The effect of nano-confinement on hydrogen uptake in metallic superlattices

Sotirios Droulias

The effect of nano-confinement on hydrogen uptake in metallic

superlattices

This Page will be Replaced before Printing

Title page logo

Abstract

The absorption of hydrogen is exothermic in vanadium whereas it is endothermic in iron and chromium. Investigations of the hydrogen uptake within Fe/V(001) and Cr/V(001) superlattices allow therefore a detailed exploration of finite size effects and the influence of boundaries on hydrogen absorption. Fe/V(001) and Cr/V(001) superlattices can be grown as single crystal structures with a small mosaic spread, as determined by X-ray reflectometry and diffraction.

Furthermore when the thickness ratio of the constituents is kept constant the crystal quality can be retained in the range from a few up to 40 monolayer repeat distances (Λ). Neutron re- flectometry was used to simultaneously determine the volume expansion and concentration of hydrogen in the vanadium layers. Large differences are found in the expansion of Fe/V(001) and Cr/V(001) superlattices, in good agreement with density functional theory (DFT) calcula- tions. The findings are consistent with tetrahedral and octahedral site occupancy in Cr/V(001) and Fe/V(001) superlattices, respectively. Full fitting of the reflectivity pattern is required to ob- tain an accurate measure of expansion if the number of repeats is small. Under these conditions the shift of the first order superlattice peak can be an inaccurate measure of the volume changes.

By using a specially designed neutron scattering chamber, allowing simultaneous neutron and optical transmission measurements, it is found that the optical transmission scales linearly with hydrogen concentration. By comparing the experimental results to ab-initio DFT calculations, it is shown that optical transmission scales with electron density changes in the samples, ex- plaining the linearity with concentration. This change is dominated by the hydrogen induced expansion of the lattices and depends therefore strongly on the site occupancy of the hydrogen.

Finally, X-ray diffraction was used to address the local strain fields and the α to β phase transi-

tion, typically observed in bulk vanadium. Below 448 K the results are consistent with an α to

β phase co-existence, separated along the surface normal of the samples.

To my family

List of papers

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

I S.A. Droulias, G.K. Pálsson, H. Palonen, A. Hasan, K. Leifer, V.

Kapaklis, B. Hjörvarsson, and M. Wolff.

Crystal perfection by strain engineering: The case of Fe/V (001). Thin Solid Films, 636, 2017.

II S.A. Droulias, G.K. Pálsson, B. Hjörvarsson, and M. Wolff.

Beating effects in multilayer systems studied with neutron reflectometry.

Submitted to Journal of Applied Crystallography.

III S.A. Droulias, O. Grånäs, O. Hartmann, K. Komander, M. Wolff, B.

Hjörvarsson and G.K. Pálsson

Proximity induced changes in nano-sized metal hydrides Submitted to Nature Communications

IV Lennard Mooij, Wen Huang, Sotirios A. Droulias, Robert Johansson, Ola Hartmann, Xiao Xin, Heikki Palonen, Ralph H. Schneider, Max Wolff and Björgvin Hjörvarsson

Influence of site occupancy on diffusion of hydrogen in vanadium, Phys. Rev. B. 95, 064310, (2017)

V Wen Huang, Gunnar K. Pálsson, Martin Brischetto, Heikki Palonen, Sotirios A. Droulias, Ola Hartmann, Max Wolff and Björgvin Hjörvarsson

Finite size effects: deuterium diffusion in nm thick vanadium layers, New J. Phys., 19, 123004, (2017)

VI Wen Huang, Lennard P A Mooij, Sotirios A Droulias, Heikki Palonen, Ola Hartmann, Gunnar K Pálsson, Max Wolff and Björgvin

Hjörvarsson

Concentration dependence of hydrogen diffusion in clamped vanadium (001) films, J. Phys. Condens. Matter, 29, 045402, (2017)

VII Wen Huang, Gunnar K Pálsson, Martin Brischetto, Sotirios A Droulias,

Ola Hartmann, Max Wolff and Björgvin Hjörvarsson

Experimental observation of hysteresis in a coherent metal-hydride phase transition, J. Phys. Condens. Matter, 29, 495701, (2017) Reprints were made with permission from the publishers.

Comments on my participation

The following is a brief description of my involvement in the publications:

I Carried out the optimization for the growth conditions and grew all sam- ples, carried out most of the measurements, did most of the analysis and all of modeling , drafted the first version of the manuscript and edited it until submission.

II Participated in the discussions on the effects seen, grew, measured and analyzed the samples. Drafted the first version of the manuscript and edited it until submission and publication.

III Participated in planning the measurements and performed the neutron scattering experiments and evaluation. Grew and characterized the sam- ples. Partly drafted the first version of the manuscript.

IV Grew and characterized the samples. Took part in the discussion about the results.

V Grew and characterized the samples. Took part in the discussion about the results.

VI Grew and characterized the samples. Took part in the discussion about the results.

VII Grew and characterized the samples. Took part in the discussion about

the results.

Contents

1 Introduction

. . .

9

2 Hydrogen in vanadium

. . .

12

2.1 Dipole force tensor and expansion

. . . .

13

2.2 The hydrogen-vanadium system

. . .

14

3 Epitaxial thin films and superlattices

. . .

16

3.1 Strain in Fe/V and Cr/V superlattices

. . . .

17

3.2 Critical layer thickness

. . .

18

3.3 Optimum thickness ratio of superlattice constituents

. . .

19

4 Growth of superlattices

. . .

21

4.1 Growth optimization

. . .

21

4.2 Reciprocal space maps

. . . .

24

5 Experimental techniques

. . .

27

5.1 Concentration determination via neutron reflectometry

. . . .

27

5.2 Expansion measurements with X-ray diffraction

. . . .

32

5.3 Optical transmission

. . .

36

6 Results and discussion

. . . .

37

6.1 Effects of substitution of the non-absorbing layer

. . .

37

6.2 X-ray diffraction and solubility limits

. . .

39

6.3 Optical transmission, concentration and expansion

. . . .

46

7 Summary and conclusions

. . .

48

8 Outlook

. . . .

49

9 Svensk Sammanfatting

. . . .

50

10 Appendix: Introduction to basic scattering concepts

. . . .

51

10.1 Interference

. . . .

51

10.2 Real and reciprocal lattice

. . .

54

10.3 Structure and form factor

. . . .

56

10.4 Superlattice form factors

. . .

57

10.5 Diffraction from superlattices

. . .

59

10.6 Reflectivity from layered structures

. . . .

61

References

. . . .

66

Papers

. . . .

71

1. Introduction

The reduction of CO ₂ emissions is crucial to mitigate global warming. In this context, a sustainable energy economy is of great importance. Hydrogen is a great candidate as an energy carrier, since it converts to water after an exothermic reaction with oxygen with no other waste products and has there- fore minimum environmental impact. Today, hydrogen is already being used for both stationary and automotive applications, by using high-pressure tanks and metal hydride batteries for storage purposes. However, a wider use of hy- drogen in energy applications is hindered by challenges with respect to storage as well as conversion. Scientific and technological progress is needed to fur- ther move towards a hydrogen based energy economy.

Metal hydrides (MH) are a promissing alternative to the currently used high- pressure gas tanks, not only in terms of safety but also because some MH sys- tems exhibit very high volumetric energy density [1]. This thesis contributes to the fundamental understanding of the hydrogen-metal systems by present- ing investigations of finite size and proximity effects on the thermodynamics of hydrogen uptake. The results are relevant for hydrogen storage as well as sensors [2].

We use vanadium hydride (VH) as a model system since the thermodynamic properties of the bulk metal hydride have been studied in detail [3]. Addition- ally, vanadium can be grown as a thin film or as part of a superlattice with high crystal quality. Superlattices are single crystalline structures of repeated layers of different materials grown on a substrate. In the case of V, it is combined typically with other transition metals, like Fe, Cr or Mo. A schematic repre- sentation of a Fe/V superlattice is presented in Figure 1.1. The use of single crystal superlattices enables the access to a variety of length scales such as atomic, chemical repeat distance and total thickness. For instance, finite size effects can be addressed by changing the thicknesses of the individual layers.

In the example depicted in Figure 1.1, the repetition distance Λ consists of only a few monolayers (ML) of each element. The thickness ratios or absolute thickness values can be chosen, as seen later in this work. Changing the thick- ness ratio of the constituents, enables the tuning of strain in the superlattice, originating from the difference in the lattice parameters of the constituents.

This can be used to match the in plane lattice parameter of a supertlattice to

that of the substrate and thereby improve the crystalline quality. In this study

the materials making up the superlattices were chosen in a way that only one of

two constituents absorbs hydrogen, for the experimental conditions addressed

in this thesis. An in-depth description of the energy landscape of V superlat-

tices can be found in [4]. The thicknesses of the hydrogen absorbing vanadium

layers in this thesis were chosen to be 7, 14, 21 and 28 monolayers (ML) to investigate finite size effects on the thermodynamics and kinetics of vanadium hydride [5, 6].

The work presented here is based on previous research, where superlattices

Figure 1.1. Schematic representation of a Fe/V superlattice. Λ is the chemical repeat distance. As an example, a superlattice with few monolayers of each element is shown.

On top the enthalpy of solution for hydrogen uptake is presented. For the experimental conditions used in this work, only V is expected to absorb hydrogen.

have been used in fundamental research on hydrogen in metals [4]. The in- fluence of biaxial versus compressive strain in Fe/V and Mo/V superlattices was addressed in [7, 8]. In this context the differences in lattice missmatch be- tween Fe/V and Mo/V result in considerable challenges concerning the sample growth and significant progress was reported in [9, 10]. This enabled a wider range of systems, like hydrogen in Mo/V [11] and Cr/V [12] to be studied.

The H induced expansion [13] and strain dependence of the thermodynamic properties was studied in Fe/V superlattices [14, 15]. Also, the orientation dependence of the H configuration in Mo/V superlattices was studied [16] as well as the thermodynamic properties [17]. Ref. [18, 19, 20] discuss diffrac- tion methods, similar to the ones applied in this work, for the investigation of elastic strain and lattice expansion in superlattices.

We are revisiting the growth and optimization of Fe/V and Cr/V to specifically promote the crystal quality in order to accurately measure proximity effects;

the V layers within both Fe/V and Cr/V superlattices have the same character- istics and since both structures have the same epitaxial relationship with the MgO substrate, the strain in the V layer is identical. In this context, fully co- herent and epitaxial growth has been achieved.

Scattering techniques have been used to study the hydrogenated superlattices.

The relation between expansion and concentration is associated with the con- figuration of the hydrogen atoms in the unit cell and depends on the type of in- terstitial occupancy. Neutron reflectometry, as shown in previous works [20], can be used to extract the absolute concentration of hydrogen in the superlat- tice and simultaneously measures the volume expansion.

Extensive studies have been conducted in numerous MH systems using optical

transmission measurements [21, 22]. These measurements rely on the fact that

the changes in optical transmission scale linearly with concentration. Here the

absolute calibration of concentration extracted from neutron reflectometry is connected to the relative change of the transmission of light through the hy- drogenated matrix.

It is concluded that the absolute concentration of hydrogen in Fe/V-2/14 and

Cr/V-2/14 superlattices, affects the optical transmission in a linear way. It

is shown that the changes in optical transmission are connected to expansion

of the lattice rather than directly to the hydrogen concentration. In addition,

X-ray diffraction is used to identify the solubility limits in the temperature-

concentration diagram.

2. Hydrogen in vanadium

When vanadium is exposed to a H ₂ atmosphere, H ₂ may dissociate at the sur- face and atomic hydrogen may enter the vanadium lattice and form a metal hydride (or solid solution). Typically, the dissociation of the H ₂ needs a cata- lyst and in this work palladium capping layers are used for this purpose. The thermodynamic driving force, for absorption of hydrogen is the difference in chemical potential between the gaseous and the MH phase. The H atoms oc- cupy interstitial sites in the crystal. Below the structure of the metal and H atoms in the lattice are introduced and the VH phase diagram is presented.

The hydrogenation of vanadium is an exothermic process. At the moment of

Figure 2.1. Schematic of the solution process of H in V and occupation of Octahedral- z, interstitial sites.

exposure to H ₂ , the hydrogen in the sample and in the gas form have a dif-

ferent chemical potential. With the help of a catalyst (like Pd) on the surface

of the V crystal, hydrogen molecules dissociate to H atoms. Then H diffuses

through the catalyst layer and the concentration of H in the sample increases (Figure 2.1). The heat of solution for V (-0.31 eV) is lower than for Pd (-0.20 eV). Thermodynamic equilibrium takes place when the chemical potential of the gas µ gas is equal to the chemical potential of the absorbed hydrogen µ _lat [23].

1

2 µ _gas = µ _lat 1

2 kT ln  P P 0



= h ₀ − uc + kT ln  c r − c

 (2.1)

P and P 0 is the gas pressure and a reference pressure respectively, h 0 the bind- ing energy per hydrogen atom in the host matrix, u is the interaction energy, c the concentration and r the number of the maximum interstitial sites per atom (or maximum concentration).

After the uptake of hydrogen, and given the dissociation of the H molecule into two atoms, the H atom will reside in an interstitial site of the host lattice.

The interstitial site occupancy that has been observed in V, is of two types:

tetrahedral and octahedral depending on concentration [24, 25]. A schematic representation of the interstitial sites is shown in figure 2.2.

Figure 2.2. Interstitial sites of the VH system: Tetrahedral site occupancy (left panel) and octahedral site occupancy (right panel) [25].

2.1 Dipole force tensor and expansion

The H atom occupying an interstitial site in the crystal, creates a local distor- tion of the lattice. The tensor associated with the H induced stress is called the dipole force tensor and is written as [26]:

P _{i j} = ∑

m f ^m _j r ^m _i (2.2)

where f _j ^m is the force acting on the m ^th atom in the direction j by a hydrogen

atom at a distance r in the direction i (Kanzaki forces) [27]. We can write the

average stress that is applied by a hydrogen concentration c as [26]:

σ _{i j} = c

Ω P i j (2.3)

where Ω is the atomic volume of the host atoms within the unit cell.

The strain induced by the hydrogen on the host metal lattice results in vol- ume expansion that can be written as (if the H atoms are evenly distributed throughout the lattice) [28]:

∆V

V = c k = c Ω

(P ₁₁ + P ₂₂ + P ₃₃ )

C 11 + 2C 12 (2.4)

where c is the concentration and k the expansion coefficient. The experimen- tal work in this thesis is done using single crystal V layers, that are bi-axially strained in the in-plane direction, and the in-plane lattice parameter conforms to the epitaxial relation with the substrate (clamped). The clamping affects the hydrogen occupancy and exclusively interstitial occupancy in the out-of- plane direction takes place. No in-plane expansion is expected or observed.

By using the stress tensor and considering clamping with the substrate, Eq.

2.4 modifies to [29]:

∆V

V = ck = c Ω



P 33 s 11 s 33 + s 12 s 33 − 2s 13 s 33

s ₁₁ + s ₁₂



(2.5)

2.2 The hydrogen-vanadium system

The two interstitial occupancy sites depicted in figure 2.2, can be associated with two phases in VH, the α and the β phase [3]. These are also the two relevant phases for the concentration range investigated in this work. Figure 2.3 depicts the phase diagram of bulk VH. A clear distinction must be made between the ordering of the H atoms within the crystal (phase) and the con- figuration of the H atom in the unit cell (interstitial occupancy). However, in bulk V, there is a difference in site occupancy between the α and β phases.

The phase observed at low concentrations, the α phase, is known to have tetra- hedral interstitial site occupancy. In addition, the α phase is disordered with respect to the H distribution in the lattice and has been described before as a lattice-gas [31]. At higher concentration the β phase is associated with the octahedral site occupancy. The β phase has a higher degree of ordering of hydrogen atoms in a sublattice [32, 24].

Previous reports on Fe/V superlattices conclude that a single phase is present

in the pressure - temperature range used in this work [13]. The bulk V-H phase

diagram is presented in figure 2.3 for reference. In the following chapters it

is shown how superlattices can be used to investigate the influence of strain,

confinement and effects of substitution of the non-absorbing layers to the V-H

system.

Figure 2.3. Phase diagram of VH from a sample with no volume restrictions (bulk)

[30].

3. Epitaxial thin films and superlattices

A superlattice is an artificial single crystal made by layers of different mate- rials (see Figure 1.1). The layers have the same in-plane lattice parameters.

For the effective growth of good quality superlattices, linear elasticity plays a crucial role. An important aspect that needs to be included in the characteri- zation is strain. A coherent single crystal is characterized by a strained lattice (left panel in figure 3.1) whereas a relaxed crystal (right panel in figure 3.1) get plastically deformed.

The simplest case of heteroepitaxy results from the growth of a layer on a sub-

Figure 3.1. Schematic representation of a fully coherent thin film (left) and a relaxed thin film (right).

strate made of a different material. Between the overlayer and the substrate, there is usually a mismatch of lattice parameters. For heteroepitaxy, stress in the in-plane direction (directions perpendicular to the growth direction) forces the atoms to conform to a common in-plane lattice parameter.

For the registry of the first monolayer of V on MgO, a 45 ^o in-plane rotation is needed. The [100] direction of V is oriented along the [110] direction of MgO (see figure 3.2). The lattice parameter of MgO is a _MgO = 4.22 Å. The in-plane lattice parameter of fully coherent, single crystalline Fe/V or Cr/V su- perlattice grown on MgO is 4.22/ √

2 = 2.98 Å. The bulk value for vanadium

is V _bulk = 3.03 Å. For an epitaxially grown V layer on MgO, this registry

with the substrate has to remain for the whole thickness of the layer, with-

out relaxation of the in-plane lattice parameter which would result in plastic

deformation. If another layer e.g. Fe or Cr is grown on the V layer and the layers remain fully coherent, all layers have to have the same in-plane lattice parameter (2.98 Å). Fe has a bulk lattice parameter of a Fe = 2.87 Å and Cr of a _Cr = 2.92 Å. In both cases, the lattice has to expand in-plane to accommo- date. In the out of plane direction (along the growth direction), the material responds according to the Poisson ratio. The strain in that direction depends on the stress in the in-plane direction, according to equation 3.3.

The single crystal structure of a superlattice is what distinguishes it from mul-

Figure 3.2. Schematic representation of the epitaxial relation between the first mono- layer of V with the MgO substrate. More information can be found in [33].

tilayers. Multilayers are made either by polycrystalline layers or amorphous and do not allow to control the strain. In the general context of this study, the diffusion of H in V superlattices was studied (Papers IV-VI) [5, 6, 34]. In those studies, a polycrystalline layer would make it more difficult to under- stand underlying processes and inherent mechanisms due to the domination of grain boundary diffusion.

3.1 Strain in Fe/V and Cr/V superlattices

For a cubic system, such as V, Fe or Cr, the analysis based on linear elasticity can be reduced to the simple case of cubic symmetry. Due to clamping, a symmetric in-plane stress is applied (σ ₁₁ = σ ₂₂ ) but no out-of-plane stress (σ 33 = 0) since the film is free to expand in that direction. Hooke’s law can be written as follows:



 

 

 

 σ ₁₁ σ ₂₂ 0 0 0 σ ₁₂



 

 

 



=



 

 

 



C 11 C 12 C 12 0 0 0 C ₁₂ C ₂₂ C ₁₂ 0 0 0 C 12 C 12 C 33 0 0 0

0 0 0 C 44 0 0

0 0 0 0 C ₄₄ 0

0 0 0 0 0 C 44



 

 

 



·



 

 

 

 ε ₁₁ ε ₂₂ ε ₃₃ ε ₂₃ ε ₁₃ ε ₁₂



 

 

 



(3.1)

Since σ 11 = σ ₂₂ , one can deduce:

σ ₁₁ = C ₁₁ · ε 11 +C ₁₂ · ε 22 + C ₁₂ · ε 33

σ ₁₁ = C ₁₂ · ε 11 +C ₂₂ · ε 22 + C ₁₂ · ε 33

0 = C 12 · ε 11 +C 12 · ε 22 + C 33 · ε 33

(3.2)

By using Eq. 3.2, and by assuming no shear stress (σ ₁₂ = 0) we can extract a relation between the in-plane and out-of-plane strain:

ε ₃₃ = −2 C 12

C ₁₁ ε ₁₁ (3.3)

To elastically deform the crystal lattices so that they conform to an in-plane parameter of 2.98 Å, strain (ε 11 ) is applied. The lattice constants of Fe, Cr and V as grown in superlattices are summarized in table 3.1.

a bulk (Å) a ^SL _k (Å) a ^SL _⊥ (Å)

V 3.027 2.979 3.072

Fe 2.866 2.979 2.736

Cr 2.910 2.979 2.923

MgO 4.213 - -

Table 3.1. Summary of the lattice parameters in Fe/V and Cr/V superlattices, as predicted from linear elasticity. a ^SL _k and a ^SL _⊥ are the in-plane and the out-of-plane lattice parameter respectively. The bulk (unstrained) value is referred to as a bulk [10].

The in-plane lattice parameter of 2.979 Å was verified by X-ray diffraction measurements (Section 3.2).

3.2 Critical layer thickness

When growing an overlayer on a substrate, for a single crystalline, heteroepi- taxial layer to be formed, the layers need to be strained. It has been shown that there is a critical overlayer thickness before misfit dislocations develope to re- lease the accumulated elastic energy in the layer [35]. This critical thickness can be calculated by the following equation [36].

h c = D(1 − ν cos ² α ) h

lnh c /b + 1 i

Y f (3.4)

where Y is Young’s modulus, which for a single crystal cubic material grown in the [001] direction is:

Y = C 11 +C 12 − 2C ₁₂ ² /C 11 , (3.5) ν is the Poisson ratio which is ν = c ₁₂ /(c ₁₁ + c ₁₂ ), b is the length of the Burger’s vector, f is the total misfit (plastic and elastic strain) and α the an- gle between Burger’s vector and the dislocation line. D is an average shear modulus of the interface given by:

D = bG o G s

π(G _o + G _s )( 1 − ν) . (3.6)

where G = (C ₁₁ −C 12 + 3C ₄₄ )/5, G _s and G _o refers to the shear modulus of the substrate and the overlayer, respectively.

The above calculations can be used to predict the maximum thickness for a layer, where the registry with the substrate is kept and no plastic deformation of the lattice is found. Hence, high quality single crystal layers can be formed as long as their thickness is below this critical value. In the next section, the impact of the critical thickness on the growth of superlattices is discussed on the basis of linear elasticity.

3.3 Optimum thickness ratio of superlattice constituents

The elastic energy stored in a continuous can be calculated as follows:

E = 1

2 ε _i C i j ε _j = 1

2 σ _i ε _j (3.7)

The total energy of a bilayer in a superlattice is then:

E tot = C ₁₁ ^V + C ₁₂ ^V − 2 C ₁₂ ^V
2

C ^V ₁₁

!

· a

d ⁰ _{V k} − 1

!

· L V

+ C ₁₁ ^Fe +C ₁₂ ^Fe − 2 C ₁₂ ^Fe
₂ C ^Fe ₁₁

!

· a

d ⁰ _Fek − 1

!

· L Fe

(3.8)

Here Fe and V is used as an example and the respective sub- and superscrips

denote values for the respective elements. In order to minimize the defect den-

sity the elastic energy stored in the layers should be minimal. The condition

for a minimum in elastic energy is found by differenciating eq. 2.8:

∂ E tot

∂ a = 0

C ₁₁ ^V +C ₁₂ ^V − 2 C ₁₂ ^V
2

C ₁₁ ^V

! 

 2 d ⁰ _Vk − a

 d ⁰ _Vk  2



 L ^V +

+ C ₁₁ ^Fe +C ^Fe ₁₂ − 2 C ₁₂ ^Fe
2

C ₁₁ ^Fe

! 

 2 a − d ⁰ _Fek

 d ⁰ _Fek  2



 L ^Fe = 0 ⇔

Y _V



 2 d ⁰ _Vk − a

 d ⁰ _Vk  2



 L V +Y _Fe



 2 a − d ⁰ _Fek

 d ⁰ _Fek  2



 L Fe = 0

(3.9)

The ratio of the respective thicknesses of the constituents is:

L Fe

L _V = Y V

Y _Fe d ⁰ _Fek

d ⁰ _Vk

 d ⁰ _Vk − a  /d ⁰ _Vk

 a − d ⁰ _Fek 

/d ⁰ _Fek (3.10)

Inserting the respective values for Cr, Fe and V in equation 2.10 it is found

that the elastic energy stored in Fe/V and Cr/V superlattices is minimal for

a relative thicknesses ration of 1/2.5 and 1/4.4, respectively. Nevertheless, it

has been confirmed experimentally that optimum crystal quality is obtained

for a ratio of 1/4.7 for both combinations. The apparent non-agreement be-

tween linear elasticity and experimental observations can be attributed to the

unknown elastic properties of the constituents in the monolayer limit [37].

4. Growth of superlattices

To investigate the of the proximity of different materials on hydrogen uptake in thin vanadium layers, Cr/V and Fe/V superlattices have been grown. For the experimental conditions considered in this thesis Cr and Fe do not take up hydrogen. The hydrogen absorbing layers within these superlattices (the vanadium layers) have the same strain state, due to the registry with the sub- strate even though the non-absorbing layer is different. All samples used in this work have been grown as fully coherent superlattices ensuring that the results from different layer thicknesses and composition are comparable. The full coherence has been confirmed by X-ray diffraction measurements. (see chapter 5).

These samples were grown by D.C. magnetron sputtering and the quality of the samples depends on the conditions during deposition. In order to opti- mize the growth conditions, a series of samples were grown under systematic variations of the growth parameters, e.g. substrate temperature, power on the magnetrons and characterized using X-ray diffraction and reflectivity.

The principles of magnetron sputtering relies on the impact of energetic ions.

Typically, inert gasses, e.g. Ar. Due to the collision with these ions target atoms are ejected and travel towards the substrate. Different electric fields are used for the acceleration of the ions, primarily alternating current Radio Frequency sputtering (R.F.) and Direct Current sputtering (D.C.). In case of magnetron sputtering, the ions and electrons that are in a plasma close to the target are confined by the use of magnetic fields.

In the next sections, the optimization of the sputtering parameters, like the substrate temperature, distance between substrate and target, as well as Ar pressure in order to achieve fully coherent growth of Fe/V and CrV superlat- tices is discussed in detail.

4.1 Growth optimization

In order to control the strain the samples had to be fully coherent and with a

constant thickness ratio. The degree of crystallinity of an epitaxial film de-

pends on the temperature of the substrate during deposition. For the FeV

and CrV superlattices considered in this thesis the coherency of the sample

in the growth direction can be assessed from the full width at half maximum

(FWHM) of the (002) peak, using the Scherrer formula:

Figure 4.1. FWHM values of the (002) reflections. There is no significant difference between grown at Ar pressures of 1.8 mTorr and 4 mTorr for a substrate temperature of 340 ^o C.

¯D = 0 .94 λ

W cos(θ) (4.1)

Here λ is the wavelength of the x-rays and θ the Bragg angle. W refers to the full width at half maximum of the peak. The prefactor, 0.94, used in the Scherrer formula depends on the geometry of the crystallite [38].

The sputtering gas pressure plays a key role in sputtering growth since it af- fects the energy of the particles impinging on the surface of the growing sam- ple. The energy of the target particles gets reduced due to collisions with the sputtering gas.

The number of collision that a sputtered atom is subjected to, before reaching the substrate, depends on the mean free path between collisions.

λ ¯ = 1 π √

2 d ² n (4.2)

where d is the atom’s diameter and n is the number of atoms per unit volume.

For high quality superlattices, not only the coherence length is of importance but also the mosaic spread measuring the angular deviation between atomic planes. In our case, we have assessed the mosaic spread in the growth direc- tion by performing rocking scans on the (002) reflection.

Figures 4.1 and 4.2 show that the mosaic spread in the grown films is min- imised for a substrate temperature of 340 ^o C and an Ar pressure of 1.8 mTorr.

The third characteristic of superlattices that needs to be optimized is the qual-

ity of the interfaces between layers. This quantity can be accessed by X-ray

Figure 4.2. FWHM values of the rocking curves of the (002) reflections. A clear minimum is seen for 340 ^o C and 1.8 mTorr Ar pressure.

reflectivity. A detailed description and analysis is presented in Paper I [37].

The optimization of the sputtering process does not only include the substrate

temperature and sputter gas pressure, but also the substrate quality, the dis-

tance between target and substrate, purity of the targets and sputtering gas,

power input of the magnetron head etc. The results of the optimization of

growth are presented in Paper I [37].

4.2 Reciprocal space maps

To gain further information on the crystal quality, full reciprocal space maps (RSMs) were performed. For RSMs the incoming and outgoing X-ray beams imping on the same surface at different angles with respect to the surface nor- mal. As a result the vector of momentum transfer has an in-plane component.

The alignment of the scattering vector along different crystallographic direc- tions provides information for lattice planes other than the z direction, using a mechanism similar to the one described by figure 10.4 in the Appendix. The scattering vector Q has direction and magnitude that is defined by the follow- ing equations [39]:

Q _kx = 2π

λ (cos(θ ₂ ) cos(φ) − cos(θ 1 )) Q _ky = 2π

λ (cos(θ 2 ) sin(φ))

(4.3)

Where θ 1 is the angle of the incoming beam, θ 2 is the angle of the outgoing beam, and φ is the angle in the plane of the sample’s surface. For a clear schematic representation the reader is referred to [39]. For this definition the reference is the macroscopic sample surface and not the lattice planes.

Consider the diffraction patterns in Fig.4.3. The scans were taken samples of good crystal quality, evident from the narrow and symmetric (002) peaks, that correspond to fully coherent samples. The layering is of good quality as re- vealed by the large number and brightness of the satellite peaks. Finally, well separated and pronounced Laue oscillations are present, that show that sam- ples are coherent from the first to the last monolayer. Nevertheless, in the case of the 2/14 and the 4/28 the first order satellite intensities are seen to be larger in the side of lower Q values with respect to the fundamental peak. Oddly, the 3/21 scan reveals the opposite. The intensity of the first order satellite has larger intensity in the right-hand side (higher Q values). At first this seems to contradict theory since the relative intensities of the satellite peaks on the left and right hand side of the (002) reflection, are known to be associated with the strain wave in the superlattice [40]. The strain state should be identical in all three superlattices, for the reasons described in chapter 2. Reciprocal space mapping was constructed from measurements on the samples, and the results for the 3/21 superlattice are shown in Fig.4.4.

The black line in the panel on the left hand side, shows the Q _⊥ direction as a black line when a conventional θ − 2θ scan is performed along the macro- scopic surface normal. The superlattice pattern is tilted by a small angle and this changes the realtive intensities of the satellites in figure 4.3. The reason is the miscut of the substrate which is replicated in the superlattice [37].

A single crystalline substrate, like the MgO substrates used in our work, may

exhibit a difference between the normal of the surface and the z direction of

the crystal structure. This makes the realignment between reflectometry and

Figure 4.3. Superlattice diffraction patterns as measured form a conventional θ-2θ scan. The three samples measured have the same thickness ratios but different absolute thicknesses.

Figure 4.4. Reciprocal space map around the (002) peak (left) and the (013) peak

(right). Q _⊥ is along the [001] while Q _k is along the [100] direction [37].

diffraction measurements necessary. In addition, the pattern is tilted with a constantly variable offset angle between θ and 2θ. The out-of-plane direction is co-linear with the direction of the normal of the interfaces between bilayers but tilted with respect to the z direction of the superlattice crystal structure.

Hence, the direction in the RSM that the satellites define is tilted with respect to the [001] direction.

The θ-2θ scan can be reconstructed using the reciprocal space maps by in- tegrating a region of interest (figure 4.5). Using this approach the apparent contradiction discussed above is revealed as an experimental artifact and the satellite intensities are as expected from theory. The Laue oscillations seen are not as pronounced as the ones in figure 4.3 because of lower resolution of the measurement.

Reciprocal space maps have also been used to measure the in-plane lattice

Figure 4.5. X-ray diffraction θ -2θ scans extracted from RSMs. The samples are Fe/V superlattices of different bilayer thicknesses but same thickness [37]

.

parameter of the Fe/V superlattices. Using the horizontal and vertical dis-

tances between the (002) and (013) reflections and by implementing the pro-

cedure described by Fewster [41], the average in-plane lattice parameter was

extracted to be 2.979 Å, in agreement with the epitaxial relation expected be-

tween substrate and over-layer. The small changes in alignment and the devia-

tions from colinearity between the sample surface normal and crystallographic

z-direction manifests in the measurement, since the sample quality is high, re-

sulting in narrow Bragg reflections.

5. Experimental techniques

To acquire information about the proximity of different non-absorbing layers and strain on the thermodynamics of H vanadium, neutron reflectometry is a suitable technique. Neutrons are sensitive to deuterium and provide direct in- formation on the deuterium content in Fe/V and Cr/V superlatices.

In addition, X-ray diffraction is sensitive to lattice plane distances. This allows to measure the lattice expansion in superlattices under hydrogen loading. For a linear expansion coefficient under hydrogen loading information about the concentration can be accessed and the solubility limits of the α and β phases can be extracted. Here we also use optical transmission to provides a rela- tive scale the H content in metal hydrides, that do not undergo metal-insulator transitions [42].

5.1 Concentration determination via neutron reflectometry

For a system where one of the two layers is absorbing H, neutron reflectometry can be used to measure the concentration of H quantitatively and absolutely.

The connection between reflectivity and concentration results from the scatter- ing length density (SLD) of the H absorbing layer. The characteristic bilayer Bragg peak of the superlattice depends on the thickness of the bilayer in terms of peak position and on the SLD difference of the absorbing and non absorb- ing layer in terms of intensity. In the case of neutrons as a probe, D is chosen instead of H to increase the sensitivity. The isotope effects of H and D have been investigated and are minimal [43].

Since H (or deuterium) is absorbed in vanadium and occupies an interstitial site, the SLD of the hydride will depend on the sum of the SLDs of both the host metal and the H (or D) atoms.

ρ(c) = ρ V + ρ _D ρ( c) = b V N _V

V uc + b D N _D V uc

V uc

N V b V ρ(c) = 1 + b D

b V c

(5.1)

b (fm) ρ lit (10 ⁻⁶ Å ⁻² ) ρ sim (10 ⁻⁶ Å ⁻² )

V -0.38 -0.23 -0.23

Fe 9.45 8.00 5.74

H -3.74 - -

D 6.67 - -

Table 5.1. Summary of the neutron scattering length and SLD values for the elements used for an Fe/V-2/14 SL. ρ lit refers to the literature value of the SLD and ρ sim refers to the one obtained from fitting the data [44].

ρ(c) is the concentration dependent SLD value, ρ _{V (D)} is the SLD of vanadium or deuterium, c the concentration and V uc is the volume of the deuterated ma- trix. The interstitial site occupancy of D in the matrix results in an expansion of the lattice crystal. However, the epitaxial thin film is clamped to the sub- strate and cannot expand in-plain. This leads to the volume expansion being equal to the linear, out-of-plane expansion.

V uc (c) − V uc (0)

V _uc (0) = L(c) − L(0)

L(0) (5.2)

Where V _uc (0) is the volume of the matrix for zero D concentration, or in other words, the volume of the V matrix. Correspondingly, L(c) is the thickness of the absorbing layer for a specific concentration and L(0) is the thickness with- out deuterium. Equations 5.1 and 5.2 can be combined to [29]:

c =

 ρ (c) ρ _V



1 + L(c) − L(0) L(0)



− 1  b _V

b D (5.3)

Equation 5.3, is used in combination with the neutron reflectivity results and provides an absolute value of deuterium concentration in vanadium. The neu- tron reflectometry measurements were done on the instrument Super ADAM (Institut Laue-Langevin, Grenoble, France) and fitted with the program GenX [18].

In figure 5.1 the SLD profiles resulting from fitting a model to the Fe/V su- perlattice data are presented. The measurements are done at different D ₂ pres- sures (the experimental set-up will be presented in the next chapter). At the bottom of the figure, the full SLD profile is shown, including the MgO sub- strate (∼ 0 on the horizontal axis), along with the Pd capping layer (∼ 750 Å), for the unloaded sample in vacuum.

At the top, three panels depict zooms of the SLD profile for different D pres-

sures. The SLD value of 5.8 × 10 ⁻⁶ Å ⁻² corresponds to the non-absorbing

layer, in this case Fe. It remains constant since Fe does not absorb D in the

pressure and temperature range investigated. The width of the rectangle cor-

responds to the thickness of the Fe layer. For the absorbing layer (V+D), the

SLD value depends on the D content and increases for higher D 2 pressures. In

addition, for the deuterated SLD profiles, the interface SLD remains the same

Figure 5.1. Neutron SLD profile for the Fe/V superlattice [45].

as the one for the non-deuterated V layer. The reason is the depleted layers in the absorbing material, that are close to the V-Fe interface. These layers are known not to absorb D [14].

In figure 5.2 the neutron reflectivity of a Fe/V-2/14 SL exposed to 25 mbar D pressure, at 190 ^o C is presented. The model used to fit the data includes the depleted layers, as seen in the SLD profile of Fig. 5.1. The lower reflectivity curve (data divided by 100) depicts the same data, but without the depleted layers included in the simulation. The SLD value of the absorbing layer is forced to fit the Bragg peak at Q=0.26 Å ⁻¹ . The model does not fit the data without including the depleted layers.

Apart from the differences in SLD, the pattern in figure 5.1 expands towards the right side of the graphs, due to the expansion of the absorbing layers for higher D contents. The SLD profile in figure 5.1 results in the simulated red curves in Fig 5.3. The characteristic Bragg peaks move towards smaller Q values, while they decrease in intensity for higher deuterium pressures. That is expected, since the SLD profile expands the Q value of the bilayer peak is expected to move towards smaller values.

The non-deuterated model was fitted with 7 parameters, including thickness and SLD for the Fe and V layers, as well as the thickness and roughness of the Pd capping, roughness of the substrate and roughness of the top V layer.

The layers in the different repetitions are coupled regarding both the thickness

and the SLD (see Tab. 5.1). Furthermore, the values of thickness were cross-

referenced with values obtained from X-ray reflectivity and diffraction. The

only parameters that were varied for the measurements at different D 2 pres- sures are the thickness and the SLD value of the vanadium layer.

Figure 5.2. Neutron reflectivity measurement of the sample in 25 mbar of D 2 . The

curve at the top includes the depleted layers and the simulation at the bottom does not

[45].

Figure 5.3. Neutron relfectivity measurements for different D 2 pressures, along with

fits extracted from GenX.

5.2 Expansion measurements with X-ray diffraction

The difference between reflectivity and diffraction is the sensitivity to different length scales. Diffraction can be used to acquire information about the plane distances of the host lattice, and the changes due to hydrogenation. The X-ray diffraction measurements were done for various pressures of H ₂ for a given temperature each time. The sample was a Cr/V-2/14 SL. For the measure- ments, a hydrogen loading chamber was used, that enables temperature and pressure control. The chamber is equipped with Be windows, that are virtually transparent to X-rays. The chamber was mounted in an X-ray diffractometer.

The radiation used was CuKα ₁ since the diffractometer was equipped with a Goebel mirror and beam compressor.

Fig. 5.4 shows the (002) reflections of the superlattice for a range of H ₂ pres-

Figure 5.4. X-ray diffraction measurements of a Cr/V-2/14 superlattice in a series of H 2 pressures, at 225 ^o C.

sures at 225 ^o C (The reader is refered to Appendix for an introduction to scat-

tering from superlattices). Not only the expansion is seen from the movement

of the peak towards lower angles, but also the intensity of the peak is seen to

change with H concentration. Since X-ray diffraction is sensitive to the rel-

ative positions of the V atoms, the position of the average lattice parameter

peak depends on the periodicity of the atomic positions in the out-of-plane di-

rection. The peak is seen to reduce in intensity since the V lattice is distorted

and the atomic positions get out of phase. For higher pressures, the intensity

increases again, due to the rearrangement of atoms forming a higher ordered

structure again [13]. The region of the graphs where the intensities are mini-

mal show single peaks of low intensity.

Figure 5.5 shows data taken for a number of H 2 pressures at 200 ^o C. The gen- eral behavior of expansion and intensity variation is similar to the data taken at 225 Â ^◦ C. However the low intensity peaks start developing a shoulder to- wards lower Q values. At lower temperatures, the extra feature seen in the low

Figure 5.5. X-ray diffraction measurements of a Cr/V-2/14 superlattice for a range of H 2 pressures, at 200 ^o C.

intensity peaks is more pronounced. Figure 5.6 depicts the scans taken at 175

o C. Clear separation of the Bragg peak is seen. At 150 ^o C the splitting into

two peaks is clearly visible (figure 5.7). That is consistent with the existence

of a second phase in the sample. The expansion of the lattice can be calculated

from the peak positions. Figure 5.8 shows the pressure of H ₂ in the chamber

against the average lattice parameter expansion for all pressures and tempera-

tures measured.

Figure 5.6. X-ray diffraction measurements of a Cr/V-2/14 superlattice for a range of H 2 pressures, at 175 ^o C.

Figure 5.7. X-ray diffraction measurements of a Cr/V-2/14 superlattice for a range of

H 2 pressures, at 150 ^o C.

Figure 5.8. Isotherms extracted from X-ray diffraction measurements. The pressure

of H 2 in the chamber is plotted against the average lattice parameter expansion for the

temperatures of 225 ^o C, 200 ^o C, ^o C, 175 ^o C and 150 ^o C.

5.3 Optical transmission

Previous studies have used optical transmission as means to assess the con- centration in metal hydride thin films. It has been shown experimentally that the optical transmission changes linearly with concentration [42]. Still optical transmission does not provide a direct measurement of the absolute concen- tration of H in the lattice [21]. However, neutron relfectometry combined with in-situ optical transmission measurements can be used to measure the trans- mission of light and the absolute vanadium concentration in the vanadium layer at the same time. This allows a calibration of the optical transmission method and a verification of the linearity with hydrogen concentration. A more detailed description of this method is found in section 5.1.

The Beer-Lambert law describes the transmitted intensity, as it is reduced due to attenuation from a material of thickness d:

I ₀ = I _in e ^−α

⁰

^d

⁰

I(c) = I in e ^{−α(c) d(c)}

I(c) = I 0 e ^α

⁰

^d

⁰

− α(c) d(c)

(5.4)

Where α(c) and α ₀ are the linear attenuation coefficients of the material with and without hydrogen, respectively. As the material absorbs hydrogen, it’s thickness changes due to expansion. d 0 is the thickness of the material before hydrogenation and d(c) after for a hydrogen concentration c. The third line in equation 5.4 is deduced from the previous two since the incoming intensity I in

is equal in both cases.

Taking the expansion of the material due to hydrogen loading and Eq.5.4 into account, we can write:

− ln I(c) I ₀

 1

d ₀ = −α 0 + α(c) d(c)

d ₀ (5.5)

The concentration dependence of the optical transmission, can be associated with the difference of the linear attenuation coefficients. The influence of hydrogen concentration and expansion on optical transmission is one of the subjects of Paper III.

It is clear that the initial thickness of the sample, before hydrogenation, is

important. Therefore, the comparison between different samples of different

thicknesses must be done carefully.

6. Results and discussion

In this chapter the results of the investigation of proximity effects, of the X-ray diffraction measurements aimed to pinpoint the solubility limits in the phase diagram of the Cr/V-2/14 SL and the relation of optical transmission to expan- sion and concentration are presented.

6.1 Effects of substitution of the non-absorbing layer

By exchanging the non-absorbing layer of the superlattices, differences have been identified between Fe/V-2/14 and Cr/V-2/14 superlattices. The two sam- ples have been compared in terms of their concentration-expansion relation.

In Figure 6.1 the left panel shows the reflectivity patterns of a Cr/V-2/14 su-

Figure 6.1. Shift of the bilayer Bragg peaks (∆Q) of the two samples in the same experimental conditions (right panel). The expansion in the case of Cr/V-2/14 is sig- nificantly larger, although the reflectivity of the empty samples are similar (left panel) [29].

perlattice (top) and a Fe/V-2/14 superlattice (bottom). In the right panel, the shift of the bilayer Bragg peak as measured with neutron reflectometry, for both the samples, at the same conditions of 190 ^o C and 1000 mTorr is plotted.

For the same temperature and deuterium pressure the Cr/V sample exhibits significantly larger expansion.

In Figure 6.2 the volume expansion vs. concentration for both samples is pre-

sented. The slope of the expansion-concentration line is different. This is

associated with the site occupancy of the deuterium atom in the crystal which

Figure 6.2. The expansion of the two samples is plotted against concentration. The average expansion and average concentration refers to the normalization of both to account for the depleted layers [29].

is Octahedral site for the Cr/V superlattice, with a value of expansion coeffi- cient of 0.166. For the Fe/V superlattice, the value of the expansion coefficient is 0.103, that is indicative of Tetrahedral site occupancy [29].

There is no apparent indication as to what the reason for the changes is, since

the absorbing layer is expected to be identical in both cases. The V layer is

identical in terms of strain, due to the registry with the substrate, and also in

terms of thickness. However, the values of the expansion coefficients are a

subject of investigation that is presented in Paper III [29]. There, a complete

thermodynamic analysis including enthalpy and entropy changes, used to ex-

plain the proximity effect in combination with ab-initio calculations.

6.2 X-ray diffraction and solubility limits

The calibration of the concentration scale for the expansion measurements, was done using the isotherms shown in Figure 6.3. The pressure and temper- ature was used to correlate the concentration to the expansion as measured by X-rays. There are noticeable differences when compared to Figure 5.8, where the expansion of the average lattice spacing was used as the horizontal axis, instead of concentration. That can be attributed to the unreliability of diffrac- tion to measure H induced volume expansion [19].

The calculated concentration from the reflectometry measurements were used to produce a concentration scale for the Cr/V-2/14 SL. The diffraction data (002) Bragg reflection) in this section are fitted with one or two peaks of ei- ther Gaussian or pseudo-Voigt line shape, in an effort to acquire information about the peak positions and peak widths.

In Figure 6.4 an example of a set of peak fits is presented. The peak on the

Figure 6.3. Expansion-concentration graphs for four temperatures. The concentra- tion values were extracted from neutron reflectometry and were associated with the depicted measurements using the H 2 pressure and temperature.

right hand side of the graph, corresponds to the (002) Bragg reflection of the

unloaded sample at a temperature of 225 ^o C. The peak was fitted with a sin-

gle Gaussian. The peak in the middle of the graph corresponds to the (002)

peak for a pressure of 12.39 Torr, at the same temperature. For that peak a

pseudo-Voigt function was used for fitting, as a Gaussian could not capture

the shoulders of the peak correctly. As a measure to quantify the deviation

Figure 6.4. A selection of peaks to be used as examples and the Pseudo-Voigt curves used to fit them are shown. The µ factor that weights the contribution of the Gaus- sian and the Lorentzian to the Voigt curve, for each fit seems to change for different pressures.

from a Gaussian fitting, the parameter µ of the fit is given. The µ parameter is the weight factor of the Lorentzian contribution in the pseudo-Voigt used for fitting. The reduction of intensity for the peak at 12.39 Torr can be attributed to the distortion of the lattice and can be described by the short-long model proposed in [13]. For the measurements at higher pressures, the peak intensity increases as the concentration of H in the sample increases in accordance with the findings of Bloch et.al. [46], while the µ parameter decreases.

In Figure 6.5 a different approach is used for the peak at 4.229 Torr pressure and at a temperature of 200 ^o C. The peak can be described effectively by a set of two independent Gaussians. In this case, the two Gaussians have different positions and different shapes. The wide feature described by the extra Gaus- sian does not have the same position with the primary peak, and thus cannot be attributed to diffuse scattering.

In Figure 6.6 a diffraction pattern fitted with a set of two Gaussians is shown.

Complementraty studies on the thermodynamics of the Cr/V-2/14 SL have shown that the critical temperature is around 150 ^o C [29]. Since a clear co- existence is seen in the diffraction data at higher temperatures, no significant deviation from the bulk V-H behavior is seen, since there the critical point is

"hidden" behind the coexistence curve [32].

In Figure 6.7 the separated peaks are fitted with a combination of two Gaus-

Figure 6.5. A combination of two Gaussian curves used to fit the peak for 4.229 Torr and 200 ^o C.

sians. A feature is seen between the two peaks, that is well within the resolu- tion of the instrument. Nevertheless, the fitting procedure was kept as simple as possible and a third Gaussian was not included.

In Figure 6.8 the coherence lengths extracted from the measured peaks, for a temperature of 150 ^o C are shown. The coherence lengths are calculated us- ing Eq. 4.1. For the measurements where two Gaussians were used for the fitting, the sum of corresponding coherence lengths is represented by the red dots. The sum of the coherence lengths of the individual peaks (red dots), have comparable values to the points that correspond to a single peak measurements (black dots). The same is seen for the coherence lengths measured at 175 ^o C (Figure 6.9).

In figure 6.10 the coherence lengths and their sums are given for a temperature of 200 ^o C. Previous solubility measurements on the same system have shown that this temperature is higher than any temperature with phase coexistence.

This is in line with the X-ray measurements since there is no peak separation.

Nevertheless, the fitted secondary Gaussians are included in the calculation of

the coherence lengths. The sum of coherence lengths is comparable to the co-

herence length of the un-loaded sample. In figure 6.11 the coherence lengths

for a temperature of 225 ^o C is plotted. The coherence lengths were calculated

based on the FWHM values of the peaks as fitted by the pseudo-Voigt curves,

regardless of the µ value. The coherence lengths of the corresponding regions

were used as composition fractions, in order to calculate the solubility limits

of the different phases. The results are presented in figure 6.12, where the

concentration limits are compared to the positions of the corresponding peaks.

Figure 6.6. A combination of two Gaussian curves used to fit the peak for 1.504 Torr and 175 ^o C.

Figure 6.7. A combination of two Gaussian curves used to fit the peak for 0.345 Torr and 150 ^o C.

The slight asymmetry seen in the panel on the right is due to differences in expansion between reflectometry and diffraction. A thorough investigation on the reliability of those techniques to measure H induced expansion, can be found in [19].

Regarding the order of the phase transition, the clear phase separation for tem-

peratures equal to and lower than 175 ^o C and the shape variations of the peaks

for 200 ^o C are observed. We can conclude that in the case of Cr/V-2/14 su-

perlattices the phase transition observed is abrupt (first order), so no criti-

cal behavior is expected, in contrast with other works where both superlattice

constituents absorb hydrogen [47]. In addition, the coherence lengths of the

Figure 6.8. The coherence lengths calculated from the measurements at 150 ^o C.

Figure 6.9. The coherence lengths calculated from the measurements at 175 ^o C.

separated peaks add up to values comparable to the coherence length of the

un-loaded superlattice. Consistent with the above observations is the notion

of a horizontal phase separation (the phases are separated in the out-of-plane

direction), where the phase boundary moves in the z direction with concentra-

tion. That is possible since it is known that the elastic boundary conditions can

affect the spatial arrangement of the different phases [48]. This explains why

the structural integrity of the sample is not degrading over cycles of loading

and un-loading with hydrogen.

Figure 6.10. The coherence lengths calculated from the measurements at 200 ^o C.

Figure 6.11. The coherence lengths calculated from the measurements at 225 ^o C.

Figure 6.12. The solubility limits are shown as extracted from the lever rule and

compared to the temperature versus peak position diagram.

6.3 Optical transmission, concentration and expansion

The optical transmission measurements of hydrogenated thin films is a robust procedure to acquire information about the change in hydrogen content in thin vanadium layers [49]. Using an in-situ hydrogen loading chamber with the possibility of neutron reflectivity and optical transmission simultaneously, the connection between concentration, expansion and optical transmission was in- vestigated.

In figure 6.13 the optical transmission is plotted against expansion (right panel).

Figure 6.13. Optical transmission versus concentration (left) and expansion (right).

The optical transmission scales exactly the same for the two samples, when plotted against expansion. The solid black line (right panel) is the expected optical transmis- sion value for a given expansion, as predicted by ab-initio DFT calculations [29].

The results suggest that the linear attenuation coefficient is constant with ex- pansion, and in addition, it does not change between samples. That indicates that the direct effect of concentration on the attenuation coefficient is mini- mum, since the two samples have a quite different expansion-concentration profile.

One can obtain the values of the attenuation coefficients in the superlattices.

The values are α _Fe/V = 78(2) µm ⁻¹ and α _Cr/V = 77(3) µm ⁻¹ . Appart from the apparent similarity, the linear attenuation coefficients are reasonable when compared with the attenuation coefficient of V that is α V = 61 µm ⁻¹ [50].

As discussed previously, the two different superlattices have different expan-

sion coefficients (see figure 6.2). By plotting the change in optical transmis-

sion against expansion, the differences in optical transmission due to effects

of substitution of the non-absorbing layer are eliminated and the optical trans-

mission is seen to scale identically for the two samples. The above indicate

that the changes in optical transmission, for a wavelength of 625 nm, of hy-

drogenated V superlattices are due to expansion of the sample. This was the

subject of the investigation described in Paper III where ab-initio calculations

were used in combination with the above experimental findings [29].

7. Summary and conclusions

In this work superlattices are used in a systematic investigation of proximity and finite size effects. The growth of Fe/V and Cr/V superlattices using D.C.

magnetron sputtering, is optimized towards single crystal samples with iden- tical strain states for different thicknesses. By changing the thickness ratio of the constituents and by optimizing the growth conditions, fully coherent single crystals were grown, with minimum mosaic spread and good interface quality (results in Paper I).

These samples were used in optical transmission measurements, for the in- vestigation of thermodynamics and kinetics in vanadium superlattices (results in Papers IV-VII). Optical transmission is a technique used to measure the changes of hydrogen content in thin films of vanadium. In this thesis, this technique was complemented by neutron reflectometry to extract the absolute scaling of hydrogen concentration and volume expansion. Possible shortcom- ings resulting from interference effects in neutron reflectometry and biasing the expansion-concentration data evaluation are discussed (results in Paper II). By using an in-situ hydrogen loading chamber, with the possibility of measuring neutron reflectometry and optical transmission simultaneously, it was proven that the optical transmission changes with concentration linearly.

For the monochromatic radiation used in this work, the main reason for the changes in the optical transmission is the expansion of the lattice due to hy- drogen loading. The profound proximity effects on the thermodynamics of hydrogen in Cr/V and Fe/V superlattices can be related to the difference in expansion coefficients (results in Paper III).

Local strain effects have been investigated by X-ray diffraction and the solu-

bility limits in the temperature-concentration diagram were determined. The

co-existence of phases in the temperature-concentration phase diagram and the

phase behavior of hydrogen in Cr/V superlattices is compared to bulk vana-

dium, as well as to other hydrogen-superlattice systems with respect to their

critical behavior.

8. Outlook

The fully coherent superlattices described in Paper I enabled very accurate concentration determination in Paper III, since the evaluation of the data and calculations were based on coherent superlattices. A next step might be the investigation of different strain states. For example, Mo/V superlattices where the lattice parameter of Mo (3.15 Å) causes in-plane, biaxial tensile strain, rather than biaxial compressive strain, as in the case of Cr and Fe. Still the clamping is preserved and as a result the expansion along the interface normal is expected to be significantly different. Nb/Ta superlattices have been used in the past in studies that include scattering techniques to characterize the criti- cal behaviour [47]. The same approach can be used to study the behavior of Fe/V superlattices close to the critical point. The difference is that in the case of Fe/V one of the two layers does not absorb hydrogen, in contrast to Nb/Ta where both layers do, however, the enthalpy of hydrogen absorption in Nb and Ta is slightly different.

X-ray diffraction measurements were performed in the contexts of this study, on Cr/V superlattices. The diffraction measurements can be performed also for Fe/V superlattices to estimate the impact of proximity effects in the regime of atomic plane distance to complement the profound differences seen in neutron reflectometry. There are interesting features in the Cr/V-2/14 measuerements that can be identified. Beyond the analysis of the (002) peak position and in- tensity, the peak shapes and the satellite peaks contain information about the strain in the lattice. In this thesis the coexistence of α and β phases has been found at surprisingly high temperatures and the data suggest that possibly the film is phase separated along the surface normal. Nuclear reaction analysis (NRA) is a technique that can reveal more information about the concentra- tion profile. Corresponding measurements with X-ray diffraction and NRA in Fe/V superlattices might provide further insight about the proximity effects.

The strain state of the superlattices can be studied for a range of H concen- trations. By using reciprocal space maps (RSM) to extract the exact θ − 2θ intensities and the method proposed by Miceli and Zabel can be used to extract the strain of the individual layers [40].

In paper III it is shown that the main reason for changes in optical transmission

is the expansion of the sample. However, that is true for a specific wavelength

and, it would be interesting to test the assumption for a wider spectrum. For

a white light source, a spectroscopic approach might provide additional infor-

mation about the electronic structure.