ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2017

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1523

Hydrogen in nano-sized metals

Diffusion and hysteresis effects

WEN HUANG

ISSN 1651-6214ISBN 978-91-554-9928-0urn:nbn:se:uu:diva-320796

Dissertation presented at Uppsala University to be publicly examined in Ång/4001, Lägerhyddsvägen 1, Uppsala, Tuesday, 13 June 2017 at 13:30 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Professor Gavin Walker (The University of Nottingham, Department of Mechanical, Materials and Manufacturing Engineering).

AbstractHuang, W. 2017. Hydrogen in nano-sized metals. Diffusion and hysteresis effects. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1523. 61 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9928-0.

Metal hydrides can be used as hydrogen storage materials for fuel cells and batteries, and as sensors for detecting hydrogen gas. The use of metal hydrides for hydrogen storage can be hindered by poor kinetics and low capacity. Moreover, poor sensitivity, long recovery and response time, limit the applications of metal hydrides as hydrogen sensors. Diffusion is an important factor affecting the hydrogen kinetics and response time. Hysteresis effects accompany the phase transition of hydrogen in metals and can influence the properties of metal hydrides as well. These need to be considered in their applications as storage materials or sensors.

This thesis concerns the possibility of tuning hydrogen diffusion and studies the mechanism of hysteresis effects of hydrogen absorption in metals. In these experiments, nano-sized vanadium is used as the model system for these studies. Hydrogen concentration is determined by the light transmission. By measuring the concentration profiles and isotherms of hydrogen, it is possible to determine the diffusion coefficients and hysteresis effects.

A profound decrease of hydrogen diffusion in Fe/V(001) superlattice has been found, as compared to that in bulk vanadium. This result is interpreted as lower zero-point energy in octahedral site than that in tetrahedral site. Profound isotope effect on diffusion has also been found. Influence of clamping of the substrate on the diffusion of hydrogen with concentration in vanadium thin film is discovered. The diffusion coefficient below c = 0.1 [H/V] is close to that in bulk vanadium and decreases substantially when c > 0.1 [H/V] compared with that in bulk vanadium. This finding is interpreted as the site change from tetrahedral to octahedral occupancy when the hydrogen concentration increases. Large finite size effect on deuterium chemical diffusion is observed, which is concluded to be caused by D-D interaction change that will influence the deuterium chemical diffusion at different thickness of vanadium layers. However, finite size has no effect on hydrogen transport at extremely low hydrogen concentrations in Fe/V (001) superlattices, this illustrates that the interface can not influence the mean free path of hydrogen in any way. This is completely different from electron transport condition in nano-sized metals. Hysteresis effect is observed below critical temperature in Fe/V(001) superlattices; this occurrence confirms the hypothesis that hysteresis effect is caused by coherency strain in coherent transformation.

Keywords: Hydrogen, diffusion, hysteresis, optical technique

Wen Huang, Department of Physics and Astronomy, Materials Physics, 516, Uppsala University, SE-751 20 Uppsala, Sweden.

© Wen Huang 2017

ISSN 1651-6214ISBN 978-91-554-9928-0urn:nbn:se:uu:diva-320796 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-320796)

To my family

List of papers

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

I Influence of site occupancy on hydrogen diffusion in vanadium.

Lennard P.A. Mooij, Wen Huang, Sotirios A. Droulias, RobertJohansson, Xin Xiao, Ola Hartmann, Gunnar K. Pálsson, Max Wolff,Björgvin Hjörvarsson.Phys. Rev. B 95 (2017) 064310

II Concentration dependence of hydrogen diffusion in clamped

vanadium (001) films.

Wen Huang, Lennard P.A. Mooij, Sotirios A. Droulias, HeikkiPalonen, Ola Hartmann, Gunnar K. Pálsson, Max Wolff, BjörgvinHjörvarsson.Journal of physics: Condensed matter 29(2017) 045402(7pp)

III Diffusion of hydrogen in ultra-thin V (001) layers.

Wen Huang, Heikki Palonen, Sotirios A. Droulias, Ola Hartmann,Max Wolff, Björgvin Hjörvarsson.Submitted to Journal of Alloys and Compounds.

IV Finite size effects as a tool to accelerate the light interstitials.

Wen Huang, Martin Brischetto, Gunnar K. Pálsson, Ola Hartmann,Heikki Palonen, Sotirios A. Droulias, Max Wolff, BjörgvinHjörvarsson.Submitted to Applied Physics Letter.

V Experimental observation of hysteresis in a coherent phase

transition.

Wen Huang, Gunnar K. Pálsson, Martin Brischetto, Ola Hartmann,Max Wolff, Björgvin Hjörvarsson.Submitted.

Reprints were made with permission from the publishers.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Aim of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Transition metal hydrides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1 Thermodynamics and phase behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.1 Basic thermodynamics concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.1.2 Stress induced state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1.3 Hysteresis effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Diffusion of hydrogen in metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.1 Diffusion regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.2 Self-trapping and isotope effects on diffusion . . . . . . . . . . . . . . . 193.2.3 Thermally activated process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.2.4 Self-diffusion and chemical diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Fick’s law and Beer-Lambert law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.1 Derivation of Fick’s second law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.2 Solution of Fick’s second law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.3 Optical transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4 Experimental techniques and data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.1 Optical setup for diffusion measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2 Combining optical transmission and resistivity measurement . . . . 294.3 Sample design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.4 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5 Results and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.1 Influence of site occupancy on diffusion of hydrogen . . . . . . . . . . . . . . . . . 365.2 Concentration dependence of hydrogen diffusion . . . . . . . . . . . . . . . . . . . . . . . 375.3 Finite size effect on hydrogen diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.4 Hysteresis effects of hydrogen in metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

7 Svensk sammanfattning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

8 Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

1. Introduction

Graham [1] discovered hydrogen absorption in palladium more than a hundredyears ago. Hydrogen and its isotopes are absorbed by metals under ambientconditions to form metal hydrides. These hydrides can be used as hydrogenstorage materials for fuel cells and batteries [2, 3, 4] and as sensors for detect-ing hydrogen gas [2].

Metal hydrides can be formed under moderate pressure levels and temper-atures and possess higher hydrogen storage volume density than hydrogen ingaseous or liquid states in pressurized or cryogenic tanks [3]. For example,the volume densities of hydrogen absorbed on interstitial sites in a host metal,liquid hydrogen in cryogenic tanks, and compressed hydrogen gas in light-weight composite cylinders are 150 (at room temperature), 70.8 (1 bar, -252◦C), and <40 kg H2/m3 (800 bar), respectively [7]. This property confersmetal hydrides with safety and volume content advantages over gas and liq-uid storage methods [4]. Metal hydrogen storage systems include Mg-basedhydrides [4], complex hydrides [4], and intermetallic compounds [4, 5]. Mg-based metal hydride (MgH2) possesses a high hydrogen storage capacity of7.7wt% and exhibits low cost and good reversibility. The main disadvantagesof MgH2 is the high temperature of decomposition and slow desorption kinet-ics [4]. Complex hydrides, such as sodium alanates [6], lithium nitrides [7],and borohydrides, have gained increasing attention due to their light weightand large capacity for holding high numbers of hydrogen atoms per metal atom[4]. For example, the hydrogen content of LiBH4 can reach 18 wt%. How-ever, complex hydrides are not considered to be rechargeable carriers becauseof their irreversibility and poor kinetics. Hydrogen storage in intermetalliccompounds, namely, AB2, AB5 [8], and Ti-based body centered cubic [4, 9],has been studied for more than 30 years. However, only prototypes of on-board storage using intermetallic compounds are available because of theirlow hydrogen storage capacity. Therefore, scholars must develop methods forimproving the storage performance of metal hydrides as storage materials forfuel cells to solve the energy crisis and environmental pollution.

Metal hydrides are also applied as hydrogen sensors in various industries[2]. For example, in nuclear power stations [2], hydrogen can be generated inradioactive waste tanks through radiolysis of water or via the unwanted reac-tion of water with the reactor core at high temperatures; hydrogen explosionis possible cause for nuclear accidents, as in the case of Fukushima accidentin 2011. Furthermore, the hydrogen concentration must be monitored duringwelding and galvanic plating to avoid hydrogen embrittlement [2]. Introducing

9

hydrogen can alter the physical properties of metals and render them useful ashydrogen sensors. For example, the principle of optical sensor is that the ex-pansion of the palladium film after exposure to hydrogen stretches the fiber inboth radial and axial directions, resulting in a change of effective optical pathlength [10]. Studies have focused on improving the sensitivity, reversibility,recovery, and response time, of metal hydrides for hydrogen sensors [11].

The use of metal hydrides for hydrogen storage can be hindered by poorkinetics and low capacity. Moreover, poor sensitivity, recovery time, and re-sponse time, limit the applications of metal hydrides as hydrogen sensors [11].Diffusion is an important factor affecting hydrogen kinetics and response timeand should be considered in the applications of metal hydrides as storage ma-terials or sensors.

Previous studies reported that hydrogen, in contrast to bulk vanadium, re-sides in octahedral site in the α phase of Fe/V (001) superlattices [12, 13].From DFT calculations, it is known that clamping affects the site preferenceof hydrogen in vanadium thin film as the hydrogen concentration increases[14]. The critical temperature of phase transition for hydrogen in vanadiumdecreases profoundly with decreasing layer thickness in the nano-scale range.This material combination is a suitable model system for studying the influ-ence of site occupancy, clamping from substrate, and finite size on hydro-gen diffusion in nano-sized materials. We also studied the hysteresis effectsof hydrogen absorption and desorption upon coherent transformation; resultselucidate the hysteresis mechanism. This mechanism can be experimentallystudied using the model system Fe/V (001) superlattices. Therefore, nano-sized vanadium is chosen as the model system to explore these effects. Opticaltechniques [15, 16] are also used for these studies.

10

2. Aim of the thesis

My aim is to understand the diffusion of hydrogen in nano-sized materials.Hysteresis of hydrogen absorption is also investigated to elucidate the hys-teresis mechanism of hydrogen in metals.

The specific aims are as follows:

• To understand the effect of site occupancy on hydrogen diffusion in vana-dium (paper I),

• To explore the effect of clamping on hydrogen diffusion with concentra-tion in thin V-(001) film (paper II),

• To understand the finite size effect on hydrogen diffusion in confinedvanadium lattices (paper III and paper IV),

• To comprehend the mechanism of hysteresis effect of hydrogen absorp-tion on confined vanadium lattices (paper V).

11

3. Transition metal hydrides

Metal hydrides are classified according to their chemical bonds [17]. For ex-ample, alkali or alkaline metals in groups 1 and 2 in periodic table are morestrongly electropositive than hydrogen and form ionic bound hydrides. Cova-lent bond is formed in groups 11 and 17 in the periodic system because of dif-ferent electron configurations. For example, metal atoms with electronegativ-ity comparable with that of hydrogen in groups 11 and 13 form covalent poly-meric hydrides; nonmetallic elements with high electronegativity in groups 14and 17 form volatile covalent bonds with hydrogen. In addition, some metals,including lanthanides, actinides, and transition metals, form metallic bondingwith hydrogen.

Figure 3.1. Phase digram of hydrogen and deuterium in bulk vanadium. This figure istaken from reference [18].

Transition metals, such as vanadium, tantalum, niobium, or titanium, pos-sess incomplete electron subshells. The main features of transition metal hy-drides are interstitial alloys, where hydrogen resides in tetrahedral (Tz or Txy)or octahedral site (Oz) at different phases [19, 20]. Fig. 3.1 [21, 22] shows thephase diagram of hydrogen and deuterium in bulk vanadium [22]; hydrogenresides randomly in tetrahedral site in α and α ′ and resides in octahedral sitein β phase [21, 22, 23]. The α phase is a disordered solid solution, wherehydrogen behaves like a lattice gas at low concentrations [22]. At high con-centration, it is called α ′ phase, which can be described by liquid [22]. Thestructure is monoclinic for V2H (bct) (c/a =1.1) and is in ordered state in theβ phase and becomes disordered in the β ′ phase [22]. In γ phase (V H2), thestructure is of the fcc type [22]. For the δ phase (V3H2), the structure is locatedin the low temperature range and exhibits a monoclinic order state [22].

12

3.1 Thermodynamics and phase behavior3.1.1 Basic thermodynamics conceptsGibbs free energy can describe the energy absorbed or released in the wholechemical process at constant pressure. For specific conditions, the Gibbs freeenergy is defined by

G = H −T S, (3.1)

where H is the enthalpy, T is the temperature, and S is the entropy. Thisthermodynamic potential is used to describe hydrogen absorption and desorp-tion in metals. Hydrogenation and dehydrogenation are accompanied by achange in Gibbs free energy in metal-hydrogen systems. The change in Gibbsfree energy is defined by

ΔG = ΔH −T ΔS. (3.2)

Specifically, hydrogenation is expressed as

ΔG = GMH −GM −GH, (3.3)

where GMH is the Gibbs free energy for product after hydrogenation, GM isthe Gibbs free energy for metal before hydrogenation, and GH is the Gibbs freeenergy for hydrogen before hydrogenation. If ΔG>0, then the hydrogenationis endothermic; otherwise ( ΔG<0), the process is exothermic. G and ΔG aremacroscopic quantities that describe the entire system. Studying the Gibbsfree energy for single hydrogen atom is useful because it represents chemicalpotential μ [24]. This parameter μ is defined by the derivative of Gibbs freeenergy with concentration, as given by

μ =∂G∂c

, (3.4)

where c is the hydrogen concentration. The chemical potential of atomic hy-drogen in metal-hydrogen systems is expressed as

μH = hMH −T sMH. (3.5)

where hMH is the enthalpy per hydrogen atom, and sMH the entropy per hy-drogen atom. The chemical potential per hydrogen atom in metal-hydrogensystems is equal to the chemical potential per hydrogen atom in gas state whenunder thermodynamically equilibrium state and is dependent on concentrationand temperature of the system. Therefore, μH [25] can be obtained by mea-suring an isotherm for different pressure levels and hydrogen concentrationsin metals. Hydrogen can be described as an ideal gas at moderate temperaturesand pressure level; the chemical potential of molecular hydrogen in gas stateis given by

μH2 = kT lnpg

p(T )−Edi, (3.6)

13

To eliminate Edi and p(T ), we introduce the reference pressure as:

μ reH2

= kT lnpre

g

p(T )−Edi. (3.7)

If we assume that the hydrogen molecules are in equilibrium with the metalhydrogen systems, the chemical potential of each hydrogen atom is given by

ΔμH = ΔhMH −T ΔsMH =12

kT lnpg

preg. (3.8)

0.00 0.01 0.02 0.03n0 [atomic unit]

-2.0

-1.0

0.0

1.0

2.0

E hom

eff

[eV]

Figure 3.2. Changes in energy (representing the interaction of hydrogen with thehomogeneous electron gas with density n0 ) with increasing electron density. Thisfigure is adapted from Reference [26].

The heat of solution of hydrogen in metals can also be described usingeffective medium theory. In this theory [27, 28], the inhomogeneous systemis replaced by an effective medium of an homogeneous gas. The total energychange in embedding hydrogen to the transition metals is obtained as the sumof different terms [27]

ΔE(R) = ΔEeffhom(n0(R))+ΔEhyb(R)+ΔEc(R)+ ..., (3.9)

where R is the position of hydrogen in metals, this theoretical calculation canbe done conveniently in a self-consistent way. ΔEeff

hom(n0(R)), representingthe interaction with the homogeneous electron gas with density n0, plays amain contribution to the energy change, ΔEhyb(R) results from the differenceof between the hybridization of hydrogen with the d band of host metal andcorresponding hybridization with the electron gas. This term essentially con-tains effects of d band, since hybridisation with s and p electrons is describedwell by the effective-medium term [27]. ΔEc(R) is interaction of hydrogenwith the core electron. Fig.3.2 shows the energy change ΔEeff

hom(n0(R)) with

14

the electron density n0. ΔEeffhom(n0(R)) for hydrogen in vanadium is smaller

than that in Fe and Pd, which is caused by higher electron density in Fe andPd. This leads to that hydrogen prefers to reside in vanadium, as compared toFe and Pd.

Based on the electron density dependence of energy, the lattice will expandafter hydrogen adsorption into vanadium, thereby decreasing the energy of thesystem; this phenomenon is accompanied by phase transition due to the long-range characteristic of elastic H-H interaction. H-H interaction is attractiveat low concentration but becomes repulsive at relatively high concentrationsin bulk vanadium and thin vanadium layers [29]. The number of missing Hneighbors increases because the interface density increases with decreasingvanadium layer thickness in Fe/V (001) superlattices, resulting in reduced H-H interaction at high concentrations [29]. However, the H-H interaction issimilar among Fe/V (001) superlattices with different concentrations of dilutedhydrogen at different vanadium thicknesses [29].

3.1.2 Stress induced stateIn the presence of tetragonal distortion of vanadium, hydrogen may reside indifferent sites compared with that in the unstrained bcc vanadium lattice. Thetetragonal distortion of vanadium lattice can be produced through two tech-niques, namely, introducing external stress to strain vanadium and clampingof the lattice of the unstrained vanadium thin film by using a specific substrate;the vanadium lattice clamped by substrate expand profoundly along the c axisas hydrogen exceeds a certain concentration, and this can be used to obtaintetragonal distortion of the lattice.

The effect of external stress on the location of hydrogen on the α phase ofbulk vanadium-hydrogen system has been investigated by channeling method.A site changes from T to 4T when external compressive stress of 7 kg/mm2 isapplied along the [100] direction [30]. The physical origin of this change canbe understood by studying the potential profiles and wave function changesof hydrogen atoms, as seen in Fig. 3.3 [24, 23]. Hydrogen is localized to theT site in the absence of lattice strain. When the lattice is elongated alongthe c axis direction, the position of minimum potential energy is displacedgradually toward the Oz or 4Txy, around which the wave function is localized;this finding indicates that hydrogen will prefer to reside in the Oz or 4Txy sitesif strain along c axis direction exists.

The same idea can be used to understand hydrogen site occupancy in Fe/V(001) superlattice, which is deposited on MgO. Vanadium in Fe/V (001) su-perlattices is under biaxial compressive strain, which is caused by the smallerlattice constant of Fe (0.286 nm) and MgO (0.296 nm) than that of vanadium(0.303 nm). This phenomenon triggers the hydrogen site occupancy in vana-

15

Oz T T

Ener

gy

(eV)

w. f.

0.1

0.06

ε = 0

0

0.2

0.4

0.6

Figure 3.3. Potential energy profiles along the lattice axis direction at ε = 0, 0.06, 0.1.The wave function representing the population of hydrogen for ε = 0.1 is also shown.This figure is adapted from reference [24].

dium from tetrahedral to octahedral site by changing the potential energy land-scape at the entire concentration range of hydrogen [31].

When hydrogen is absorbed by the transition metal, it attracts or localizesthe neighboring metal d electrons, leading to weakened binding of interatomicmetals [32, 33] and eventually lattice expansion. To understand this physicalprocess, we first discuss the interaction of hydrogen with metals. The po-tential energy U of the metal-hydrogen system is a function of all hydrogencoordinates Y and metal atom coordinates X [34]:

U(X ,Y ) = Φ(Xo)+n

∑a=1

τaψ(X ,Ya), (3.10)

where Φ(Xo) is the potential energy in the periodic metal lattice without hy-drogen; τa is the occupation number of hydrogen in interstitial site a; andψ(X ,Ya) is the energy change after introducing hydrogen to the metals. Thederivative of potential energy change with the atom coordinate at the equilib-rium state is given by

ψa =∂ψ(X ,Ya)

∂X, (3.11)

which represents the force between the hydrogen and metal atoms. In theexperimental observation, the presence of lattice strain leads to increased vol-ume dilation upon hydrogen loading [35]. The volume dilation is determinedby force dipole tensor P, which is expressed as:

P = ψaR. (3.12)

16

In bcc metals, two distinct high-symmetry sites, namely, tetrahedral and oc-tahedral sites, exist. The dipole tensor can be used to describe lattice responseand is expressed as: [36]

Pi j =

⎡⎢⎢⎣

B 0 0

0 B 0

0 0 A

⎤⎥⎥⎦ . (3.13)

In nearly unstrained clamped lattice, for example, 50 nm-thick film, hydro-gen is exclusively found in Tz site at low concentrations. As concentrationincreases, the force exerted by hydrogen on metal atoms expands the latticealong the c axis direction because of clamping, thereby inducing changes inhydrogen site occupancy [36]. DFT calculations [14] show that increasingthe hydrogen concentration in the clamped vanadium layers promotes the Ozsite to become energetically favorable for hydrogen because of the tetragonaldistortion arising from uniaxial lattice deformation.

3.1.3 Hysteresis effectHysteresis effects are experimentally observed in transition metals, such asbulk vanadium, niobium, and palladium [37, 38, 39]. During phase transitionfrom α to β phase, large lattice expansion occurs along the c-axis direction, forexample in vanadium. This expansion generates defects, resulting in hystere-sis effect due to irreversible energy loss [37, 38]; hence, the pressure for hy-dride formation is larger than that for hydride decomposition, similar to phasetransition from β to γ phase [40, 38]. Fig. 3.4 shows the diagram of pressure-concentration isotherms, which represent the hysteresis effect of hydrogen intransition metals. It assumes that maximum concentration is 1 [H/M], cor-responding to the maximum pressure and hysteresis results in the process ofabsorption and desorption below c = 1 [H/M]. Experiments on hysteresis ef-fect are mainly conducted with heating and cooling processes or absorptionand desorption by changing the pressure level. In addition, no hysteresis ef-fect exists for phase transition from α to α ′ above critical temperatures inmetal-hydrogen systems [44].

Schwarz and Khachaturyan [41] theoretically studied the hysteresis effectand concluded that hysteresis can be due to coherency strain, which generatesthe barrier for hydrogen in coherent transformation. The system is locked ina metastable state until the increase in the chemical potential of hydrogen issufficient to overcome the macroscopic barrier during absorption [39]. Thisphenomenon results in hysteresis of pressure versus concentration betweenabsorption and desorption at a given temperature [41, 42].

17

0.0 0.2 0.4 0.6 0.8 1.0Concentration [H/M]

Pres

sure

[a.u

.] Absorption

Desorption

Figure 3.4. Schematic illustration of pressure-concentration hysteresis during hydro-gen absorption and desorption process. Maximum concentration is assumed to be 1[H/M].

3.2 Diffusion of hydrogen in metals3.2.1 Diffusion regimesHydrogen exhibits strong mobility in metal systems, and its mobility is largerthan any other elements in metals. Quantum effects can be observed becauseof the smaller mass of hydrogen than that of other interstitials; these effectsmay influence the diffusion of hydrogen in metals. Fig.3.5 represents therough subdivision of different regimes, namely, muon, protium, deuterium,and tritium, for hydrogen diffusion and shows the possible diffusion mecha-nism at different temperature ranges [43].

In the lowest temperature range, the light interstitial in metals is delocalizedin the form of band state if it is not trapped by the lattice defect. This phe-nomenon is called coherent tunneling, and the potential energy is the same foreach site where hydrogen can reside. As the temperature increases, hydrogenwill be localized in the lattice. The diffusion becomes a thermally activatedprocess from one interstitial site to another. Hydrogen exhibits diffusion bytunneling or hopping over the potential barrier from one site to another. Ther-mal activation is necessary to bring the energy of both interstitial sites to thesame height for the first case (this phenomenon is called incoherent tunneling).A higher energy is needed to overcome the barrier height for the second case(thermally activated jumps over barrier height); the activation energy (barrierheight) Ea is the difference of potential energy at the saddle point and theminimum (self-trapped) position for hydrogen in metals (Fig.3.5). This pro-cess will be discussed in detail in the next section. At the highest temperature

18

ranges, the hydrogen atom will be mainly in the states above the potential bar-rier height. This region is called fluid-like diffusion, where diffusion occurssimilar to that in dense gas.

Temperature

Band propagation (coherent tunneling)

Thermally activated tunneling (incoherent)

Thermally activated jumps over barrier

Fluidlike diffusion

Ea

Figure 3.5. Regimes of hydrogen diffusion mechanisms in metals at different temper-ature ranges. This figure is adapted from [43]. Ea is shown in this figure to clarify thebarrier height for hydrogen diffusion in thermally activated jumps.

3.2.2 Self-trapping and isotope effects on diffusionAs shown in Fig. 3.6, when hydrogen or deuterium is absorbed into metals,the local strain field introduced by hydrogen isotope to induce local strain,which decays as r−2, where r is the distance from the hydrogen atom [44].The displacement of the metal lattice in response to hydrogen isotopes altersthe potential energy landscape. After the relaxation of the lattice, the systemsare in equilibrium state, which is called self-trapped state [45, 46].

The energy difference between the minimum point for the self-trapped stateand the minimum point in the region free of self-trapping for hydrogen iso-topes in metal is known as self-trapped energy (Fig. 3.6). In the self-trappedstate, proton and its corresponding strain field is called polaron. Schaumann[47] reported the importance of the polaron effect on the diffusion of hydrogenin metals. Flynn and Stoneham [48] applied small polaron concepts on hydro-gen diffusion in metals. In the absence of lattice distortion, hydrogen isotopes,particularly for proton, similar to electrons, would propagate through the rigidlattice [49].

For hydrogen and deuterium self-trapped in metals, zero point energy of

hydrogen can be expressed as E0 =12 h̄√

km , where m is mass of isotopes, and

k is a spring constant. The zero point energy of deuterium is smaller thanthat of hydrogen because of the mass effect on different isotopes (the massof deuterium is twice as heavy as that of hydrogen) [43]. This phenomenon

19

Self-trapping energy

H D

ΔE

Figure 3.6. Illustration of self-trapping and isotope effect. Low high grey value linesrepresent potential energy landscape experienced by a hydrogen in metals before andafter relaxation of the hosting lattice, respectively. The red point represents a hydrogenatom. The enlarging drawing in the right represent the isotope effect on potentialenergy landscape.

results in faster hydrogen diffusion in metals compared with deuterium [50].The isotopic differences in hydrogen diffusivity are large, particularly at lowtemperatures in BCC metals V, Nb, and Ta. For example, hydrogen diffusesfaster than tritium by a factor of 20 or more at temperatures below -75 ◦C [50].

3.2.3 Thermally activated processThis section describes thermally activated tunneling and thermally activatedjumps for hydrogen in metals. In the thermal activation region, the proton islocated at the interstitial site, and hydrogen is self-trapped by the relaxationof the lattice. The neighbor sites will have high potential energy, and thetransfer of hydrogen to other sites needs thermal activation. Fig. 3.7 showsthermally activated tunneling process, which occurs at low temperatures ifthermal activation creates the configuration of landscape with equal potentialenergy in different sites. The transition rate is given by [43]

Γ ∝ J2exp(−Ea

kBT). (3.14)

where J is the tunneling matrix element [24], and Ea is the thermal activa-tion for the configuration in Fig. 3.7.

At high temperatures, hydrogen atoms are treated as classical particles,which induce thermally activated jumps over barrier height (thermal excita-

20

(a) (b) (c)

E

Figure 3.7. Thermally activated tunneling process. (a) The lattice is relaxed becauseof hydrogen at the left site, the proton has a lower energy. (b)Thermal activation hasbrought both energy levels to the same height, this makes tunneling process possible.(c) The lattice is relaxed at the right site, a new equilibrium state is created. The greyregions are wave function, which represent the probability that hydrogen atoms exist.This figure is adapted from reference [43].

tion). Temperature plays a significant role in diffusion in this region. Basedon Maxwell-Boltzmann statistics, the probability that a hydrogen atom willjump is given by

f (ξ ) =N(E > Ea)

Nt, (3.15)

where N(E > Ea) is the number of hydrogen atom with energy levels higherthan Ea; and Nt is the total number of hydrogen atoms. The jump frequencyis proportional to the probability f (ξ ), and the hydrogen diffusion is propor-tional to the jump frequency. Therefore, diffusion in thermally activated jumpsover barrier height is given by Arrhenius relation

Ds = D0(c)exp(−Ea

kBT). (3.16)

This equation is used to describe the temperature dependence of hydrogendiffusion in the classical diffusion region, where Ea is the activation energyfor hydrogen diffusion [51, 52]; kBT is the thermal energy; and D0(c) is theprefactor that contains a number of physical constants, including attempt fre-quency (hydrogen isotopes mass), and lattice structure (jump distance) [24].

3.2.4 Self-diffusion and chemical diffusionSelf-diffusion is a spontaneous movement of hydrogen atoms in metals andoccurs in the absence of concentration gradient. This process describes the

21

random walk of solute hydrogen atoms in metals. The hydrogen atoms are inincessant motion because of the action of fluctuating force exerted by the sur-rounding metal atoms. In this case, the net radial displacement of a diffusingatom is given by total displacement [53]

�Rn = �s1 +�s2 +�s3 . . .+�sn =n

∑i=1

�si, (3.17)

�si represents the jump vector in i step. If the individual jumps take place withequal probability and similar jump distances in all direction, then Rn is zero.This condition does not mean that the diffusing atom jumps back to the startingpoint but indicates that the jumps in all directions are equally probable. Toobtain the value of the magnitude of �Rn, we take the square of �Rn, as given by[53]

�Rn2=

n

∑i=1

�s j2 +2

n−1

∑j=1

n

∑k= j+1

�s j�sk. (3.18)

If we assume all lengths of individual jump vector as equal to s in n jumps

(jumps are random), thenn−1

∑j=1

n

∑k= j+1

�s j�sk = 0, Eq. 3.18 is then reduced to [53]

�Rn2= ns2. (3.19)

We collect the sum of square of jump lengths to the diffusion coefficients Dsin 3D cases with [53]

ns2 = 6Dst, (3.20)

where t is the total time in n jumps, and 6 is derived from diffusion in 3D forhydrogen in metals. The self-diffusion Ds can be expressed with an effectivediffusion length s between jumping sites and residence time τ in each site asfollows [53]

Ds = s2/6τ. (3.21)

If the random diffusion is described classically, then we can have the Einsteinrelation [54] Ds = kT B, which is based on Langevin equation. B is the mobilitydefined by B = v

f , which is the coefficient that represents the average velocityv of particle under the action of average force f .

Chemical diffusion is a net transport process that occurs in the presence ofconcentration gradient [24]. This process is always in nonequilibrium and isdriven by chemical potential. The chemical diffusion Dc can be described as

Dc =− fmBc∂ μ∂c

, (3.22)

where fm describes the change in the total contribution to flux when subse-quent rearrangement jumps of nearby atoms are included; B is the mobility;

22

∂ μ∂c is the derivative of chemical potential with concentration; and c is concen-tration. μ can be given by

μ = h+ kT ln(

cco − c

), (3.23)

where co is the maximum hydrogen concentration. For dilute hydrogen con-centration c ≈ 0, μ can be reduced to

μ = h+ kT ln(c)− ln(co) , (3.24)

If the mobility correlation factor fm equals to unity at dilute concentration,then,

Dc → kT B = Ds. (3.25)

This equation shows that chemical diffusion coefficient Dc approaches theself-diffusion coefficient Ds at low concentrations. In self-diffusion, a geo-metrical correlation exists among consecutive jumps. An atom that has justjumped tends to jump back with a larger probability than jumping to othersites. Thus, we need to introduce the mobility correlation factor ft for self-diffusion. The ratio of chemical diffusion and self-diffusion is given by

Dc

Ds=

1HR

ckT

∂ μ∂c

, (3.26)

where HR = ftfm

is the Haven’s ratio, and ckT

∂ μ∂c is the thermodynamic factor

Ttherm.By combining Eq. 3.26 and Eq. 3.16, the activation energy is included into

the relation of chemical diffusion and self-diffusion:

Dc =1

HR

ckT

∂ μ∂c

∗D0(c)exp(−Ea/kT ). (3.27)

Self-diffusion and chemical diffusion in bulk vanadium have been studiedin different concentrations and temperature ranges [24]. Self-diffusion co-efficients increase with increasing temperature and decrease with hydrogenconcentrations. These phenomena indicate that activation energy increaseswith concentrations, and prefactors do not depend on hydrogen concentra-tions [55]. The chemical diffusion coefficients decrease first and then increasewith increasing concentrations in bulk vanadium [56]. This phenomenon indi-cates that the chemical diffusion of hydrogen is influenced by H-H interaction,which is highly related to ∂ μ

∂c .

23

3.3 Fick’s law and Beer-Lambert law3.3.1 Derivation of Fick’s second lawFick’s first law connects the diffusive flux to the concentration under the as-sumption of steady state. This law describes that flux goes from regions ofhigh density to that of low density, with a magnitude that is proportional to theconcentration gradient. In 1D, the law is given by

J =−Dc∂c∂x

, (3.28)

where J is the diffusion flux that measures the amount of substance thatwill flow through a unit area in a unit time, Dc is the chemical diffusion, cis the concentration of substance, and x is the position. This process is un-der nonequilibrium conditions driven by a gradient in the chemical potential.Basing on the continuity equation [17]

∂c∂ t

+∂J∂x

= 0, (3.29)

we obtain the second law, which is expressed as:

∂c∂ t

=∂∂x

(Dc

∂c∂x

). (3.30)

Fick’s second law describes the evolution of hydrogen concentration, which isdriven by the concentration gradient as a function of position x and time t.

3.3.2 Solution of Fick’s second lawFig.3.8 shows the geometry of a sample in which hydrogen is applied and thendiffuses along x direction. At low concentrations, the diffusion coefficient isassumed to be independent of concentration. Fick’s second law is transformedinto

∂c∂ t

= Dc∂ 2c∂x2 . (3.31)

If the initial condition is

c(x = 0, t = 0) = co, (3.32)

c(x > 0, t = 0) = 0, (3.33)

then the boundary condition is

∂c∂x

|x=L= 0,∀t ≥ 0, (3.34)

24

H

x = 0 x = L

x

x = R

Figure 3.8. Geometry of a sample in which hydrogen is introduced at one side, asshow in the grey region (R ≤ x ≤ 0). Hydrogen then diffuses along x direction, whichis shown by the arrow.

Finally the solution of the Fick′s second law for the initial and boundary con-ditions given above is

c(x, t) = co

∞

∑k=1

[erfc

(2(k−1)L+ x

2√

Dct

)+erfc

(2kL− x2√

Dct

)](−1)k−1. (3.35)

If diffusion coefficients are not constant with concentration, then the an-alytical expressions are not available. Consequently, analysis of the data isrestricted to times at which the profiles fulfill the specific boundary and ini-tial condition. Under these conditions, concentration dependent Dc can beextracted from the profiles c(x) at different times t. The idea of integrating"Fick’s law" was introduced by Boltzmann [57]. The described absorptionconditions also fulfill the required criterion for applying Boltzmann method.Boltzmann reported that Dc is a function of c only, and c is expressed by a sin-gle variable x

2√

t ; thus, both sides of the Fick’s law equation are transformedinto new forms by introducing a new variable η , which is expressed as

η =x

2√

t. (3.36)

The new forms are∂C∂x

=1

2√

tdCdη

(3.37)

25

and∂C∂ t

=− x

4t32

dCdη

, (3.38)

then the solution is

Dc =− 12t

(dcdx

)−1 ∫ c

c0

x(c′)dc′. (3.39)

In this derivation, the concentration is constant at x= 0 for the initial condition,and the concentration derivative with position is zero for x = L. This solutionis used for semi-infinite condition in 50 nm in the current work.

A slight variation in Boltzmann’s method can be formulated as follows.Both sides of the equation can be integrated from x to L to obtain

∫ L

x

∂c(x, t)∂ t

dx = Dc∂c(x, t)

∂x|x=L −Dc

∂c(x, t)∂x

|x, (3.40)

where L is the length of the area in which the particles diffuse. If the boundarycondition at x = L position is

limx→L

∂c(x, t)∂x

= 0, (3.41)

the diffusion constant can be obtained from Eq. 3.40 by dividing by ∂c∂x and

is given by

Dc =−[∫ L

x∂c(x,t)

∂ t dx]

∂c(x,t)∂x

. (3.42)

To identify these two methods, we call the latter integration method. Thissolution is used to extract diffusion coefficients in the geometry (Fig. 3.8)when the derivative of concentration with position ∂c(x,t)

∂x is 0 for x → L. Thisalso holds for the boundary condition that concentration is 0 for x = L, whichis semi-infinite system.

3.3.3 Optical transmissionAfter incoming light passes through a metal, the intensity of the transmittedbeam is reduced by reflection and absorption. Light absorption can be under-stood in a way that the energy of photons is absorbed to activate electrons inthe metal. If the metal thickness (without hydrogen in our case) is t, then theabsorption per unit length is κ(λ ,0), transmitted light is Tr0, and incident lightis Ti; based on Beer-Lambert’s law, the flux of photons through the absorbingmaterials decays exponentially and is given by [25]

Tr0 = Tie−tκ(λ ,0), (3.43)

26

where λ is the wavelength of light. When absorbed by the metal, hydrogenexhibits different absorption coefficients caused by changes in the electronicstructure and lattice expansion. The transmitted light is given as:

Tr = Tie−(t+Δt)κ(λ ,c), (3.44)

where Δt is the increasing thickness caused by hydrogen, and c is the hy-drogen concentration. The relative change in transmission is

Tr

Tr0= e(t+Δt)κ(λ ,c)−tκ(λ ,0). (3.45)

By taking the natural logarithm, we obtains

ln(

Tr

Tr0

)= t(κ(λ ,c)−κ(λ ,0))+Δtκ(λ ,c). (3.46)

This equation can reflect the hydrogen content in metals and is a phe-nomenological description of changes in optical transmission due to hydro-gen; in this thesis, the main method used for studying hydrogen diffusion andhysteresis is based on hydrogen-induced optical transmission change in metal.

27

4. Experimental techniques and data analysis

4.1 Optical setup for diffusion measurementsFig. 4.1 shows the setup used for diffusion measurement. The setup consistsof a sample chamber, monochromatic light source, silicon detector, sampleholder, CCD camera, thermocouple, pressure gauges, multimeter, and vacuumpump. These components will be discussed in detail.

Figure 4.1. Schematic illustration of the setup used for hydrogen diffusion measure-ment in the samples. The figure is taken from reference [15].

The sample chamber consists of a viewport and stainless steel components.The window material is borosilicate glass, which is transparent for wave-length ranging from 400 nm to 2500 nm. A copper sample holder is placedbetween the sample and the chamber to maintain good thermal conductiv-ity. Monochromatic light (590 nm for all measurement) from light-emittingdiodes is driven by programmable stable power supply; the light shines onthe transparent glass, which is used to split the beam, allowing simultaneoustransmission measurement through the sample and fluctuation of light source.The system is passively cooled by the heat sink for uniform heat distributionthe environment. Between the mirror and the sample, a diffusor is used tohomogenize light illumination before transmission through the sample. Thelight source intensity is simultaneously detected by the amplified Si detectorto avoid the effect of light source fluctuation. A 8-bit charged couple camera is

28

used to detect light through the sample with and without hydrogen every fewseconds to record light transmission. The setup is enclosed in a box to avoidexternal light contamination.

Heating band wrapped around the sample chamber is used to heat the sam-ples. Thermocouple (K-type) is used to monitor the temperature on the surfaceof the sample chamber. Another thermocouple (K-type) is connected to theedge of the sample surface and is placed inside the chamber; this device candirectly monitor the temperature of the samples during the experiment.

The entire vacuum system is pumped by a turbomolecular pump backedwith an oil pump (Preiffer Vacuum Company). Residual gas analyzer is usedto detect hydrogen gas impurities and leakage. Pressure gauges with differentmeasurement ranges are used to evaluate the actual pressure in our experiment.The pressure values measured with the gauges are displayed with multimetersfrom Keithley. The metal valves from Swagelok are used to control hydrogenflow in the system. The hydrogen and deuterium gas (99.99%) used in theexperiment are from Air liquid. The gases are purified with getter materials(purifier) before being introduced into Fe-Ti hydride, which is used for tem-porary storage of hydrogen and deuterium for the experiment. The hydrogenand deuterium gases are further purified by absorbing into the Fe-Ti hydride.

The detailed sample information for the experiment is shown in Fig.4.4 andFig.4.5. After the sample is placed into the sample chamber, the system evap-orates within 2 days at 423 K. The pressure decreases to 10−9 mbar beforethe experiment. The camera capture images every few seconds when the mea-surement is running. If an image representing the sample with hydrogen isnormalized by the first image for the sample without hydrogen, then the con-centration at different positions can be extracted. The concentration profiles atdifferent times can be obtained after all images are normalized using the firstimage.

4.2 Combining optical transmission and resistivitymeasurement

Fig. 4.2 shows the sketch of the setup used for hydrogen isotherm measure-ment. This instrument consists of vacuum chamber, autovalve, sample holder,light source, light detector, pressure gauge, current source, and heating unit,and so on. The isotherms of hydrogen pressure versus light transmission aremeasured automatically with this technique by the step-wise pressure changewhen it is in equilibrium state at each point for absorption and desorption mea-surement. This process uses 1000 Torr gauge and 10 Torr gauge to measurehigh and low hydrogen isotope pressure levels, respectively; the pressure mea-surement range is 10−3 mbar to 103 mbar. A valve (216 server driven valveassembly) is controlled by MKS 244 controller to regulate the pressure in the

29

Figure 4.2. Schematic of the setup used for isotherm measurement. This measurementis to measuring hydrogen concentration by detecting light transmission change withhydrogen at different pressures, resistivity is used to detect hydrogen ordering anddisordering. This figure is taken from reference [58].

0.00 0.10 0.20 0.30-ln(T r / T r0 )

10 -2

10 0

10 2

p [m

bar]

513 K, Abs463 K, Abs

Figure 4.3. Pressure-transmission isotherms of Fe4/V28 superlattice.

sample chamber for absorption. Gas valves are also mounted to control thepressure automatically for desorption measurements.

A 625 nm single wavelength light source (LED) is selected for measur-ing hydrogen content, and the source is driven by power supply unit. Thiswavelength displays a larger transmission change after exposing to hydrogencompared with other wavelengths, as shown in the reference [58]. To increaselight transmission signal-to-noise ratio, a lock-in amplifier in an ac mode isselected. The used light source is incoherent so that this can decrease theinterference of the light speckled by sample and the incoming light. The heat-ing unit from Delta electronics is used to provide the current in the heating

30

jacket from hemi heating, which is used to heat the chamber and sample. Twothermocouples are connected to chamber and sample, respectively. The lighttransmitting through the sample and reflected by the mirror are detected bydifferent monitors. The function of the monitoring of light source is used tocompensate the effect from the fluctuation of light source. Four-point probetechnique is used to measure the in-plane resistance of the sample, a sourcemeter is used to provide current to the sample from external two pins, voltageacross the internal two pins is measured using nanovoltmeter, then the resis-tance can be calculated. Fig. 4.3 shows the pressure-transmission isothermsfor hydrogen absorption in Fe4/V28 superlattice at two different temperatures,which are measured through this optical technique [58].

4.3 Sample designVarious nano-sized thin films, including single crystalline V thin films andFe/V superlattices, are used in this project. All samples are grown usinga magnetron sputtering technique. Representative sketches of samples areshown in Fig. 4.4 and Fig. 4.5.

Figure 4.4. Sample is a 50 nm film of vanadium deposited on MgO (001) followedby 7 nm of palladium and 10 nm of Al2O3. Part of the film surface is left uncoveredof Al2O3 enabling dissociation and uptake of hydrogen. This figure is taken fromreference in [59]. No Al2O3 appeared on top for isotherm measurement.

The growth chamber uses high-purity argon as sputtering gas and high-purity materials as targets. The substrates are double-side polished MgO (001)to allow light to penetrate through the entire samples. MgO (001 ) is selectedas it exhibits a lattice parameter of MgO (001) = 0.421 nm, and the unit cell is

31

rotated by 45◦ for close to perfect matching when growing films. The distanced between the planes in the [110] direction for MgO is a110 =

aMgO√2

= 0.298nm. This result is close to the lattice parameters of vanadium (aV = 0.303 nm),iron (aFe = 0.287 nm), thereby allowing the epitaxial growth of these metals onMgO (001). Each sample is covered by a 7 nm-thick palladium capping layer

Figure 4.5. Scheme of the sample geometry [60]. m symbolizes the number of Fe/Vbilayer repetition, which are 46, 23, 11 for n = 1, 2, 4. The enthalpies of hydrogen inPd and Fe are higher than that in vanadium. So hydrogen mainly exists in vanadiumin the samples. Lateral diffusion along [110] direction is observed as shown by thearrow in the figure.There is no Al2O3 on top for hydrogen isotherm measurements inFe2/V14 and Fe4/V28 superlattices.

to prevent vanadium oxidation. In addition, palladium is catalytically activefor molecule hydrogen dissociation above room temperature. Palladium alsohas a higher chemical potential than vanadium, resulting in negligible effectson the outcome of the experiments. A 10 nm-thick optically transparent amor-phous Al2O3 thin film is deposited on top and sides of the sample, leaving a0.1 cm strip of the sample uncovered at one end, where hydrogen can migrateinto the vanadium layer. The film is oriented in such a way that the hydrogendiffuses in the [110] direction in the vanadium layer due to the epitaxial re-lationship between the film and the substrate. The samples are characterizedthrough X-ray scattering techniques. The detailed information of the samplequality is reported in reference [61].

32

4.4 Data analysisBased on Beer-Lamber law, hydrogen content is measured by

c = αln(

Tr

Ir0

), (4.1)

as discussed in the references [15, 58], α is scaling factor. α = -1.73 for Fe/V(001) superlattices is extracted by comparing the transmission in current hy-drogen absorption measurement to concentration from neutron measurementin ILL on similar samples. α = -1.38 for 50 nm thin film is extracted by com-paring the transmission in current experiment to the hydrogen concentrationin bulk vanadium in literature.

x [cm]0.0 0.1 0.2 0.3 0.4

c [H/

V]

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Figure 4.6. Black points show the concentration profiles at low concentration inFe4/V28 superlattices in 290 s after exposure to hydrogen. Red line is the fit withsolution of Fick’s second law [60].

If diffusion coefficients do not depend on concentration, particularly at lowlevels, then the diffusion coefficients are extracted by fitting the concentra-tion profiles with the solution in Eq. 3.35. The profile (black dots) and fit(red line) are shown in Fig. 4.6. The decrease in absorption rate may lead tounderestimation of the diffusion coefficients; the slow absorption rate at lowtemperatures in the studied ranges leads to overestimation of the activationenergy by 20% to 25%.

The present investigation also focuses on concentration-dependent diffu-sion. Numerical methods shown in Eq. 3.39 and Eq. 3.42 are used to extractthe diffusion coefficients from the concentration profiles shown in Fig. 4.7.The former is called Boltzmann’s method, and the latter is named integra-tion method. Experimentally, these methods hold for t ≤ 110 seconds in thepresent high concentration experiments. The methods are suitable becauseall c(x, t) values are available at constant intervals in x and t; the derivatives

33

x [cm]0.0 0.1 0.2 0.3

c [H

/V]

0.0

0.1

0.2

0.3

0.4

0.5110 s65 s20 s

Figure 4.7. Hydrogen concentration profiles at different time at high concentration in50 nm vanadium film, which is taken from Huang et al., measurement [59].

can be found easily. Compared with Boltzmann method, integration methodwould also be advantageous, that is, if the time t = 0 or the position x = 0are not accurately known (which is not the case here). For hydrogen diffusionat high concentrations, chemical diffusion is corrected to self-diffusion withthermodynamics factor in Eq. 3.26 for Arrhenius analysis. The thermody-namic factor Ttherm = c

kT∂ μ∂c can be obtained with Eq. 4.1 and Eq. 3.8 utilizing

the measured isotherms. For numerical methods discussed, large uncertain-ties (the uncertainty is 10−6cm2/s) of chemical diffusion coefficients appearin the low concentration ranges due to its sensitivity to the position deriva-tive and time derivative in the low concentration range (Fig. 4.7). Boltzmannmethod is used for low concentrations due to its smaller sensitivity to the timederivative.

In this study, resistivity is measured to detect the order magnitude of hydro-gen in materials by using four-point probe technique. The following equationsare used to calculate resistivity [62]:

Rs = fa × VI, (4.2)

ρ = Rs × t, (4.3)

where Rs is the sheet resistance, V is the voltage between two internal probes,I is the current between two external probes, fa=π/ln2 is the geometric factorwhen the thickness of the vanadium layers are smaller than the distance ofpins, ρ is the resistivity, and t is the thickness of the sample. The uncertainty

34

of resistivity is 0.001 μΩ · cm, which is small because of sufficient waitingtime for the system to fully reach the thermal equilibrium.

35

5. Results and conclusions

5.1 Influence of site occupancy on diffusion of hydrogenH diffusivity in the Fe3/V21 superlattice at low concentrations is investigatedusing optical technique [63] (paper I). As shown in Fig. 5.1, the hydrogendiffusion coefficients decrease compared with that in bulk vanadium at lowconcentrations in the α phase when the vanadium layers are confined by adja-cent iron layers. Hydrogen is forced to reside in octahedral site in Fe3/V21 dueto the compressive stress from iron and MgO, but hydrogen resides in tetra-hedral site in the α phase in bulk vanadium. The barrier height for hydrogenwith Oz site occupancy in Fe3/V21 is larger than that for hydrogen with T siteoccupancy in bulk vanadium; as such, the hydrogen diffusion coefficients inFe3/V21 are smaller than that in bulk vanadium.

Figure 5.1. Arrhenius relation for hydrogen and deuterium diffusion in Fe/V superlat-tices, which are shown with solid and empty red circles. Red lines are fit to the results.Other points are from literature used for comparison [63].

First-principle method is used to calculate the corresponding potential en-ergy landscape of vanadium [63] , as shown in Fig. 5.2. Hydrogen prefers toreside in Tz sites when c/a = 1, whereas hydrogen moves to Oz sites when c/a= 1.1 due to the energy landscape change. A decrease in zero point energyis obtained when hydrogen changes occupancy from tetrahedral to octahedralsite. Consistent with the experimental results, the barrier height for hydrogenjump in Oz sites, increases compared with that in Tz sites.

The diffusion rates between octahedral sites are higher than that in the or-dered β2 phase, consistent with significant blocking at high concentrations. As

36

shown in Table. 5.1, the activation energy for hydrogen and deuterium differsslightly more than the uncertainties of the fit, this small difference is explainedby the reduced zero point energy of deuterium compared to that of hydrogenin the self-strapped state.

Figure 5.2. Vanadium lattice structure and its different interstitials. Potential energylandscape is also shown for tetrahedral sites and octahedral sites for both c/a = 1 andc/a = 1.1 conditions [63].

Table 5.1. Activation energies and prefactors of hydrogen and deuterium for Fe3/V21.

Parameters Ea(eV ) D0(10−3cm2/s)H 0.217 ± 0.017 4.4 ± 1.9D 0.261 ± 0.027 9.0 ± 6.6

5.2 Concentration dependence of hydrogen diffusion(paper II) As shown in Fig. 5.3, the chemical diffusion coefficient decreasesat low concentrations, becomes minimum at approximately 0.3 H/M, and in-creases as the concentration further increases in the 50 nm thin film in the mea-sured temperature ranges. A similar trend was also found in bulk vanadiumhydride obtained by the Gorsky method [56]. However, the absolute diffusioncoefficient values at relatively high concentrations significantly differ betweenthe film and bulk vanadium.

The chemical diffusion is driven by the gradient in chemical potential withincreasing concentration, which is related to the H-H interaction. The correla-tion between the hydrogen motions, usually captured by Haven’s ratio HR(c)

37

c [H/V]0 0.1 0.2 0.3 0.4 0.5

D c [cm

-5/s]

100

101

523 Kbulk

523 K50 nm

503 K50 nm

483 K50 nm

Figure 5.3. Concentration dependence of chemical diffusion in vanadium at differ-ent temperatures. Circles represent current experiment and black triangles representresults from bulk vanadium.

c [H/V]0.0 0.1 0.2 0.3 0.4 0.5

[eV]

-0.20

-0.18

-0.16

-0.14

-0.12

-0.10

-0.08

c [H/V]0.0 0.1 0.2 0.3 0.4 0.5

f ther

m

0

1

2

3

4523 K483 K

523 K

483 K

Figure 5.4. Chemical potential extracted from the isotherm measurement from thesetup in Fig. 4.2. This figure is obtained from the study of Huang et al. [59].

(temperature independence) also influences the diffusion coefficient; HR(c) isthe ratio of the tracer correlation coefficient and the mobility correlation co-efficient [24]. Chemical potential and thermodynamics factors are extractedfor 50 nm V thin film to minimize H-H interaction (Fig. 5.4). Thermodynamicfactors are used to correct chemical diffusion to self-diffusion at different tem-peratures for thin film (Fig. 5.5).

The chemical diffusion is driven by the gradient in chemical potential withconcentration, which is related to the H-H interaction. Another effect that in-

38

c [H/V]0.0 0.1 0.2 0.3 0.4 0.5

D [10

-5 c

m2/s

]

0

1

2

3

4

5

6

7

8

bulk Ref. [4]

50 nm

Figure 5.5. Self-diffusion of hydrogen in a thin and bulk vanadium [55] at 483 K.

fluences the diffusion coefficient is the correlation between the hydrogen mo-tions, usually captured by Haven’s ratio HR(c) (temperature independence),which is the ratio of the tracer correlation coefficient and the mobility corre-lation coefficient [24]. In order to eliminate the effect of H-H interaction,the chemical potential and thermodynamics factors are extracted for 50 nmV thin film, as seen in Fig. 5.4. The thermodynamic factors are used to cor-rect chemical diffusion to self-diffusion at different temperatures for thin film,as shown in Fig. 5.5. Representative analysis of the temperature dependenceof the self-diffusion at three concentrations are shown in Fig. 5.6. Arrhe-nius analyses describe the temperature dependence in an adequate manner, inwhich the activation energy is extracted. The deduced change in the Ea withhydrogen concentration is illustrated in Fig. 5.7. The activation energy is ob-tained by the two different methods described above (Boltzmann and Integra-tion), which are applicable at low and moderate/high hydrogen concentrationregimes, respectively. The results of both methods overlap around hydrogenconcentration at 0.1-0.2 H/V, thereby highlighting the consistency of the meth-ods. At the lowest concentration range, we obtain activation energy close tothat in bulk vanadium. With increasing concentration, the activation energyincreases from 0.1 eV to approximately 0.5 eV in a relatively narrow concen-tration range. The blue triangles represent the results of the self-diffusion inexperiment by Kleiner (using NMR) and show the increase in the activationenergy with concentration up to approximately 0.12 eV at 0.67 H/M. Largerincreases are observed in the activation energy with increasing concentrationthan that reported by Kleiner et al. in bulk vanadium. This difference revealsthe profound effect of boundary effects on the obtained diffusion rate, in viewof the following reasoning.

39

1000/T [1/K]1.90 1.95 2.00 2.05 2.10 2.15

D [

10

-5 c

m2/s

]

1.0

10

0.04 [H/V]

0.23 [H/V]

0.43 [H/V]

Figure 5.6. Temperature dependence of hydrogen self-diffusion coefficient D for threeconcentrations (α and α ′ phases). The straight line shows the fits to the experimentresult with Arrhenius equation D = D0 exp(− Ea

kBT ).

c [H/V]0.0 0.2 0.4 0.6 0.8

Ea [e

V]

0.0

0.1

0.2

0.3

0.4

0.5

Oz2

Oz1

12

bulk

50 nm

50nm

Figure 5.7. Concentration dependence of hydrogen activation energy in vanadiumthin film (current results, red circles for results extracted from the Bolzmann methodand black squares for the integration method) and bulk (literature). The activationenergies Ea marked by red triangles and squares are from Oz1 and Oz2 sites in βphase for hydrogen in bulk vanadium [32]. The activation energies marked with bluetriangles are obtained in α ′ phase for the bulk vanadium hydrogen system [55] andthe activation energy of hydrogen in bulk vanadium at extremely low concentration is0.045 eV, as shown with black solid circle [50].

If the vanadium layer is clamped by the MgO substrate, then the lattice ex-pansion caused by hydrogen will be restricted to the direction perpendicular to

40

the surface. As hydrogen concentration increases, the expansion of the layerswill alter the tetragonality of the vanadium structure. This phenomenon re-sults in changes in the hydrogen site occupancy from the tetrahedral site to theoctahedral site [36]. Further insights in the involved processes are providedby DFT studies [14], which confirm a shift from tetrahedral to octahedral siteoccupancy at around c = 0.1 H/V. The observed increase in activation energyis therefore concluded to be caused by the uniaxial expansion of the vanadiumlayer with concentration and the resulting change from tetrahedral to octahe-dral sites. Results indicate the importance of strain on hydrogen diffusion in V,in which the site occupancy is affected by tetragonal distortion. Large changesare observed for prefactor with hydrogen concentration, and these changesmay be related to quantum effects at elevated temperatures [50]. However,these mechanisms are still not understood and require further experiment aswell as theoretical study. The approach described in the current work, whichallows a simultaneous determination of the diffusion coefficients for a largerange of concentrations in a single experiment, is highly promising as a routetoward achieving better understanding of hydrogen in metals.

5.3 Finite size effect on hydrogen diffusionThis work is first study on the interface or finite size effect on hydrogen dif-fusion in confined systems, as seen in references [60, 64] (paper III and pa-

per IV).

Figure 5.8. Sketch of energy landscape of bilayer along the direction perpendicular tothe surface of the Fe/V(001) superlattices.

Fen/V7n (n=1,2,3,4) superlattices are used as a model system; ratio of 1 to 7ensures well-defined strain states through all superlattices. Fig. 5.8 shows theenergy landscape of the samples. At low hydrogen concentrations, hydrogendiffusion in Fen/V7n (n=1,2,4) superlattices is very close to that in Fe3/V21.The Arrhenius relation of diffusion coefficient values for Fe4/V28 are shown

41

Figure 5.9. Arrhenius plot of hydrogen diffusion at extremely low concentration inFe/V(001) superlattices. The diffusion data for the three samples almost overlap. Dif-fusion coefficient values for Fe4/V28 are shown in the plot, while the diffusion valuesfor Fe2/V14 and Fe1/V7 are shifted for clarity by a factor of ln(7) and ln(49), respec-tively. The lines represent the Arrhenius fit in the plot [60].

in Fig. 5.9, whereas the values for Fe2/V14 and Fe1/V7 are shifted for clarityby multiplying a factor of ln(7) and ln(49).

First, hydrogen resides in the interior region, and the effects of site depen-dence on hydrogen diffusion in vanadium were confirmed.

Figure 5.10. Diffusion coefficients with bilayer period at 493 K and 423 K for lowhydrogen concentration. Changes of the resistivity in Nb/Cu multilayers [65] are alsoincluded in the plot [60].

42

Second, finite size has no effect on hydrogen chemical diffusion at lowhydrogen concentration in Fe/V(001) superlattices. This result is consistentwith the negligible influence of H-H interaction at different thickness valuesof vanadium layers at low concentrations of hydrogen. On the other hand, theinterfaces do not affect the mean free path of hydrogen diffusion, compared tothe electron transport condition in metallic superlattices [65, 66], as shown inFig. 5.10.

2.0 2.2 2.4 2.6

0.10

0.15

0.20

0.25

0.30

0.35

2.0 2.2 2.4 2.6 2.0 2.2 2.4 2.6

-2

-1

0

1

Figure 5.11. Contour of temperature dependence of chemical diffusion coefficients atdifferent concentrations for different extension of vanadium layers [64].

In paper. IV, the concentration dependence of deuterium diffusion in Fen/V7n(n = 2,3,4) superlattices is investigated. The significant dependence of thedeuterium chemical diffusion coefficients on the extension of the vanadiumlayers at different temperatures and relatively high concentrations are found(Fig. 5.11). The deuterium diffusion coefficients at low concentrations aresimilar within the uncertainty (Fig. 5.12). The red square and triangle cor-respond to diffusion coefficients in Fe4/V28 and Fe3/V21, respectively, fromcomplementary error function (erfc) fit [64].

0.0 0.1 0.2 0.3 0.4 0.50.1

0.5

1.0

2.0

4.0

Figure 5.12. Deuterium diffusion coefficients plotted against concentration at differentextension of vanadium layers at Fen/V7n (2,3,4) superlattices. The red square andtriangle correspond to Fe4/V28 and Fe2/V14, respectively, from erfc fit [64].

43

Deuterium diffusion coefficients are shown in Fig. 5.12 and quantitativelycompared at different concentrations and vanadium thicknesses. A minimumdiffusion constant is found for each superlattice at concentrations between 0.2to 0.25 [D/V], which we define as Dcm.

1.8 2.0 2.2 2.4 2.6 2.8T!1 [10!3 K!1]

40

80

160

320

640

1280

Dcm"T

[10!

5cm

2K

/s]

Fe2V14

Fe3V21

Fe4V28

Figure 5.13. Product of deuterium minimum diffusion coefficients and tempera-ture verse inverse temperature at different extension of vanadium layers for Fen/V7n(2,3,4) superlattices [64].

Fig. 5.13 depicts the product of Dcm and temperature T and plotted againstinverse temperature for different superlattices. To obtain an idea of what maydominate the change in diffusion coefficients at similar temperature for differ-ent extensions of vanadium layers, the data can be fitted with Arrhenius model[59] and extract the activation energy and ∂ µ

∂c for the three samples. Aftermoving T to the left side of Eq. 3.27 and using the logarithm function on bothsides, the following is obtained:

ln(Dc(c,T )∗T ) = ln(ck

∂ µ

∂c∗Do(c)/HR(c))−Ea/kT. (5.1)

From the measurements at low concentrations, Ea and Do(c) are similar withinthe uncertainty for different thicknesses of the vanadium layers [60], and thusthe activation energy remained constant for the fits in Fig. 5.13. The slope isactivation energy, whereas the intercept in the fits indicate the product c

k∂ µ

∂c ∗Do(c)/HR(c). The parameters are provided in Table. 5.2. Based on Eq. 3.27,the ratio of the chemical diffusion at similar temperature and concentration atdifferent thickness values of vanadium layers can be simply reduced to ∂ µ

∂c ,which is given by

44

Table 5.2. Activation energy Ea and prefactors for Fen/V7n(n−−2,3,4). Prefactorsc

kB

∂ μ∂c Do(c)/HR(c) are extracted by fitting Arrhenius relation in eq. 5.1, as seen in

Fig. 5.13.

Sample Ea(eV ) ckB

∂ μ∂c Do(c)/HR(c)

(cm2 ·K/s

)Fe1V7 0.40 ± 0.01 72.0 ± 18.5Fe2V14 0.40 ± 0.01 25.1 ± 6.4Fe4V28 0.40 ± 0.01 11.5 ± 2.8

∂ μ∂c

|D14:∂ μ∂c

|D21:∂ μ∂c

|D28= 6.2 : 2.2 : 1. (5.2)

The increasing chemical diffusion is caused by decreasing D-D interaction asthe thickness is reduced. This result is consistent with previous results thatH-H interaction decreases as thickness of vanadium layers decreases [29].

5.4 Hysteresis effects of hydrogen in metalsWe also study hysteresis effects on H absorption and desorption in Pd/ [Fe4/V28]11system (paper V). Fig. 5.14 shows the isotherms of absorption and desorptionof Pd/ [Fe4/V28]11 system at different temperatures [67]. No hysteresis ef-fect is found at 503 and 483 K in single-crystal Fe4/V28 superlattice. At high

Figure 5.14. This shows isotherm for hydrogen absorption and desorption at differenttemperatures in confined vanadium lattice. The red ones represent desorption. Theconcentration is c =−1.73× ln(Tr/T0). This figure is taken from reference [67].

pressure levels (gray region) at 373 and 323 K, a large hysteresis is observed.These temperature and pressure ranges correspond to phase transition of α ⇀↽

45

β in Pd. The transition can be identified from increasing light transmissionwith hydrogen pressure, which is opposite to the behavior in vanadium [68].

Figure 5.15. Small pressure composition hysteresis is observed at 393 K, 383 K and372 K. The red ones represent the desorption. The concentration is c = −1.73 ×ln(Tr/T0). This figure is obtained from reference [67].

Figure 5.16. Changes in resistivity and transmission change during hydrogen absorp-tion at 393 K, which corresponds to the plateau region. The measurement shifts tonext point upon reaching thermodynamics equilibrium. This figure is obtained fromreference [67].

46

However, a small hysteresis effect is observed in Fe4/V28 at 393 and 383K, as shown in Fig. 5.15. To obtain an idea on what causes this small hystere-sis effect, a change in transmission and resistivity with time is shown in theabsorption measurement, as shown in Fig. 5.16. The change in resistivity andtransmission with time becomes very small after hydriding for some hours.This result indicates that full thermodynamics equilibrium is achieved at eachstep in the absorption before the pressure increases to next step. The case issimilar for desorption, which is not shown here. Thus, the kinetics reasonfor the hysteresis effect, namely not enough waiting time, can be excluded,as shown in Fig. 5.16. As shown in 5.17, Δρ is the same at the same hydro-gen concentration during absorption and desorption below and above criticaltemperatures. These results show similar magnitude of order-disorder for hy-drogen in Fe4/V28 during absorption and desorption. This occurrence canexclude the possibility that hysteresis is caused by order-disorder transitionmechanism.

Figure 5.17. Resistivity change with concentration at different temperature. The con-centration is c =−1.73× ln(Tr/T0). This figure is taken from reference [67].

In the phase transformation, from α to β in Fe/V (001) superlattices, thestructure from X-ray measurements is preserved [18]. This result can re-veal that it is coherent transformation in the phase transition from α to β inFe4/V28, where large spatial hydrogen concentration variations lead to mod-ulation of lattice without disrupting it. The macroscopic energy is generatedduring this process [41, 42, 39] leading to hysteresis effect.

A simple model [41] characterizing the thermodynamic hysteresis is

lnpabspdes

=4v0Gs

1+σ1−σ ε0(cst

β − cstα)

kT, (5.3)

47

where cstβ − cst

α is the difference of concentration at which the phase transitionstarts from β and α , respectively, v0 is the ratio of the parent phase matrixof volume and total number of interstitial sites, Gs is shear modulus, σ is thePoisson’s ratio, and ε0 = da

adc is the lattice expansion coefficient.

Figure 5.18. Hysteresis ln(PabsPdes

) for hydrogen in strained vanadium is plotted as afunction of inverse absolute temperature T. The critical temperature is extracted withGriessen model [39]. This figure is taken from reference [67].

Hysteresis is absent at and above 466 K in Fe4/V28, but small hysteresis ispresent below this temperature (Fig. 5.3). In Fe4/V28, the critical temperatureof order-disorder phase transition is 459 (10) K, which is extracted from thelinear model in previous study [29]. The extracted critical temperature is 466K, as obtained using the Griessen model [39]. The critical temperatures fromtwo methods are consistent and also these results confirm the theoretical modelindicating hysteresis does not exist above the critical temperature, similar toprevious study on bulk vanadium-hydrogen system [22].

The energy loss is given by ΔGloss = RTln(PabsPdes

). The energy loss for allsamples are given in table.5.3. The large hysteresis effects on bulk vanadiumfor the region of β ⇀↽ γ transformation, thin and bulk palladium for α ⇀↽β phase transformation, are caused by irreversible energy loss due to plasticlattice deformation [69]. However, no plastic lattice deformation exists forphase transition in Fe4/V28 superlattice, and the hysteresis effect is reducedprofoundly because of the non-irreversible energy loss.

Therefore, the contribution to the hysteresis includes two parts: elastic co-herent stain and defect generation. The hysteresis effect observed in bulk vana-dium in the region of solution ⇀↽ hydride transformation is small, which isclose to that in Fe4/V28 superlattice. This reveals that there is negligible con-tribution from defect generation in bulk vanadium, which may be caused bythe fact that not so much defects are generated during the phase transformation

48

Table 5.3. Energy loss ΔG = RT ln( pabspdes

) for different samples. The bulk V data isobtained from reference. The data for Fe4/V28 and 7 nm Pd film is from current study.Bulk Pd data used for energy loss calculation is from reference [70]. The 66 nmnanocubes data used for energy loss calculation is from reference [71]. 65 free filmused for energy loss calculation is from reference [68].

Sample T (K) ΔG(J/mol)Fe4/V28 372 417bulk V 1 313 300bulk V 2 313 19227 nm Pd film 323 17457 nm Pd film 372 61865 nm free Pd film3 324 265166 nm nanocubes4 262 1848bulk Pd5 323 8881 This is from heating and cooling experiment. The

phase transition is in the region of α ⇀↽ β transfor-mation. The parameter used for calculating the hys-teresis loss energy is solvus composition for hydrideformation and decomposition.

2 This is phase transition from β to γ in bulkvanadium-hydrogen system. The pressure composi-tion temperature isotherm is extracted in the experi-ment.

3 Optical transmission technique.4 From optical absorption for nanocube of Pd.5 From volumetric method for isotherm measurement.

from α to β , even there is large lattice expansion along c axis direction in βphase. However, this needs further study for phase transition of α to β in bulkvanadium to clarify the mechanism of the observed small hysteresis effect inbulk vanadium.

49

6. Summary and outlook

This work is the first systematic study of hydrogen diffusion in nano-sizedtransition metal lattice. Fen/V7n (n=1,2,3,4) superlattices and a clamped sin-gle crystalline 50 nm vanadium film are selected as our model systems. Alarge influence of site occupancy, clamping from the substrate and finite sizeon hydrogen diffusion is observed.

A profound influence of site occupancy on hydrogen diffusion in vanadiumhas been found. Diffusion coefficients in Fe3/V21 (octahedral site occupancyfor hydrogen) are three to five times smaller than that in bulk vanadium (tetra-hedral site occupancy). This result is interpreted as lower zero-point energyin octahedral site than that in tetrahedral site. Profound isotope effect has alsobeen found in Fe3/V21 superlattice. This is caused by the lower zero-pointenergy for deuterium in octahedral site compared with hydrogen, which leadsto slower diffusion coefficients for deuterium. The influence of clamping ofthe substrate on the diffusion of hydrogen with concentration in vanadium thinfilm is found. The diffusion coefficient below c ≈ 0.1 [H/V] is close to that inbulk vanadium and decreases substantially when c > 0.1 [H/V] compared withthat in bulk vanadium. This finding is interpreted as the site change from tetra-hedral to octahedral occupancy when the hydrogen concentration increases.This site change due to lattice expansion along the direction perpendicular tothe surface of clamped film as hydrogen concentration increases, which willalter the tetragonality of vanadium structure. This site change is also reflectedby activation energy that at c > 0.1 [H/V] is larger than that below c ≈ 0.1[H/V] in 50 nm. Large finite size effect on deuterium chemical diffusion isobserved, which is concluded to be caused by D-D interaction change thatwill influence the deuterium chemical diffusion at different thickness values ofvanadium layers. However, finite size has no effect on hydrogen chemical dif-fusion at extremely low hydrogen concentrations in Fe/V(001) superlattices.Therefore, the diffusion behavior of hydrogen in nano-sized vanadium differsfrom that in bulk vanadium because of substrate clamping and confinement ef-fect on nano-sized vanadium; the difference is indirectly attributed to changesin site occupancy and H-H interaction. However, some open scientific ques-tions must be addressed to elucidate hydrogen diffusion in nano limit region;in particular, scholars must investigate the proximity effect on hydrogen iso-tope transport, finite size effect on hydrogen self-diffusion, and isotope effecton self-diffusion at high concentrations.

Hysteresis effect of hydrogen absorption on confined vanadium lattice isinvestigated. Hysteresis effect is observed below critical temperature; this oc-

50

currence confirms the hypothesis that hysteresis effect in coherent transforma-tion is caused by coherency strain. Large hysteresis occurs in Pd film aftersome cycles. This occurrence could be mainly related to irreversible energyloss due to plastic deformation. However, the hysteresis effect on Fe3/V21superlattice is small and is close to that in bulk vanadium in the region of α ⇀↽β transformation, although much defect generation appears in the transforma-tion from previous study in bulk vanadium. To obtain complete understandingof hysteresis effect of hydrogen absorption in metals, further study for transi-tion from α to β phase in bulk vanadium is required to clarify the mechanismof small hysteresis effect in its incoherent transformation. In addition, hys-teresis effect in the high pressure ranges, which correspond to the region of β⇀↽ γ transformation in bulk vanadium, should also be investigated in confinedvanadium lattice.

In conclusion, tuning of diffusion and hysteresis effect is achieved by con-fining the hydrogen in the nano-sized materials. These effects play a signif-icant role in hydrogen storage and the corresponding applications. However,further study on hydrogen self-diffusion and hysteresis effect on nano-sizedmaterials must be performed to elucidate behavior of metal-hydrogen systemsin nano limit region.

51

7. Svensk sammanfattning

Vid rätt förhållanden absorberas väte och dess isotoper i metaller och bildarmetallhydrider. Dessa hydrider kan användas i tillämpningar för lagring avväte, bränsleceller, batterier och sensorer för detektion av vätgas. Långsamdiffusion och låg lagringskapacitet kan utgöra hinder vid tillämpningar avmetallhydrider av metallhydrider för vätelagring. Låg mottaglighet, återhämt-ningstid och långsam reaktionstid hämmar metallhydriders duglighet som sen-sorer. Diffusion och reaktionstid är viktiga faktorer för metallhydrider som banbör ta hänsyn vid utveckling av applikationer för lagring och sensorer. Tidi-gare studier har visat att väte i multilager av Fe/V (001) sitter i andra positionerän vad det gör i bulk-vanadin. Det har visats i teoretiska beräkningar att klämn-ing av vanadin påverkar väteatomernas läge i tunnfilmen. Inom nanoskala ärden kritiska temperaturen för fasomvawdling starkt avtagande när lagertjock-leken minskar. Fe/V supergitter utgör ett utmärkt modellsystem för studier avväteläge, klämning och effekter på nanoskala i tunnfilmer. Vi har också stud-erat hystereseffekten av väte vid absorption och desorption. Dessa effekt kanexperimentellt studeras i Fe/V (001) multilager därför har vi valt detta systemför att undersöka dessa effekter, till exempel med optiska tekniker.

Vätets position har en stor inverkan på dess diffusion i vanadin. Diffu-sionskoefficienter i Fe3/V21 multilager (i vilket väte sitter i de oktaedriskahålen) är tre till fem gånger mindre än de bulk-vanadin (i vilket väte sitter i detetraedriska hålen). Det här resultatet tolkas som en lägre nollpunktsenergi ioktaedriska hål än den i tetraedriska hål. En stor inverkan från isotopeffektenobserverades i Fe3/V21. Det här är orsakat av den lägre nollpunktsenergin fördeuterium i oktaedriska hål jämfört med den för väte, vilket leder till lägrediffusionskoefficienter för deuterium. Inverkan från substratets klämmandeeffekt observerades i vanadinfilmen. Diffusionskoefficienten när vätets kon-centrationen är under c ≈ 0.1 [H/V] är nära i bulk-vanadin och avtar kraftigtnär c > 0.1 [H/V]. Det här resultatet tolkas som att vätet går från att besittade tetraedriska hålen till att besitta de oktaedriska hålen när koncentrationenökar. Den här förändringen uppstår eftersom att gittret expanderar vinkel-rätt mot substratets yta när koncentrationen ökar, vilket ändrar den tetragonalastrukturen hos vanadin. Förändringen i besittning reflekteras även av aktiver-ingsenergin som, då c > 0.1 [H/V], är större än den då koncentrationen är lägreän c ≈ 0.1 [H/V] i 50 nm vanadinfilm. En stor nanoeffekt observerades hosdiffusion av deuterium, vilket är orsakat av en förändring i D-D interaktionersom inverkar på diffusionen vid olika tjocklek på vanadinlagren. Däremothittades ingen nanoeffekt på vätediffusion vid extremt låga koncentrationer i

52

Fe/V(001) multilager. Därav skiljer sig beteendet hos diffusionen av väte imycket tunt vanadin från det i massivt vanadin på grund av substratets kläm-mande effekt och det finita utrymmet. Skillnaden är också indirekt koppladtill förändring i vätets position på grund av hur substratet klämmer och H-Hinteraktioner. För att full förståelse vätediffusion i nanoområdet återstår docknågra obesvarade frågor. speciellt närhetseffekten hos transporten av väteiso-toper, finita-utrymmeseffekten av vätes självdiffusion, och isotopeffekten hossjälvdiffusion vid högre koncentrationer.

Hystereseffekten vid väteabsorption i begränsade vanadingitter har under-ökts. Hysteres har observerats under den kritiska temperaturen; detta bekräf-tar hypotesen att hystereseffekten vid koherent transformation orsakas av ko-herenstöjningar. Stor hysteres har även observerats i Pd-film efter flera cykler.Det här skulle kunna vara främst relaterat till energiförluster på grund av plas-tisk deformation. Däremot är hystereseffekten hos Fe3/V21 liten och nära deni bulk-vanadin runt transformationen α ⇀↽ β , men tidigare studier har visatstor defektgenerering i massivt vanadin. För att få en komplett förståelse förhystereseffekten vid absorption av väte i metaller krävs ytterligare studier omden inkoherenta omvandlingen från α-fas till β -fas i massivt vanadin för attklargöra mekanismen hos den lilla hystereseffekten. Dessutom bör hystere-seffekten vid högt tryck, vilket motsvarar transformationen β ⇀↽ γ i massivtvanadin, undersökas i det begränsade vanadingittret.

Sammanfattningsvis, diffusion och hysteres kan justeras genom att begränsavätet i material i nanostorlek. Dessa effekter spelar en betydande roll i vätela-gring och dess applikationer. Dock krävs ytterligare studier på vätets självd-iffusion och hystereseffekt i nanomaterial för att ge en djupare förståelse avmetall-väte systemet i nanoområdet.

53

8. Acknowledgement

First of all, I am sincerely thankful to my supervisor Pro. Björgvin Hjörvars-son. You provided me the chance to do PhD study in materials physics group.You shared me your profound physics knowledge and philosophy of life dur-ing my PhD period. I will always remember the help I obtained from you inmy future endevors.

I would also like to thank to my co-supervisor Max Wolff. Thank you somuch for your discussion with me during my time in the group.

I will give my special thanks to Ola Hartmann. Thank you for your contri-bution to my project. Your contribution deepens the understanding about theexperimental technique used for diffusion study.

I am also thankful to Lennard P.A. Mooij. Thank you so much for yourguidance and patience. I learn a lot from you about experimental details andcode.

Thank you Gunnar K. Pálsson for your invaluable discussion in science andselfless help in writing.

I also would like to give my special thanks to Pro. Bengt Lindgren. I alwaysremember that you make me start to know diffusion analysis with Matlab.

I am also thankful to Heikki Palonen and Sotirios A. Droulias for providingme excellent samples.

I am thankful to Martin Brischetto. I will always remember the summertime that you were in the Lab, and the latter time that we work together. I amimpressed by your excellent experimental and programming skills. I am alsoglad for our good friendship.

My special thanks also go to Emil Melander for driving me some times andother help from you.

Thank you Franz Adlmann, Reda Moubah, and Andreas Frisk for helpingme and being my friends.

I also would like to give my special thanks to Anders Olsson. I am im-pressed by your excellent manual dexterity in Lab.

I also thanks my collaborator Robert Johansson, thanks so much for thediscussion and help.

I am also thankful to my colleagues Sebastian George, Hauke Carstensen,Maciej Kaplan, Jithin James Marattukalam, Agne Ciuciulkaite, Vassilios Ka-paklis, Gabriella Andersson, Nouhi Shirin, Erik östman, Giuseppe muscas,Henry Stopfel, Fridrik Magnus, Petra Jönsson, Maja Hellsing, Björn ErikSkovdal, Spurve Saini, Xin Xiao, Andreas Bliersbach, et al. I will remem-ber every one of you that helped me directly or indirectly.

54

I would also like to express my gratitude to all my Chinese friends in Up-psala and Stockholm, Zhang Peng & Guo Yan, Hailiang Fang & Ya Hu, HuLi& Jiangwei Liu, Song Chen & Shu Li, Mingzhi Jiao & Yurong Hu, Yi Ren& Xiao Wen Li, Liyang Shi & Jingyi Hong, Lei Tian & Rui Sun, JiaojiaoYang & Jun Luo, Da Zhang & Man Song, Xiaorong Huang & Li Zhang, Shu-jiang Wang & Chao Cai, Jingbao Zhang & Li Yang, Ruijun Pan & QiuhongWang, Fei Huang & Na Xiu, Jingxin Huo & Yinyin Zhu, Bo Cao & Jie Wen, Dou Du, Qin Tao, Lei Zhang, Wenxing Yang, Teng Zhang, Shihuai Wang,Xi Chen, Junxin Wang, Bo Tian, Xin Chen, Cui Li, Tianbo Duan, Lei Liu,Dan Wu, Yuanyuan Han, Shunguo Wang, Weijia Yang, Yue Hone, Ling Xie,Yu Zhang, Hongji Yan, Yi Jin, Liguo Wang, Qifan Xie, Huiyin Qu, ChenjuanLiu, Huan Wang, Fengzhen Sun, Mingkai Ni, Huimin Zhu, Yan Hao, et al.

Finally, I would like to give my thanks to my family. Especially, I wouldlike to thank my parents for bringing me up and for selfless help. I am alsothankful to my brother and sister for their support. I am also grateful for theencouragement and love given by Mengyu Wang.

55

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