Hunting Hydrogen: Structure-property relations in High Entropy Alloy-based metal hydrides

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UNIVERSITATISACTA UPSALIENSIS

UPPSALA

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 2033

Hunting Hydrogen

Structure-property relations in High Entropy Alloy- based metal hydrides

GUSTAV EK

ISSN 1651-6214 ISBN 978-91-513-1187-6

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Dissertation presented at Uppsala University to be publicly examined in Häggsalen, Ångströmlaboratoriet, Polacksbacken, Lägerhyddsvägen 1, Uppsala, Friday, 4 June 2021 at 09:15 for the degree of Doctor of Philosophy. The examination will be conducted in English.

Faculty examiner: Professor William I.F. David (University of Oxford, Oxford, United Kingdom/ISIS Neutron and Muon Source, Didcot, United Kingdom).

Abstract

Ek, G. 2021. Hunting Hydrogen. Structure-property relations in High Entropy Alloy-based metal hydrides. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 2033. 78 pp. Uppsala: Acta Universitatis Upsaliensis.

ISBN 978-91-513-1187-6.

Metal hydrides have many uses when switching the energy system from fossil fuels to renewable sources, such as rechargeable batteries, hydrogen storage, hydrogen compression and thermal storage. State of the art materials for these applications such as LaNi5 and TiFe, however, suffer certain limitations such as degradation during repeated hydrogen cycling and harsh activation conditions for initial hydrogen uptake, promoting the need for novel materials. One class of materials that are interesting options are High Entropy Alloys (HEA), which are solid solutions where typically four or more different elements occupy a single crystallographic site in a simple structure such as body centered cubic (bcc) or cubic close packed (ccp). Due to the random distribution of the elements, there is a large variety of local environments for hydrogen, potentially unlocking sites that are unavailable in conventional transition metal hydrides. There is also the possibility of vast chemical tunability when using this many principal elements.

It is therefore imperative to establish design rules to enable tuning of the hydrogen sorption properties of these materials by changing the composition. The effect of having many differently sized metals on the crystal structure is also not fully understood, and is believed to have a high impact on the bulk properties such as hydrogen sorption in these materials.

This thesis covers the experimental synthesis of a wide range of HEAs and subsequent evaluation of their structural and hydrogen sorption properties. Several new design rules have been established, such as that the atomic size mismatch between the constituent metals has no effect on the maximum hydrogen capacity, that the addition of large elements like Zr leads to phase separation and that controlling the valence electron concentration, VEC, destabilizes the HEA-based metal hydrides. Based on these findings, the material TiVCrNbH8 has been identified as a candidate with properties rivaling that of TiFeH2.

Keywords: Hydrogen, metal-hydride, High Entropy Alloy

Gustav Ek, Department of Chemistry - Ångström, Inorganic Chemistry, Box 538, Uppsala University, SE-751 21 Uppsala, Sweden.

urn:nbn:se:uu:diva-439292 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-439292)

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Till Mamma,

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List of papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Structure and hydrogenation properties of HfNbTiVZr High-Entropy Alloy.

D. Karlsson, G. Ek, J. Cedervall, C. Zlotea, K.T. Møller, T.C. Hansen, J. Bednar˘cík, M. Paskevicius, M.H. Sørby, T.R. Jensen, U. Jansson, M.

Sahlberg

Inorganic Chemistry 57 (2018) 2103-2110

II Hydrogen sorption in TiZrNbHfTa high entropy alloy.

C. Zlotea, M.A. Sow, G. Ek, J.-P Couziné, L. Perriére, I. Guillot, J.

Bourgon, K.T. Møller, T.R. Jensen, E. Akiba, M. Sahlberg Journal of Alloys and Compounds 775 (2019) 667-674

III Hydrogen storage in high-entropy alloys with varying degree of local lattice strain.

M.M. Nygård, G. Ek, D. Karlsson, M. Sahlberg, M.H. Sørby, B.C.

Hauback

International Journal of Hydrogen Energy 44 (2019) 29140-29149

IV Counting electrons - a new approach to tailor the hydrogen sorption properties of high-entropy alloys.

M.M. Nygård, G. Ek, D. Karlsson, M.H. Sørby, M. Sahlberg, B.C.

Hauback

Acta Materialia 175 (2019) 121-129

V Elucidating the effects of the composition on hydrogen sorption in TiVZrNbHf-based high-entropy alloys.

G. Ek, M.M. Nygård, A.F. Pavan, J. Montero, P.F. Henry, M.H. Sørby, M. Witman, V. Stavila, C. Zlotea, B.C. Hauback, M. Sahlberg

Inorganic Chemistry 60(2) (2021) 1124-1132

VI Local order in high-entropy alloys and associated deuterides - a total scattering and reverse monte carlo study.

M.M. Nygård, W.A. Sławi´nski, G. Ek, M.H. Sørby, M. Sahlberg, D.A.

Keen, B.C. Hauback

Acta Materialia 199 (2020) 504-513

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VII Vibrational properties of high entropy alloy based metal hydrides probed by inelastic neutron scattering.

G. Ek, Ø.S. Fjellvåg, P. Vajeeston, J. Armstrong, M. Sahlberg, U.

Häussermann Submitted

VIII Data-driven discovery and synthesis of novel high entropy alloy hydrides with targeted thermodynamic stability.

M. Witman, G. Ek, S. Ling, S. Agarwal, J. Wong, M.D. Allendorf, M.

Sahlberg, V. Stavila Submitted

Reprints were made with permission from the publishers.

Disclaimer: Parts of this thesis is based on my licentiate thesis entitled Shin- ing light on novel metal hydrides (Uppsala University, 2019).

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The author also contributed to the following published works which are not included in this thesis:

i Li-ion batteries using electrolytes based on mixtures of poly(vinyl alcohol) and lithium(triﬂouromethane) sulfonamide salt.

G. Ek, F. Jeschull, T. Bowden, D. Brandell Electrochimica Acta 246 (2017) 208-212

ii Hydrogen induced structure and property changes in Eu3Si4. G. Ek, R. Nedumkandathil, R. Johansson, J. Montero, C. Zlotea, M.S.

Andersson, P. Nordblad, C. Tang, M. Sahlberg, U. Häussermann Journal of Solid State Chemistry 277 (2019) 37-45

iii Thermal stability of the HfNbTiVZr high-entropy alloy.

V. Pacheco, G. Lindwall, D. Karlsson, J. Cedervall, S. Fritze, G. Ek, P.

Berastegui, M. Sahlberg, U. Jansson Inorganic Chemistry 58 (2019) 811-820

iv TiVZrNb multi-principal element alloy: synthesis, structural and hydrogen sorption properties.

J. Montero, C. Zlotea, G. Ek, J-C. Crivello, L. Laversenne, M. Sahlberg Molecules 24 (2019) 2799

v Hydrogen storage properties of the refractory Ti-V-Zr-Nb-Ta multi- principal-element alloy.

J. Montero, G. Ek, L. Laversanne, V. Nassif, G. Zepon, M. Sahlberg, C.

Zlotea

Journal of Alloys and Compounds 385 (2020) 155376

vi Interstitial carbon in bcc HfNbTiVZr high entropy alloy from ﬁrst principles.

L. Casillas-Trijillo, U. Jansson, M. Sahlberg, G. Ek, M.M. Nygård, M.H.

Sørby, B.C. Hauback, I. Abrikosov, B. Alling Physical Review Materials 4 (2020) 123601

vii Improving the hydrogen cycling properties by Mg addition in Ti-V- Zr-Nb refractory high entropy alloy.

J. Montero, G. Ek, M. Sahlberg, C. Zlotea Scripta Materialia 194 (2021) 113699

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Comments on the authors’ contribution to the papers:

I Synthesized the sample for ex-situ neutron diffraction, performed the measurement and analyzed the data. Wrote parts of the manuscript with input from the co-authors.

II Planned, carried out and analyzed the in-situ synchrotron diffraction.

Wrote parts of the manuscript with input from the co-authors.

III Took part in the conceptualisation of the paper together with the ﬁrst author. Carried out synchrotron diffraction and data interpretation as well as prepared samples for microscopy. Wrote parts of the manuscript with input from the co-authors.

IV Prepared all samples for microscopy as well as synthesized some compositions. Wrote parts of the manuscript with input from the co-authors.

V Planned and carried out most of the experimental work. Performed all the data analysis and wrote the manuscript with input from the co- authors.

VI Took part in the conceptualisation of the paper together with the ﬁrst author. Synthesized and prepared all samples and carried out both synchrotron and neutron measurements together with the ﬁrst author. Took part in discussions during data analysis. Wrote parts of the manuscript with input from the co-authors.

VII Conceptualized the study, planned and carried out all experimental work as well as synthesized all the samples. Analyzed the experimental data and wrote the manuscript with input from the co-authours.

VIII Took part in the conceptualisation of the paper. Synthesized all samples and took part in evaluating the experimental data. Wrote parts of the manuscript with input from the co-authours.

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Abbreviations

A list of the abbreviations used in this thesis.

Abbreviation Meaning

BCC Body-Centered Cubic

BCT Body-Centered Tetragonal CCP Cubic Closed Packed CST Concentrated Solar Thermal

DC Direct Current

DSC Differential Scanning Calorimetry FCC Face-Centered Cubic

HCP Hexagonal Close Packed

HEA High Entropy Alloy

INS Inelastic Neutron Scattering LENS Laser Engineered Net Shaping

ML Machine Learning

Ni-MH Nickel-Metal Hydride NPD Neutron Powder Diffraction PCI Pressure Composition Isotherm PDF Pair Distribution Function

RE Rare Earth

RMC Reverse Monte Carlo

SG Space Group

SRO Short-Range Order

STA Scanning Thermal Analysis TDS Thermal Desorption Spectroscopy TGA Thermal Gravimetric Analysis

ToF Time-of-Flight

VEC Valence Electron Concentration XRPD X-Ray Powder Diffraction

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1. Introduction

1.1 Applications of metal hydrides

Hydrogen is the most abundant element in the universe, however molecular hydrogen is not readily available on earth since most of it is bound to oxygen in water. It is heavily used in industry as a key component in the production of ammonia used in fertilizer with annual productions approaching 75 million tonnes in 2018 [1]. Most industrial H2is produced by steam reforming from methane by the reaction:

CH4(g) + 2H2O(g) → CO2(g) + 4H2(g) (1.1) leaving carbon dioxide as a byproduct. With today’s society facing the threat of global warming, the emissions of CO2 are of great importance. Alterna- tively, clean H₂can be obtained by electrolysis of water:

2H⁺(l) + 2e⁻→ H2(g) (1.2)

if the electricity used to drive the reaction comes from renewable energy sources such as wind or solar. The use of clean H2 as a low carbon fuel to phase out fossil fuels is known as the hydrogen economy, a term ﬁrst coined in 1970 [2].

What makes hydrogen special compared to other energy storage technologies is that it can ﬁll roles in almost all aspects of the modern energy system rang- ing from large scale long term grid storage, transport and heating [3, 4], some of which beneﬁt from hydrogen being incorporated into a metal hydride [5].

The following sections will give a brief overview of some of the applications of metal hydrides in energy storage, along with the beneﬁts and drawbacks of these kind of materials, motivating why there is a need to further develop novel metal hydrides.

1.1.1 Hydrogen storage

Hydrogen is a gas at normal conditions, which makes it inherently difﬁcult to handle and with low volumetric energy density compared to other fuels such as gasoline and methane. The main way to increase the volumetric energy density is compacting the gas by either condensation to liquid or compression to 300-700 bar in tanks such as those found in commercial fuel cell vehicles on the market today. However, the volume can be even further reduced by incorporation into metal hydrides, as is illustrated in ﬁgure 1.1 [6, 7].

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Figure 1.1. Overview of selected materials and their volumetric and gravimetric hy- drogen densities. Metallic and complex hydrides are shown as blue and magenta respectively, and liquid carriers as stars. The ﬁgure is adapted from reference [7].

Replacing pressurized tanks as a hydrogen storage medium for mobile applications with metal hydrides is a challenge since the metals are heavy, reducing the gravimetric energy capacity greatly. Therefore a lot of research for these applications has focused on complex hydrides with light metals such as Li, Na, Mg and Al that can reach hydrogen contents as high as 18 wt % for LiBH4. Unfortunately, these often suffer from irreversible and complex dehydrogenation reactions making them impracticable for mobile applications.

For larger storage where weight is not of major concern, interstitial hydrides constitute very promising candidates compared to pressurized tanks in terms of safety and energy savings. State of the art materials such as TiFe can, for instance, absorb 1.89 wt % of hydrogen at 5 bar H2 (room temperature) and has excellent volumetric capacity [8]. However, this alloy suffers in terms of a rigorous activation procedure required for the surface to be reactive with hydrogen [9].

1.1.2 Hydrogen compression

Due to the drawbacks of solid state hydrogen storage mentioned in section 1.1.1, the most common way to store and transport hydrogen today is in pres-

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surised tanks. The main reason that widespread use of hydrogen is not yet realized is the high cost of the hydrogen value chain, especially when it comes to the compression which is estimated to account for more than 50% of the cost in a hydrogen refueling station [10]. Compression is needed since H₂produced in electrolyzers typically output their gas at low pressure (∼ 1-10 bar) where the energy density is low, which is impracticable in for instance fuel cell vehicles. This high costs comes from the fact that hydrogen is not easily compressed, due to it’s volatility and sensitivity towards contamination from lubricants commonly found in mechanical compressors. Hydrogen therefore requires special types of compressors where the hydrogen is separated from the lubricants such as in those based on diaphragms and centrifugal techniques which increases the cost. Non-mechanical compressors for hydrogen solve most of these problems, enabling signiﬁcant savings where large amounts of hydrogen are needed, for instance when the Swedish steel industry is replacing the use of coal which is one of the biggest sources of CO₂-emission in Sweden [11].

Non-mechanical compressors can be based on metal hydrides, by exploit- ing the fact that the pressure where a metal/alloy absorbs hydrogen is highly dependant on temperature which is illustrated in ﬁgure 1.2. The working prin- ciple is that the metal hydride is formed at low temperature and pressure, by subsequently heating the material the gas is then released at higher pressure.

The energy needed to heat the system can be excess heat generated during other industrial processes, providing cheaper operating costs than mechanical counterparts. There is also an absence of moving parts, which reduces the need for regular maintenance and lubricants. This technology requires metal hydrides with very specific properties and thermodynamics to reach the high pressures at refueling stations of around 875 bar for fast filling of a 700 bar tank. Therefore, only a limited amount of the metal hydrides studied in the literature so far meet these criteria, and they often need to be used in series to reach sufficient pressures [12].

1.1.3 Thermal storage

The fact that hydrogen absorption in metal hydrides is exothermic can be ex- ploited to store heat from the sun in concentrated solar thermal (CST) power systems [13]. This is done by combining a metal hydride with high desorption temperature (such as MgH2 or CaH2) with a metal hydride with lower desorption temperature (TiFe, LaNi₅). The process works by releasing H₂by heating the stable metal hydride during the day, and incorporating it in the low temperature analogue making it act as a secondary hydrogen storage:

Day : 3MgH₂+ LaNi5+ heat → 3Mg + LaNi5H₆ (1.3) During the night, the stable hydride is cooled down, and it begins to reabsorb, thus lowering the hydrogen pressure in the system. This in term makes hydro-

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gen release from the low-temperature metal hydride favourable, thus complet- ing the cycle.

Night : 3Mg+ LaNi5H₆→ 3MgH2+ LaNi5+ heat (1.4) The exothermic reaction of absorption by the high-temperature metal hydride during the night can then be used to produce electricity. The technique requires large amount of direct sunlight to be directed by mirrors into a focusing tower, where the heat can be stored. The geographical locations of CST is therefore limited, but countries such as Spain, USA and Australia either have or are planning such energy systems.

1.1.4 Electrochemical energy storage

The most common use of metal hydrides is in electrochemical energy storage, most importantly in Nickel-Metal Hydride (Ni-MH) batteries. The metal hydride makes up the anode of the battery and is typically based on LaNi5H_x coupled with a NiOOH/Ni(OH)₂ cathode in KOH solution. These kinds of rechargeable batteries were extensively used in consumer electronics and hy- brid electric vehicles but has now largely been replaced by lithium-ion technology, since it offers higher energy densities. There are however applications where Ni-MH technology is preferred over lithium-ion such as in maritime applications, requiring fast recharge and reduced cost for big battery packs and the extra weight can be used as ballast.

Metal hydrides have also been gathering attention for use as solid electrolytes in Li and Na-ion batteries for improved safety. A number of complex cage-like borohydride derivatives have shown high conductivities of Li and Na-ions, approaching that of liquid electrolytes at elevated temperatures [14–

17].

1.2 The Metal-Hydrogen system

Hydrogen is the simplest element in the periodic table, consisting of only one proton and one electron. Because of it’s single electron, it is commonly situ- ated at the head of the alkali metals but could also be placed in group 17 since it needs only one electron to ﬁll it’s valence. An affect of this large polarity of hydrogen is that it forms compounds with almost all other elements in the periodic table (where most are metals). It also has a central position in the electronegativity series (2.2 on the Pauling scale), which combined with the wide range in electronegativity of metals, causes the bond characteristics of metal hydrides to be vastly different, including ionic, covalent and metallic characteristics.

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1.2.1 Ionic metal hydrides

When hydrogen interacts with an electropositive metal such as the alkali or alkaline earth metals of group I and II, hydrogen acts as the hydride ion (H^–) forming stoichiometric compounds such as LiH and MgH₂. Due to the large difference in electronegativity, the bonding has ionic characteristics and as a consequence they are rather stable and tend to crystallize in common salt structures such as NaCl (group I) and PbCl2or rutile type (group II).

Among the ionic hydrides is MgH2, which has the highest energy density of all reversible metal hydrides (9 MJ/kg Mg) and has therefore been studied extensively for on-board hydrogen storage in fuel cell electric vehicles [5, 18].

However, the high stability of ionic hydrides leads to unfavourable operating conditions since the desorption temperature of MgH2 is around 300 ^◦C at 1 bar H₂with a slow rate of hydrogen release.

1.2.2 Covalent metal hydrides

Covalent metal hydrides form with metals from the p-block in the periodic table such as Al, Ga and Sn. Since the covalent bonding is weak, these systems are typically unstable. The group 14 hydrides which are the equivalent of methane (germane GeH4 and stannae SnH4) are highly ﬂammable gases in normal conditions, but crystalline phases have been reported for low temperatures [19]. Group 13 hydrides with Al, Ga and In form networking or polymeric structures.

Another class of covalent hydrides are the complex hydrides, which com- bine a positive group I or II metal with a negative hydrogen containing p-block anion such as alanate ([AlH4]^–), amide ([NH₂]^–) or borohydride ([BH₄]^–).

These compounds offer very high gravimetric hydrogen storage capacities of up to 18 wt% for LiBH₄, but are usually not reversible and very sensitive to moisture, evolving hydrogen gas in contact with water [20]. It has been shown that the reversibility problem can be improved by addition of Ti-additives to NaAlH4, enabling dehydrogenation at moderate conditions [21, 22]. Mono and bi-metallic borohydrides also offer some very rich crystal chemistry, usually with several different polymorphs per compound [23].

1.2.3 Metallic metal hydrides

The transition metals in the d-block of the periodic table along with the lan- thanoid series have electronegativities comparable to that of hydrogen. When they form hydrides, the bond is often classiﬁed as metallic due to the fact that they keep their metallic luster and electrical conductivity properties. By the nature of the metallic bond character, the hydrogen concentration in the MHx

exists in a wide range of non-stoichiometric compositions (0≤ x ≤ 2 for transition metals and 0≤ x ≤ 3 for the lanthanoids). The composition is often

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described as the ratio of H atoms to that of the number of metal atoms (M), (H/M) and are commonly shown in phase diagrams with hydrogen pressure on the y-axis and isotherms measured at different temperatures as is illustrated in ﬁgure 1.2

T

₁

T

₂

T

₃

+

Figure 1.2. Schematic phase diagram for a metallic metal hydride with isotherms at different temperatures.

For low concentrations (x≤ 0.5) hydrogen is dissolved randomly in the host metal structure (known as theα-phase) in interstitial sites (typically octahedral), followed by an expansion of the metal lattice that is proportional to the hydrogen concentration by 2-3 Å³per hydrogen atom [24]. At higher concentrations, H-H interactions become more pronounced, and a phase transition takes place in the metal lattice to the more orderedβ-phase seen as a plateau in the isotherm. Due to spatial restrictions, theβ-phase is often face-centered cubic with metal atoms occupying the corners and each face of the cubic structure, and the hydrogen atoms occupy the tetrahedral interstitial sites (¹₄,¹₄,¹₄) in the structure. When all tetrahedral sites are filled, a maximum H/M ratio of 2 is reached which is known as the fluorite structure (CaF₂) illustrated in figure 1.3 a). Further filling of the octahedral interstices occurs in the lanthanoids but not in the transition metals. The reason for this is that the distance between the sites in transition metals is small, and there is an empirical rule known as the Switendick criterion, or the rule of 2 Å, which states that hydrogen atoms can be no closer than 2 Å due to H-H interactions [25].

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Figure 1.3. The possible interstitial sites for hydrogen (pink) in a fcc metal lattice (blue), where a) shows the tetrahedral and b) the octahedral geometries.

1.2.3.1 ABxinterstitial hydrides

A common strategy to improve the hydrogen sorption kinetics is to alloy strong hydride formers in the early d-block with later transition metals to destabilize the M-H bond. These are usually referred to as AB_x interstitial hydrides where A and B denote different metals. Common compositions are AB₅ and AB₂where the metallic radius r_m(A) > rm(B). This family of compounds is often investigated for hydrogen storage applications due to the high volumetric hydrogen capacity such as in LaNi5(AB₅) and Laves-phase based AB₂ alloys which is higher than that of liquid hydrogen [6]. Due to the high weight of transition metals their gravimetric hydrogen capacity is rather low (<2 wt%) which limits their applications to stationary large scale storage.

Moreover, they also often suffer from degradation during repeated hydrogen cycling [26, 27]

1.2.3.2 AB interstitial hydrides

AB alloys, where rm(A) ≈ rm(B) commonly crystallize in W-type bcc or CsCl- type structures. The most famous example for hydrogen storage applications is TiFe which is made up from relatively cheap and abundant metals. TiFe however has severe problems with surface passivation and kinetics, requiring rigorous conditions for hydrogen absorption in the range of 600 ^◦C and a hydrogen gas pressure of several hundred bar [9, 28]. Another family of compounds in this category is bcc alloys based on Ti and V that have hydrogen capacities as high has 4 wt% with overall decent sorption properties for storage applications [29]. One key feature of this alloy system is that the thermodynamic stability and sorption kinetics can be tuned by varying the Ti/V ratio or alloying with other elements such as Fe and Mn [30–32]. The use of Fe as an alloying elements also has an economical advantage where it could be

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possible to replace expensive high-purity V with much cheaper ferrovandium which contains about 20% Fe [33].

1.3 High Entropy Alloys

1.3.1 Core concepts

A new alloying strategy was introduced by Yeh et al. in 2004 where you mix (typically) four or more elements in near equimolar concentrations, thereby moving away from the corners and into the middle of the phase diagram [34].

This kind of alloying has attracted a lot of attention in the recent years due to some excellent reported high temperature mechanical properties, magnetism, corrosion resistance, energy storage and conversion [35, 36]. The alloys are often called High Entropy Alloys, since it is believed that the high entropy of mixingΔSmixstabilize their simple crystal structures such as bcc, ccp or hcp in favour of intermetallic phases. The entropy of mixing,ΔSmixcan be estimated with the Boltzmann formula for an equimolar alloy containing N elements as is shown to the left in figure 1.4. The community have among other definitions of HEAs stated that the entropy of mixing has to be larger than 1.6R (where R is the gas constant), which according to figure 1.4 corresponds to a minimum of five principal elements.

Figure 1.4. Illustration of the increase in mixing entropy when adding more principal elements (left) and the random solid solution it is believed to stabilize (right)

One key feature of these alloys is that they are ascribed to be inherently strained in their crystal structure originating from the different sizes of the constituent elements. This is often quantiﬁed by the parameter δ calculated

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using equation 1.5, where c_i and r_i are the atomic fraction and radius of ele- ment i and ¯r is the average atomic radius.

δ =

N i=1

∑

ci(1 −ri

¯r) · 100% (1.5)

A big effort of the HEA community has been to establish design rules for predicting the formation of solid solutions in HEAs over other intermetallic phases. One example is that theδ should be below 6.6% and that the entropy of mixing has to be bigger than the enthalpy of mixing at the melting point [37]. Another descriptor that has proven successful is the valence electron concentration, V EC:

V EC=

∑

^N

i=1

c_i(VEC)i (1.6)

which is a weighted sum of the valency among the constituent elements. It has been suggested in the literature that bcc solid solutions are formed if V EC<

7.6 and a VEC > 7.6 promotes ccp phases [38, 39].

1.3.2 Hydrogen sorption in HEAs

Combining hydride forming d-block elements into a HEA produces alloys with potential hydrogen sorption properties similar to that of the W-type AB interstitial alloys described in section 1.2.3.2. What is interesting about these kind of metal hydrides is the possibility of vast chemical tunability.

The ﬁrst investigations into HEAs for hydrogen storage were done by Kao et al. and Kunce et al. on the compositions Ti_xV_yZr_zMnFeCo, TiVCrFeNiZr and TiVZrNbMo [40–42]. X-ray diffraction revealed that these compositions are not single-phase solid solutions, but have other intermetallic phases present such as hexagonal C14-type Laves phases (P63/mmc). Kunce et al. also produced a HEA based on LaNi5 with additional Fe, V and Mn by Laser En- gineered Net Shaping (LENS). These alloys were also comprised of multiple crystalline phases which changes fromσ +La(Ni, Mn)5to f cc+La(Ni, Mn)5

upon hydrogenation [43].

Sahlberg et al. investigated the hydrogen uptake of bcc (Im¯3m) TiVZrNbHf [44]. This alloy showed a remarkably high hydrogen uptake of 2.5 hydrogen per metal, usually only observable in RE based metal hydrides such as CeH2+x. Full occupation of the tetrahedral and octahedral sites would yield H/M = 2 and H/M = 1 respectively, requiring both interstitial to be substantially ﬁlled simultaneously in this metal hydride. This is usually not the case for transition metals, as the distance between these sites is less than 2 Å, and thereby violates the Switendick criterion [25].

This effect was ascribed to the fact that the metal hydrides phase adopts a bct (I4/mmm) crystal structure, which is symmetry related to fcc (Fm¯3m)

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but elongated along one axis, making the distance between the sites slightly longer. It was also suggested that the large atomic size-mismatch,δ = 6.96%, would cause locally distorted surroundings for H, making more sites available for hydrogen occupation than in a conventional alloy.

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2. Scope of this thesis

The work presented in this thesis aims to investigate the hydrogen sorption in the rather new class of materials known as High Entropy Alloys. Due to the vast chemical tunability available in this kind of materials, it is imperative that new design rules are established so that new compositions can be developed by tuning only a select number of elements similar to that of ABx-type metal hydrides. Moreover, a HEA based metal hydride,TiVZrNbHf, has shown remarkably high hydrogen contents, exceeding that of it’s binary counterparts, which has been suggested to be an effect of the atomic size mismatch of the constituent elements. To address these topics, detailed understanding of the materials crystalline structure, one of the most fundamental property of a material (which dictates it’s bulk properties) is needed. With these aspects in mind, the present work aims to;

• Synthesize a wide range of HEAs.

• Explore the hydrogen sorption properties of these materials systemati- cally and develop design strategies for HEA-based metal hydrides.

• Investigate the origins of the high hydrogen content in TiVZrNbHf.

• Study the effect of using differently sized elements on the crystalline structure at the local level.

• Design novel HEAs for hydrogen storage.

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3. Methodology

The results covered in this thesis are mainly experimental, covering the synthesis of new alloys and subsequently establishing relations between the crystalline structures and their hydrogen sorption properties. Therefore, this chap- ter will ﬁrst cover the techniques used during synthesis of the alloys and their corresponding metal hydrides/deuterides by high temperature techniques and solid-gas reactions. Following this is a brief introduction to the scattering techniques that have been used to establish the structural parameters of the materials in real time during hydrogen uptake or release or more detailed at the local level.

3.1 Synthesis

3.1.1 Arc melting

All alloy samples covered in this thesis were produced by high temperature synthesis from the constituent elements by arc melting. In arc melting, a DC voltage is applied between a W cathode and a water cooled copper hearth, striking an electric arc which ionizes the gas creating a plasma. This enables very high heating rates to high temperatures. The high entropy alloys were all synthesized by arc melting in argon atmosphere to protect the alloys from oxidation. Prior to melting, the chamber was ﬂushed with Ar several times, and a Ti "getter" piece was melted prior to melting the samples to reduce O2

contamination in the chamber. The samples were remelted several times and ﬂipped between each melting step to improve the homogeneity.

3.1.2 Hydrogenation

Metallic metal hydrides can be synthesized by direct solid-gas reactions between the bulk metal or alloy with hydrogen gas. The reaction is exothermic and spontaneous but requires what is called activation of the sample due to surface oxides preventing hydrogen diffusion into the bulk. This activation step is typically done by heating in dynamic vacuum or low pressure hydrogen atmosphere or repeated hydrogen sorption cycles. Hydrogen can then be absorbed by the sample with the introduction of hydrogen gas to the stainless steel autoclave in setups similar to what is illustrated in ﬁgure 3.1.

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Vent /

P

vaccum

H

₂

Pressure transducer

V

_ref

V

_cell

Figure 3.1. Schematic illustration of a Sieverts type apparatus for manometric sorption measurements.

3.2 Characterization

3.2.1 Thermodynamics and kinetics

The process of hydrogen absorption into a metal, M, by a combination of ad- sorption on the metal surface, dissociation of the H₂molecule and dissolution into the bulk that can be summarized by the chemical reaction:

M+x 2H2

absorption

−−−−−−

−−−−−−_desorption MHx+ ΔQ (3.1) whereΔQ is the speciﬁc heat of the reaction. At equilibrium, the chemical potential of the gaseous hydrogen is equal to that of hydrogen in the metal.

The equilibrium constant can therefore be simpliﬁed to be a function of only the hydrogen content and the partial pressure of hydrogen in what is known as Sievert’s law [45]:

K= H M·

P_H₂ (3.2)

3.2.1.1 Pressure-composition-isotherms

There are a variety of techniques available to measure the uptake of hydrogen in metals and alloys under various constraints. The most common one is called the Sievert’s method and operates by measuring the change in pressure (manometric) in a constant well calibrated volume. The technique is very popular due to it being cost effective, easy to set up and reliable. A schematic view of a Sieverts type apparatus is illustrated in ﬁgure 3.1.

The measurement is conducted by introducing hydrogen gas into a well calibrated reference volume (Vre f), and then subsequently dosed into the sample

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volume (V_cell) by opening the valves and measuring the pressure drop. If the system and sample volume are well known, one can calculate the expected pressure drop if no hydrogen enters the sample and from this estimate the hydrogen uptake. This is commonly done in various pressure steps at a constant temperature, and then displayed in so called Pressure-Composition Isotherms, with hydrogen content on the x-axis and the equilibrium pressure on the y-axis as is illustrated in ﬁgure 1.2. A plateau in the isotherm corresponds to theα toβ transition described previously.

Thermodynamic information about the hydrogen absorption can then be extracted by measuring the plateau pressure at different temperatures and making a linear ﬁt to the Van’t Hoff’s equation:

ln(Peq

P0) = −ΔH RT +ΔS

R (3.3)

where P₀is a convenient reference pressure (most often 1 bar H₂),ΔH (J/mol) andΔS (J/mol·K) are the enthalpy and entropy of the hydrogen-metal reaction, R and T are the gas constant (J/mol·K) and temperature (K).

The manometric measurements in this thesis were done in either a commercial automatic SETARAM PCT-PRO (papers I, V, II, VIII) or a home-built system (papers III,IV and V) [46].

3.2.1.2 Thermal analysis

The release of hydrogen from a metal hydride is endothermic, and is therefore often studied using different kinds of thermal analysis. There are different kind of parameters that can be monitored as a function of temperature such as pressure (thermal desorption spectroscopy, TDS), weight (gravimetry, TGA) and energy (differential scanning caliometry, DSC). While TGA gives information about the amount of hydrogen that is released, the other two give a characteristic temperature where the reaction rate is at it’s maximum, T_m, for a certain linear heating rate. This information can be used to evaluate how quickly or slowly the reaction takes place by using the Kissinger equation:

ln( β

T_m²) = − Ea

RTm+ ln(k0) (3.4)

where β is the heating rate, Ea is the activation energy, and k₀ is a reaction constant [47]. By measuring desorption at different heating rates, and ﬁtting a straight line of ln(_T^β2

m) versus_T¹_m, giving a slope equal to^E_R^a which can be used to estimate the activation energy of the reaction.

Thermal analysis covered in this thesis was done by TDS using a home built vacuum system (paper II) or by simultaneous TGA/DSC with a Netzsch STA 449 F3 Jupiter apparatus (papers III, IV and V).

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3.2.2 X-ray powder diffraction

X-ray diffraction is a powerful and common tool to study crystalline materials due to easily available lab sources. The technique utilizes the fact that the wavelength of the X-ray waves is similar to that of inter-atomic distances in crystalline solids, and can therefore scatter coherently. If there is long range order, the scattered waves will interact in constructive or destructive ways, giving rise to a pattern. This pattern is characteristic for a speciﬁc crystal structure and can hence be determined by diffraction. The diffraction conditions are described by Bragg’s law:

nλ = 2dsinθ (3.5)

where n is an integer, λ the wavelength, d the distance between the crys- tallographic planes and θ the scattering angle. From this, the symmetry and lattice cell parameter can be calculated by studying the angles of the observed peaks. Bragg’s law does not take into consideration the species that scatter, which is needed to explain the crystalline structure. We therefore need also consider the intensity of the diffraction peak, which is proportional to the square of the structure factor, F_hkl given by equation 3.6:

Fhkl=

∑

^N

n=1

fne²^πi·(hxⁿ^+kyⁿ^+lzⁿ⁾ (3.6) where f_nis the atomic scattering factor and 2πi(hxn+kyn+lzn) is the phase angle of atom n at coordinates x_n,yn,zn in the lattice. Since X-rays scatter off the electrons of atoms, fn is proportional to the atomic number (i.e. the number of electrons), which makes hydrogen practically invisible to X-rays in the presence of heavier elements such as Ti.

Diffraction patterns can be analysed using least square reﬁnement of the crystal structure to the experimental diffraction pattern by the Rietveld method [48]. In this method, the intensity of a reﬂection I_hklis described by:

I_hkl= S · Mhkl· Lhkl· Phkl· |Fhkl|² (3.7) where S is the scale factor, M_hkl the multiplicity of the reﬂections, L_hkl the Lorentz-polarization, Phkl the preferred crystallographic orientation and Fhkl

the structure factor. The shape of the peak is in turn described by a Pseudo- Voigt function (combination between a Gaussian and a Lorentzian):

Γ =

U·tan²(θ) +V ·tan(θ) +W (3.8) where U , V and W are reﬁnable peak shape parameters.

The laboratory X-ray diffraction data covered in this thesis were collected using Cu K_α(λ = 1.5046 Å) radiation on Bruker D8 diffractometers in Bragg- Brentano (papers I, II, V and VIII) or Debye-Scherrer geometry (capillary

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mode using 0.5 mm borosilicate glass capillaries) (papers III, IV and VII).

The data was analyzed using the Rietveld method implemented in the software packages Fullprof (papers I and II), TOPAS academic (papers V and VII) or GSAS I/II (papers III, IV and VI) [49–52].

3.2.2.1 Synchrotron X-ray powder diffraction

In addition to lab sources, X-rays can also be produced at a synchrotron light source. The source operates by accelerating electrons in a linear or cyclic accelerator to very high velocities. The electrons are then injected into a larger storage ring where they circulate without gaining speed by the use of electro- magnets. At certain points in the storage ring, light is produced by changing the direction of the moving electron, forcing it to emit light. If the electron is moving fast enough, the light will be in the X-ray energy range. The simplest way of doing this is by use of so called bending magnets, which also is the main tool to keep the electrons in their circular path around the ring. More modern synchrotron facilities use undulators to produce their radiation, which consists of a complex magnetic array, causing the electrons to a wavy trajec- tory. The beneﬁt of undulators versus bending magnets is that the energy range of the emitted X-rays is much narrower. The produced radiation then travels to a beamline, which consists of focusing optics and an experimental end station typically equipped with a large area detector for powder diffraction.

There are many beneﬁts of using synchrotron radiation in comparison with lab source X-rays. The energy of the photons can be tuned to the experimental needs, such as high energy X-rays to shoot through a thick sample environ- ment. The amount of photons per unit time (ﬂux) is also much greater than with laboratory sources, allowing very fast data collection to follow chemical reactions in-situ such as during heating or cooling. These properties of synchrotron radiation make it a powerful technique to follow the hydrogenation pathways of metal hydrides during solid-gas reactions with hydrogen. How- ever, high hydrogen pressures are often required at elevated temperatures, requiring the use of specialized sample holders.

To study hydrogenation pathways in metal hydrides, two different gas-cells have been used in this thesis based on designs by Norby (paper IV) and Jensen et al. (papers I, II and III) [53, 54] illustrated in figure 3.2. The Norby type cell consists of a basic Swagelok T-junction where the ends are connected to the gas panel, the goniometer and a capillary respectively. The capillary used in this setup is made of quartz and is fixed to the gasket with epoxy. The benefit of this cell is it’s simplicity and small size, allowing for some rotation during data collection to improve the powder statistics. The main drawback is that quartz capillaries and epoxy can only withstand low hydrogen pressures (<∼40 bar). To study reactions at higher pressures, the Jensen type cell was used which uses single crystal sapphire (Al2O3) capillaries which are rated to around 300 bars. The capillary is fixed into the gas cell by graphite ferrules at both ends, and subsequently pressurized from both ends simultaneously to

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avoid the powder being pushed into the opposite direction during quick gas loading. Both the setups enable heating of the sample by placing a hot-air blower close to the capillary, or in the Jensen setup a heating element wrapped around the capillary.

Gas

Thermocouple

a) b) Gas

Figure 3.2. Illustration of a) Jensen and b) Norby type gas cells for in-situ X-ray powder diffraction.

The synchrotron radiation X-ray diffraction covered in this thesis was conducted at the P02.1 beamline at the German Electron Synchrotron (DESY) in Hamburg, Germany (papers I, II and III) using λ = 0.2071 Å and a Perklin Elmer XRD1621 area detector, the Swiss-Norwegian beamlines (SNBL) at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France for papers III and IV at BM01 withλ = 0.7896 Å and a Dectris Pilatus 2M detector and for paper VI at BM31 withλ = 0.3171 Å and a CMOS DEXELA 2D detector.

3.2.3 Neutron powder diffraction

To determine the hydrogen position in crystalline structures, one can instead of X-rays use neutrons as the incoming scattering wave. The neutron scatters of the nucleus of the atom instead of the electrons, and therefore the scattering power is more randomized across the periodic table as is illustrated in ﬁgure 3.3. This makes the hydrogen isotope deuterium highly visible to neutrons.

Another property of the neutron is that it interacts weakly with matter, requiring much larger sample sizes than the ones used with X-rays. However, this is not always a drawback as it enables the use of more complicated and bulky sample environments around the sample such as cryostats, furnaces or pressure cells. The neutron also has a spin, which enables it to probe magnetic properties of materials.

Neutrons are not as easy to produce as X-rays however, as the two primary techniques used to generate them are nuclear ﬁssion and spallation which require big central facilities. In nuclear ﬁssion, a heavy nucleus such as enriched Uranium splits into two or more lighter nuclei, subsequently releasing several

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D

H C O Al Si Fe X-ray cross section

Neutron cross section

Figure 3.3. Comparison between the scattering cross section of selected elements with X-rays (top) and neutrons (bottom)

neutrons and γ-radiation, resulting in a steady stream of neutrons from the reactor core. A large amount of energy is also released from this reaction, which must be removed, limiting the total neutron ﬂux that can be generated at research reactors. There is also the problem with accumulation of nuclear waste by this process, which remains hazardous for a considerable time span.

Spallation produces neutrons by bombarding a heavy nuclei such as mercury, tantalum or tungsten with high velocity protons from an accelerator. Most modern neutron facilities operate by this technique, including the European Spallation Source (ESS) currently under construction near Lund in Sweden.

Both ﬁssion and spallation produce neutrons that are too fast for practical uses such as scattering techniques. Therefore they have to be moderated, i.e.

slowed down before being guided to the instruments, by passing through a medium such as liquid H2, CH4or H2O.

The neutron powder diffraction covered in this thesis was carried out at the JEEP-II reactor at the Institute for Energy Technology (IFE) in Kjeller, Norway for paper I on the PUS diffractometer using monochromatic neutrons with a wavelength of 1.54 Å [55] and at the ISIS pulsed Neutron and Muon source in Oxfordshire, UK on the instruments GEM (paper VI) and Polaris (paper V) [56, 57]

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3.2.4 Total scattering

A perfect crystalline material with all atoms at rest in a periodic pattern would only allow scattering in directions allowed by Bragg’s law (equation 3.5).

Such materials do not really exist as the atomic arrangement in real crystals will always exhibit some degree of disorder such as thermal vibrations, substi- tutional disorder, vacancies, dislocations or stacking faults. This gives rise to what is known as diffuse scattering between and underneath the Bragg peaks.

In regular diffraction, this is inseparable from the background and therefore most often ﬁtted with a polynomial and then discarded.

Total scattering is then an extension of conventional diffraction where one also takes into account this diffuse scattering along with the Bragg scattering.

These experiments require careful extra measurements in order to decouple the diffuse scattering from the background, such as an empty sample container, the empty instrument and in the case of neutrons a V-rod to normalize the data.

Subtracting these signals from the diffraction pattern yields what is known as the total structure factor, F(Q).

Analysis of total scattering data is often conducted in real space (instead of reciprocal space as conventional diffraction) with the pair distribution function (PDF) G(r) which is a histogram of the distances between atom pairs in the structure. This can be obtained experimentally by a Fourier transform of F(Q):

G(r) = 1 (2π)³ρ0

_∞ 0

4πQ²F(Q)sin(Qr)

Qr dQ (3.9)

where ρ0 is the average number density of the scattering system. As can be seen in the integral of equation 3.9, it is necessary to cover a very wide range in Q during the measurement to obtain a high quality PDF. This is often accomplished for neutrons by using time-of-ﬂight (ToF) based diffractometers with large arrays of detector banks at spallation sources and for X-rays with short wavelengths and placing a 2D-detector very close to the sample at a synchrotron source. A more formal deﬁnition of the the G(r) is:

G(r) =

∑

ⁿ

i=1

∑

n j=1

cicjbibj[gi j(r) − 1] (3.10) where it is summed over all n different chemical species within the system that have concentration c_i and coherent scattering length bi. This can also be described as a sum of all the partial pairs in the system by the partial PDF, gi j(r):

gi j(r) = 1 ρj

n_{i j}(r)

4²dr (3.11)

where ρj = cjρ0 and ni j is the number of atoms of type j at a distances between r and r+ dr from a central atom of type j. Figure 3.4 illustrates the PDF of a (2D) simple cubic system containing only one atom type. To the left

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Figure 3.4. Illustration of the pair distribution function G(r).

one can see the coordination rings stemming from the central atom which then in turn generate peaks in the G(r) to the right at a distance dr from the central atom, where the intensity correlates to the amount of atoms at that distance.

The corrections and Fourier transforms for total scattering covered this thesis (paper VI) was done using the softwares GudrunN and GudrunX [58].

Structural analysis is then carried out on either a small or a big box of atoms.

Small-box modelling is very similar to the Rietveld method described in section 3.2.1 but in real space instead of reciprocal space. In this case, one uses the symmetry of the crystal system to reduce the amount of atoms needed to calculate larger distances in the PDF. Big-box modelling is often done by the reverse monte carlo algorithm on boxes containing more than 10,000 atoms.

The algorithm works by first constructing the big structure model based on crystallographic information obtained from a Rietveld refinement and calcu- lating a theoretical version of the G(r). An atom is then selected at random within the model and is allowed to move by either a slight translation or swap- ping places with another atom. The algorithm then calculates a new theoretical G(r) after the swap, and the move can then be either accepted or discarded depending on how it effects the agreement with the experimental data. A discarded move can also be accepted based on a certain probability to get the most disordered structure possible that fits with the experimental data. The

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RMC modelling covered in this thesis was done in the software RMCProﬁle v7 [59].

3.2.5 Neutron spectroscopy

The diffraction based scattering covered so far in this thesis is elastic, meaning the energy of the incoming and outgoing scattering wave is the same. How- ever, energy can also be transferred between the neutron to the scattering system and vice versa making the scattering inelastic. Measuring both the energy transfer and direction of the scattered neutrons enable a wide variety of dynamics and excitations of materials to be investigated. The measured intensity of a scattered neutron beam is related to the simpliﬁed double differential cross section avaraged over time:

d²σ dΩdEf = 1

N

kf

k_i

1 2π

_∞

−∞

∑

dd

∑

j j

b^∗_jb je^−iEte^−Q·R^j⁽⁰⁾e^−Q·R^j^(t)dt (3.12)

The important part of equation 3.12 is the term b^∗_jb jwhich represents and average over spin and isotope distributions, particularly important for hydrogen.

The term can be split depending on if the isotopes and spins are correlated or not:

b^∗_jb j=

b^∗_db_d i f j= j

|b^∗_d| i f j= j (3.13) The results from equation 3.13 is that we can measure both collective dynamics (coherent, phonon dispersions) and single particle dynamics (incoherent, vibrational properties). Hydrogen has a very large incoherent cross section for neutrons (79.7 barn), making INS an ideal tool to probe it’s vibrations. This technique is very similar to more readily available vibrational spectroscopy such as infrared or Raman, but it does not suffer from any selection rules, meaning all vibrations can be measured. The INS covered in this thesis (paper VII was measured at ISIS Neutron and Muon source, Oxfordshire, UK on the indirect-geometry spectrometer TOSCA [60].

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4. Results and discussion

A transition metal HEA, TiVZrNbHf, has been reported to have breached the limit of H/M = 2, and also reaching this content in a single step, indicating that it behaves more like RE-based metal hydrides rather than ones based on transition metals [44]. This large hydrogen content was speculated to be due to the size mismatch,δ, of the constituent metals causing local distortions of the interstitial sites, making some of the octahedral ones accessible for hydrogen occupation.

In paper I the structural and hydrogen sorption properties of TiVZrNbHf is studied in more detail.

The effect of theδ parameter on the hydrogen sorption is the main focus of papers II and III. In paper II this was tested by replacing the smallest element, V, by Ta (one closer in size to the others) thereby reducing the mismatch. Paper III is a more extended study that spans a wider range in δ by varying the Zr and Ta contents in the systems TiVZr1+zNb where z∈ (0,0.20,0.50,0.75,1) and TiVZr_zNbTa_{1 – z} where z∈ (0,0.15,0.50,0.74). The focus of paper IV is to test the effect of another HEA parameter, V EC, on the hydrogen sorption properties on HEAs based on TiVNb.

Paper V then revisits TiVZrNbHf with the knowledge of HEA parameters on hydrogen sorption obtained in papers II, III and IV in an attempt to discover the reason for the unusually high hydrogen content reported in the literature.

An inherent effect of having many elements occupying the same crystallographic site is that hydrogen will have a wide range of different possible local metal-hydrogen coordination’s in the structure. Papers VI and VII probe the local environments of hydrogen using neutron scattering to see if it preferen- tially sits in the proximity of certain elements.

Finally, a data-driven approach is used to predict hydrogenation properties of HEAs with targeted stability for experimental validation.

4.1 TiVZrNbHf, the benchmark HEA

The hydrogenation pathway in TiVZrNbHf was described in the literature to be in a single step, combining the reaction pathways of ordinary transition metal and RE metal hydrides [44]. To further elucidate this behavior, in-situ XRPD was performed during hydrogen absorption at elevated hydrogen pressures, as well as cycling between hydrogen and vacuum. It was seen that the α to β transition takes place just below 300 ^◦C. The α phase was seen to

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accommodate a volume expansion of up to 4 Å³(not accounting the thermal expansion), which using the Piesls relation [61] (volume expansion of 2.9 Å³ per hydrogen in Laves phase metal hydrides) accounts for a hydrogen content of H/M = 1.38. The β phase observed during the in-situ experiments showed a decrease in the c-direction when lowering the symmetry from cubic (Fm¯3m) to tetragonal (I4/mmm), instead of the increase seen previously in reference [44] which could be due to either thermal behaviour or the elevated pressure of 100 bar. Switching from hydrogen back-pressure to dynamic vacuum proved that the hydride phase is stable at 300^◦C, while at 400^◦C a slight decrease in the unit cell parameter is observed, indicating that some hydrogen is released from the structure (0.3 H/M using the Piesls relation). At 500^◦C, the reaction is fully reversible as can be seen in figure 4.1. The reaction rate of hydrogen absorption was extracted from the quasi-linear region of phase contents from sequential Rietveld refinements. It was seen that the rate increases as a function of the cycle number up to a maximum of 20 % after 3 cycles. This is commonly observed in metal hydrides as continued absorption- desorption introduces strain and particle refinements in the material [62, 63].

Further increase in temperature was seen to induce phase separation after the ﬁrst absorption-desorption cycle. It has later been shown that this HEA is only meta-stable, and separates into two hcp phases and a C14-type Laves phase at around 600^◦C if heated in Ar [64].

Figure 4.1. Densiometric view of X-ray diffraction patterns during hydrogen cycling (left) and Rietveld ﬁt to ex-situ neutron diffraction data (right)

The unusually high H/M content of 2.5 also requires signiﬁcant occupation of both tetrahedral and octahedral interstitial sites. To locate hydrogen within the structure, both in-situ and ex-situ neutron diffraction was employed. The in-situ experiments used a stainless steel sample holder to be able to withstand the high deuterium pressures required. However, steel is a very strong neutron scatterer, and TiVZrNbHfDx is not. The results were therefore dominated by the signal from the sample holder, rendering the data quality quite poor. Ex- situ measurement on a deuterated sample provided much clearer data as is

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presented in ﬁgure 4.1. These data could be ﬁtted well in a tetragonal crystal system (I4/mmm) with deuterium located in both tetrahedral (0¹₂¹₄, 0¹₂³₄) and octahedral interstices (00¹₂) at 92.9 % and 5.2 % occupancy respectively (H/M

= 1.91). These data could, however, also be ﬁtted very well in cubic symmetry (Fm¯3m) with deuterium exclusively in tetrahedral interstices (¹₄¹₄¹₄) with only a slight increase in the agreement factor to the data (Rwp= 3.68% compared to R_wp= 3.48%, lower is better), making the results a bit inconclusive.

Figure 4.2. Pressure composition isotherms of TiVZrNbHf during absorption and the corresponding Van ’t Hoff plot

The thermodynamics were also evaluated using PCI measurements and subsequent Van ’t Hoff analysis. Three different temperatures were measured at pressures up to about 10 bar that is presented in ﬁgure 4.2. It s clear that H/M

= 2.5 could not be reproduced, which is attributed to the lower pressure used in these experiments (10 bar in comparison to 50 bar for H/M = 2.5). The thermodynamics obtained from the Van ’t Hoff is in range of what is expected from a quite stable metal hydride with ΔH = -59 kJ/mol H2 in good agreement to the high desorption temperature observed in the in-situ XRPD. ΔS is often seen as constant in metal hydrides at around 130 J/(K mol H2) as it is dominated by the entropy of gaseous hydrogen. This makes the measured value quite low (82 J/(K mol H2)), which is probably an effect of having to measure the isotherms at elevated temperatures due to slow kinetics (asΔS is temperature dependant and often tabulated at standard conditions).