga 00] [Bi 80b], [Fa 85] [Bi 80b], [Fa 85] [Bi 80a], [Fa 85] [Ga 00] [Bi 80b], [Fa 85] [Bi 80b], [Fa 85] [Bi 80a], [Fa 85] [Ga 00] [Ga 00]

[Wh 92] [Wh 92]

[SAD 08] [SAD 08] [SAD 08], [Ha 71] [SAD 08] [Ga 00] [Ha 71] [SAD 08], [SAD 08], [Sh 17] [SAD 08], [SAD 08], [SAD 08], [Sh 17] [SAD 08], [SAD 08], [SAD 08], [SAD 08], [SAD 08], [SAD 08]

[SAD 08] [Ga 00] [Ga 00] [Ga 00] [Ga 00] [Ga 00]

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Applied Energy 258 (2020) 113955

23

571 715 720 765 770 803 840

865 946

Cu Alloys 49.1Cu-46.3Al-4.6Si 91Cu-9P 69Cu-17Zn-14P 74Cu-19Zn-7Si 56Cu-27Si-17Mg 80Cu-20Si 83Cu-10P-7Si

Si Alloys 49Si-30Mg-21Ca 56.5Si-43.5Mg

180

0.86 1.49

0.79

0.75 0.50

0.54

26

4

200

1.39

0.42

130

1.2

1.30 1.11 1.11

1.13

1.51

20

20

70

70

80

78.6 76.2

100.3 99.8 80.6 99.7 86.7 96.9 90.9

75.0 92.3 97.9 97.9 111.3 100.5 100.6 100.5 90.4 89.9 89.0 88.8 90.8 90.8 63.0 86.6 95.2 74.2

28.0 28.0

28.0 50.0 28.1 28.0 28.0 28.0 28.0

35.0 28.8 28.0 28.0 28.0 11.1 48.2 48.2 28.0 28.0 36.7 11.0 28.0 28.0 28.6 28.2 41.7 27.9

600 1539

1533 789 1769 864 1568 1160 459

446 836 1101 1101 1403 1078 1118 1183 1160 1309 745 1285 1217 1268 1016 1057 864 681

88,607 139,767

160,039 114,443 154,101 119,757 150,495 136,782 83,330

74,667 113,361 133,930 133,930 161,202 134,294 136,855 140,706 132,100 139,931 105,074 137,856 135,637 138,436 103,251 123,444 117,012 91,703

52,896 84,699

84,537 81,022 91,047 63,452 85,505 73,536 46,254

50,997 63,292 71,634 71,634 80,859 44,690 94,768 97,453 73,534 78,105 67,505 48,601 75,312 76,892 69,520 70,420 77,502 56,217

[Fa 85] [Bi 80c] [Fa 85] [Fa 85] [Fa 85] [Fa 85] [Bi 80b], [Fa 85] [Bi 80a], [Fa 85]

[Ga 00] [Bi 80b], [Bi 80b], [Bi 80b], [Bi 80b], [Bi 80b], [Bi 80b],

[Bi 80a], [Bi 80b], [Fa 85] [Bi 80b], [Fa 85] [Ga 00] [Bi 80b] [Bi 80b], [Fa 85] [Ga 00] [Bi 80a], [Bi 80c], [Fa 85] [Ga 00] [Ga 00] [Bi 80a], [Bi 80c], [Fa 85] [Bi 80b], [Fa 85] [Ga 00] [Ga 00], [Wa 15] [Bi 80a], [Bi 80c], [Fa 85] [Bi 80a], [Fa 85] [Bi 80b], [Fa 85] [Bi 80a] [Bi 80b], [Fa 85]

RoHS non-compliant, or Tl/As containing. References [Ar 02] Archer, D. G., The Enthalpy of Fusion of Gallium. Journal of Chemical & Engineering Data 2002, 47, 304–309. [Ar 03] Archer, D. G.; Rudtsch, S., Enthalpy of Fusion of Indium: A Certified Reference Material for Differential Scanning Calorimetry. J. Chem. Eng. Data 2003, 48, 1157–1163. [Ar 04] Archer, D. G., Enthalpy of Fusion of Bismuth: A Certified Reference Material for Differential Scanning Calorimetry. J. Chem. Eng. Data 2004, 49, 1364–1367. [Bi 80a] Birchenall, C. E.; Riechman, A. F., Heat Storage in Eutectic Alloys. Metall. Trans. A 1980, 11, 1415–1420. [Bi 80b] Birchenall, C. E.; Güceri, S. I.; Farkas, D.; Labdon, M. B.; Nagaswami, N.; Pregger, B. Heat Storage in Alloy Transformations; University of Delaware: Newark, DE, 1980; p 163. [Bi 80c] Birchenall, C. E.; Harrison, A. J.; Balart, S. N., Determination of Density Changes During Melting by X-Ray Absorption. Metallurgical and Materials Transactions A 1980, 11, 1213–1218. [Ch 98] Chase, M., Nist-Janaf Thermochemical Tables, Fourth Edition. J. Phys. Chem. Ref. Data 1998, Monograph No. 9. [Fa 85] Farkas, D.; Birchenall, C., New Eutectic Alloys and Their Heats of Transformation. Metallurgical Transactions A 1985, 16, 323–328. [Ga 00] Gasanaliev, A. M.; Gamataeva, B. Y., Heat-Accumulating Properties of Melts. Russian Chemical Reviews 2000, 69, 179–186. [Ha 71] Hale, D.; Hoover, M.; ONeill, M. Phase Change Materials Handbook; Huntsville, AL, 1971; p 232. [Ja 88] Janz, G. J., Thermodynamic and Transport Properties for Molten Salts: Correlation Equations for Critically Evaluated Density, Surface Tension, Electrical Conductance, and Viscosity. Journal of Physical and Chemical Reference Data 1988, 17. [Li 10] Lide, D. R., Crc Handbook of Chemistry and Physics, 90th Ed. ed.; CRC Press: Boca Raton, FL, 2010. [Li 13] Lipchitz, A.; Harvel, G.; Sunagawa, T., Determination of Specific Heat of Eutectic Indium–Bismuth-Tin Liquid Metal Alloys as a Test Material for Liquid Metal-Cooled Applications. Appl. Mech. Mater. 2013, 420, 185–193. [Ni 16] Nieto-Maestre, J.; Iparraguirre-Torres, I.; Velasco, Z. A.; Kaltzakorta, I.; Zubieta, M. M. In Novel Metallic Alloys as Phase Change Materials for Heat Storage in Direct Steam Generation Applications, AIP Conference Proceedings, AIP Publishing: 2016; p 050032. [Pr 90] Preston-Thomas, H., The International Temperature Scale of 1990 (Its-90). Metrologia 1990, 27, 3. [Ri 15] Risueño, E.; Faik, A.; Rodríguez-Aseguinolaza, J.; Blanco-Rodríguez, P.; Gil, A.; Tello, M.; D’Aguanno, B., Mg-Zn-Al Eutectic Alloys as Phase Change Material for Latent Heat Thermal Energy Storage. Energy Procedia 2015, 69, 1006–1013. [SAD 08] Solder Alloy Directory; 97,720 (A4) R3; Indium Corporation: Clinton, NY, 2008; p 15. [Sh 17] Shamberger, P. J.; Mizuno, Y.; Talapatra, A. A., Mixing and Electronic Entropy Contributions to Thermal Energy Storage in Low Melting Point Alloys. Journal of Applied Physics 2017, 122, 025105. [So 11] Sobolev, V. Database of Thermophysical Properties of Liquid Metal Coolants for Gen-Iv; SCK•CEN-BLG-1069; Belgian Nuclear Research Centre: Boeretang, Belgium, 2011. [St 99] Stølen, S.; Grønvold, F., Critical Assessment of the Enthalpy of Fusion of Metals Used as Enthalpy Standards at Moderate to High Temperatures. Thermochim. Acta 1999, 327, 1–32. [Wa 15] Wang, Z.; Wang, H.; Li, X.; Wang, D.; Zhang, Q.; Chen, G.; Ren, Z., Aluminum and Silicon Based Phase Change Materials for High Capacity Thermal Energy Storage. Applied Thermal Engineering 2015, 89, 204–208. [Wh 92] White, C. E.; Okamoto, H., Phase Diagrams of Indium Alloys and Their Engineering Applications. Indium Corp. of America: Utica, NY, 1992; Vol. 8.

a

545 548 548 555 560 568 575 579 579 588 705 717 800

517 520 525 524

84Mg-16Ca 54Al-22Cu-18Mg-6Zn 68.5Al-26.5Cu-5Si 68.5Al-26.5Cu-5Si 65Al-30Cu-5Si 64.3Al-34Cu-1.7Sb 66.7Al-33.3Cu 66.9Al-33.1Cu 83.1Al-11.7Si-5.2Mg 82.4Al-13.1Si-4.6Mg Mg2Cu * 86.4Al-9.4Si-4.2Sb 87.8Al-12.2Si 87.6Al-12.4Si MgZn2 * 49Zn-45Cu-6Mg CaMg2 * 47Mg-38Si-15Zn

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Applied Energy 258 (2020) 113955

P.J. Shamberger and N.M. Bruno

Appendix D. Temperature-dependent densities of elemental liquid metals of the form: ρliq/[kg·m−3] = A - B·T/[K]. PCM Aluminum Antimony Arsenic Barium Bismuth Cadmium Calcium Cesium Copper Gallium Germanium Gold Indium Lead Lithium Magnesium Mercury Nickel Phosphorous Potassium Rubidium Selenium Silicon Silver Sodium Strontium Sulfur Tellurium Thallium Tin Zinc

Al Sb As Ba Bi Cd Ca Cs Cu Ga Ge Au In Pb Li Mg Hg Ni P K Rb Se Si Ag Na Sr S Te Tl Sn Zn

Tfus o C

A

B

ρliq(Tfus) kg·m−3

Rep. Unc. (%)

Refs

660.3 630.638 817.01 726.85 271.416 321.079 841.85 28.4 1084.63 29.7646 938.26 1064.19 156.5985 327.43 180.54 649.85 −38.86 1454.85 596.85 63.2 39.5 220.81 1411.85 961.79 97.83 776.85 115.21 449.52 304.01 231.928 419.527

2668 7014 5803 3556 10,689 8751 2350 2009 9109 6262 6073 19,325 7349 11,400 569 1834 14,245 9568 2124 910 1604 4490 2995 10,377 1014 2555 2188 6382 11,925 7308 7171

0.311 0.608 0.535 0.299 1.213 1.251 0.897 0.571 0.819 0.611 0.485 1.440 0.762 1.239 0.120 0.266 2.387 0.988 0.989 0.242 0.451 1.050 0.264 0.877 0.235 0.283 0.982 0.778 1.200 0.652 0.884

2377 6464 5220 3257 10,028 8008 1350 1837 7997 6077 5485 17,400 7022 10,656 515 1589 13,686 7861 1263 829 1463 3971 2551 9294 927 2258 1807 5820 11,232 6979 6559

0.7 0.8 0.5 1 0.5 0.6 0.9 0.2 1.3 0.4 0.5 0.9 0.1 1 1 0.6 0.2 1.7 n.r. 0.2 0.2 0.5 2.2 0.9 0.5 1 1.5 0.5 0.9 1 0.7

[As 06] [As 12b] [Cr 74] [Hi 07] [As 12b] [As 12a] [Cr 74] [Cr 74] [As 10] [As 12a] [Cr 74] [Pa 08] [As 12a] [As 12b] [Cr 74] [Cr 74] [Cr 74] [As 12b] [Ho 94] [Cr 74] [Cr 74] [Cr 74] [As 12a] [As 12b] [So 11] [Hi 07] [Es 07] [Cr 74] [As 12a] [As 10] [As 12a]

References [As 06] Assael, M. J.; Kakosimos, K.; Banish, R. M.; Brillo, J.; Egry, I.; Brooks, R.; Quested, P. N.; Mills, K. C.; Nagashima, A.; Sato, Y., Reference Data for the Density and Viscosity of Liquid Aluminum and Liquid Iron. Journal of physical and chemical reference data 2006, 35, 285–300. [As 10] Assael, M. J.; Kalyva, A. E.; Antoniadis, K. D.; Michael Banish, R.; Egry, I.; Wu, J.; Kaschnitz, E.; Wakeham, W. A., Reference Data for the Density and Viscosity of Liquid Copper and Liquid Tin. Journal of Physical and Chemical Reference Data 2010, 39, 033105. [As 12a] Assael, M. J.; Armyra, I. J.; Brillo, J.; Stankus, S. V.; Wu, J.; Wakeham, W. A., Reference Data for the Density and Viscosity of Liquid Cadmium, Cobalt, Gallium, Indium, Mercury, Silicon, Thallium, and Zinc. Journal of Physical and Chemical Reference Data 2012, 41, 033101. [As 12b] Assael, M. J.; Kalyva, A. E.; Antonia, K. D.; Banish, R. M.; Egry, I.; Wu, J.; Kaschnitz, E.; Wakeham, W. A., Reference Data for the Density and Viscosity of Liquid Antimony, Bismuth, Lead, Nickel and Silver. High Temperatures–High Pressures 2012, 41. [Cr 74] Crawley, A., Densities of Liquid Metals and Alloys. International Metallurgical Reviews 1974, 19, 32–48. [Es 07] Espeau, P.; Céolin, R., Density of Molten Sulfur in the 334–508 k Range. Thermochimica acta 2007, 459, 127–129. [Hi 77] Hiemstra, S.; Prins, D.; Gabrielse, G.; Van Zytveld, J., Densities of Liquid Metals: Calcium, Strontium, Barium. Physics and Chemistry of Liquids 1977, 6, 271–279. [Ho 94] Hohl, D.; Jones, R., Polymerization in Liquid Phosphorus: Simulation of a Phase Transition. Physical Review B 1994, 50, 17047. [Mi 50] Miller, R., Liquid Metals Handbook. In Liquid-Metals Handbook, Lyon, R. N., Ed. Office of Naval Research: Washington, DC, 1950; pp 29–52. [Pa 08] Paradisa, P.; Ishikawaa, T.; Koikeb, N., Density of Liquid Gold Measured by a Non-Contact Technique. Gold Bulletin 2008, 41, 242–245. [So 11] Sobolev, V. Database of Thermophysical Properties of Liquid Metal Coolants for Gen-Iv; SCK•CEN-BLG-1069; Belgian Nuclear Research Centre: Boeretang, Belgium, 2011.

Appendix E. Temperature-dependent thermal conductivities of elemental liquid metals of the form: kliq/[W·m−1·K−1] = A - B·T/[K]. PCM Aluminum Antimony Arsenic Barium Bismuth Cadmium Calcium Cesium Copper Gallium Germanium Gold Indium Lead

Al Sb As Ba Bi Cd Ca Cs Cu Ga Ge Au In Pb

Tfus o C

A

B

kliq(Tfus) W·m−1·oC-1

Refs

660.3 630.6 817.0 726.9 271.4 321.1 841.9 28.4 1084.6 29.76 938.3 1064.2 156.60 327.4

122.2 27.1

0.0314 0.0060

93 22

[Mi 50] [Vi 72]

18.2 7.3 50.7 118.5 25 120 11.2 49.4 105 16.0 9.2

0 −0.0095 0.0105 0 0 0 −0.0500 0 0 −0.0390 −0.0110

18* 13 45 119* 25 120 26 49* 105 33 16

[Ii 88] [So 11] [Vi 72] [Ro 79] [Mi 50] [Po 65] [Vi 72] [Ii 88] [Va 08] [Sa 10] [So 11]

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Applied Energy 258 (2020) 113955

P.J. Shamberger and N.M. Bruno Lithium Magnesium Mercury Nickel Phosphorous Potassium Rubidium Selenium Silicon Silver Sodium Strontium Sulfur Tellurium Thallium Tin Zinc

Li Mg Hg Ni P K Rb Se Si Ag Na Sr S Te Tl Sn Zn

180.5 649.9 −38.9 1454.9 596.9 63.2 39.5 220.8 1411.9 961.8 97.8 776.9 115.2 449.5 304.0 231.93 419.53

46 16.6 3.5 60

0 −0.0676 −0.0188 0

46 79 7.9 60

[Cu 63] [Vi 72] [Vi 72] [Va 08]

55.8 30

0.0234 0

48 30

[Vi 72] [Vi 72]

56 175 104 29.5

0 0 0.0470 0

56 175 87 30*

[Va 08] [Va 08] [So 11] [Ro 79]

25 13.9 62.7

0 −0.0287 0.0064

25 28 58

[Cu 63] [Sa 11] [Vi 72]

* Calculated from Wiedemann-Franz relationship from reported electrical conductivity (see §4.5 in full paper). References [Cu 63] Cusack, N., The Electronic Properties of Liquid Metals. Reports on progress in physics 1963, 26, 361. [Ii 88] Iida, T.; Guthrie, R. I., The Physical Properties of Liquid Metals. Clarendon Press, Walton Street, Oxford OX 2 6 DP, UK, 1988. 1988. [Mi 50] Miller, R., Liquid Metals Handbook. In Liquid-Metals Handbook, Lyon, R. N., Ed. Office of Naval Research: Washington, DC, 1950; pp 29–52. [Po 65] Powell, R., Correlation of Metallic Thermal and Electrical Conductivities for Both Solid and Liquid Phases. International Journal of Heat and Mass Transfer 1965, 8, 1033–1045. [Ro 79] Rottman, C.; Van Zytveld, J., Electronic Properties of High-Purity Liquid Calcium and Strontium. Journal of Physics F: Metal Physics 1979, 9, 2049. [Sa 10] Savchenko, I.; Stankus, S.; Agazhanov, A. S., Heat Transfer Coefficients of Liquid Indium in the Temperature Range 470–1275 K. Thermophysics and Aeromechanics 2010, 17, 121–125. [Sa 11] Savchenko, I. V. e.; Stankus, S. V.; Agadjanov, A. S., Measurement of Liquid Tin Heat Transfer Coefficients within the Temperature Range of 506–1170 K. High Temperature 2011, 49, 506–511. [So 11] Sobolev, V. Database of Thermophysical Properties of Liquid Metal Coolants for Gen-Iv; SCK•CEN-BLG-1069; Belgian Nuclear Research Centre: Boeretang, Belgium, 2011. [Va 08] Valencia, J. J.; Quested, P. N., Thermophysical Properties. In Casting, Viswanathan, S., Ed. ASM International: Materials Park, OH, 2008; Vol. 15, pp 468–481. [Vi 72] Viswanath, D.; Mathur, B., Thermal Conductivity of Liquid Metals and Alloys. Metallurgical Transactions 1972, 3, 1769–1772.

Appendix F. Thermal-fluid properties of PCMs in Fig. 8a and 8b. PCM

β

ρ m3·K−1

μ g·cm3

Pr kg·m−1·s−1

Ra

Ga Alloys 67Ga-20.5In-12.5Zn 78.6Ga-21.4In 75.5Ga-24.5In 82Ga-12Sn-6Zn 74Ga-22Sn-4Cd 86.5Ga-13.5Sn 93Ga-5Zn-2Cd 96.5Ga-3.5Zn

1.06·10-4 1.02·10-4 1.03·10-4 1.02·10-4 1.01·10-4 9.98·10-5 1.03·10-4 1.02·10-4

6.42 6.32 6.35 6.27 6.4 6.23 6.16 6.11

1.75·10-3 1.75·10-3 1.75·10-3 1.75·10-3 1.75·10-3 1.75·10-3 1.75·10-3 1.75·10-3

3.88·10-2 4.07·10-2 4.06·10-2 4.37·10-2 4.46·10-2 4.48·10-2 3.91·10-2 3.94·10-2

666 650 657 781 819 774 582 573

Bi/In/Pb/Sn Alloys 44.7Bi-22.6Pb-19.1In-8.3Sn-5.3Cd 49Bi-21In-18Pb-12Sn 50.0Bi-26.7Pb-13.3Sn-10.0Cd 52Bi-30Pb-18Sn 55.5Bi-44.5Pb 58Bi-42Sn 63Sn-37Pb 91Sn-9Zn

1.14·10-4 1.11·10-4 1.18·10-4 1.12·10-4 1.19·10-4 1.05·10-4 9.87·10-5 9.78·10-5

9.23 9.08 9.7 9.67 10.5 8.61 8.07 7.06

4.46·10-4 4.46·10-4 4.46·10-4 4.46·10-4 4.46·10-4 4.46·10-4 5.38·10-4 5.38·10-4

8.81·10-3 9.11·10-3 7.82·10-3 8.41·10-3 7.35·10-3 8.55·10-3 8.21·10-3 6.67·10-3

1.29·104 1.24·104 1.28·104 1.24·104 1.33·104 9.17·103 3.96·103 1.25·103

Zn/Al/Mg Alloys 49Mg-47Zn-4Al 52Zn-48Mg 93.9Zn-3.7Al-2.4Mg 59.0Al-35.0Mg-6.0Zn 64.9Al-35.1Mg 55Al-33Cu-12Mg 54Al-22Cu-18Mg-6Zn 66.7Al-33.3Cu 66.9Al-33.1Cu 82.4Al-13.1Si-4.6Mg 87.6Al-12.4Si

1.57·10-4 1.58·10-4 1.36·10-4 1.44·10-4 1.44·10-4 1.31·10-4 1.36·10-4 1.26·10-4 1.26·10-4 1.29·10-4 1.27·10-4

2.65 2.76 5.86 2.17 2.1 2.98 2.74 3.19 3.18 2.4 2.44

1.41·10-3 1.41·10-3 1.41·10-3 1.49·10-4 1.49·10-4 1.49·10-4 1.49·10-4 1.49·10-4 1.49·10-4 1.49·10-4 1.49·10-4

2.49·10-3 3.79·10-3 1.46·10-3 5.61·10-3 5.42·10-3 3.18·10-3 5.11·10-3 2.54·10-3 2.54·10-3 4.85·10-3 5.19·10-3

72.7 121 179 910 722 739 1260 462 460 890 975

Cu Alloys 69Cu-17Zn-14P 56Cu-27Si-17Mg 80Cu-20Si

1.81·10-4 1.19·10-4 1.03·10-4

4.81 3.72 5.89

3.01·10-4 3.01·10-4 3.01·10-4

3.92·10-3 5.35·10-3 3.48·10-3

982 531 756

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Applied Energy 258 (2020) 113955

P.J. Shamberger and N.M. Bruno Water H2O

8.00·10-5

1

1.67·10-3

11.4

5.98·104

Organics Polyglycol E400 Polyglycol E600 Paraffin C18 Paraffin C22-C45 Paraffin Wax Naphthalene Caprylic acid Capric acid Palmitic acid Stearic acid

1.00·10-3 1.00·10-3 1.00·10-3 1.00·10-3 1.00·10-3 1.00·10-3 1.00·10-3 1.00·10-3 1.00·10-3 1.00·10-3

1.13 1.13 0.774 0.795 0.79 0.976 0.901 0.878 0.85 0.848

8.33·10-3 6.16·10-3 5.46·10-3 3.18·10-3 2.89·10-3 2.27·10-3 6.99·10-3 5.05·10-3 2.89·10-3 2.67·10-3

111 81.5 92.2 37.9 43.3 43 117 82.5 44.6 38.9

2.00·106 2.65·106 2.30·106 2.07·106 3.56·106 1.11·107 2.41·106 3.00·106 4.38·106 4.18·106

Hydrated Salts (inorganic) CaCl2·6H20 Zn(NO3)2·6H20 Ba(OH)2·8H20 Mg(NO3)2·6H20 MgCl2·6H20

1.00·10-3 1.00·10-3 1.00·10-3 1.00·10-3 1.00·10-3

1.56 1.83 1.94 1.55 1.45

5.35·10-3 4.68·10-3 2.34·10-3 2.00·10-3 1.40·10-3

24.8 25.2 8.95 10.2 6.16

7.19·105 1.53·106 1.73·106 2.30·106 2.12·106

1

β and μ were computed using the methods described in §5.1.3 in full paper.

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