Hydrogen in Yttrium Films Structure and Phase Formation

DISSERTATION

zur Erlangung des Grades eines Doktors der Naturwissenschaften der Fakultat¨ fur¨ Physik und Astronomie an der Ruhr–Universitat¨ Bochum

vorgelegt von

Arndt Remhof

Bochum 1999

Hydrogen in Yttrium Films Structure and Phase Formation

DISSERTATION

zur Erlangung des Grades eines

Doktors der Naturwissenschaften

der Fakultat¨ fur¨ Physik und Astronomie

an der Ruhr-Universitat¨ Bochum

vorgelegt von

Arndt Remhof

Bochum 1999 Mit Genehmigung des Dekanats vom 16. Juli 1999 wurde die Dissertation in englischer Sprache verfasst. Eine deutschsprachige Zusammenfassung beﬁndet sich am Ende der Arbeit.

Dissertation eingereicht am ...... 01.12.1999

Erstgutachter ...... Prof. Dr. Hartmut Zabel

Zweitgutachter ...... Prof. Dr. Ulrich Kohler¨

Tag der Disputation ...... 01.02.2000 CONTENTS

1 Introduction 1

2 Hydrogen in metals 5

2.1 Hydrogen dissociation and hydride formation ...... 6

2.2 The lattice gas model ...... 8

2.3 Phase transitions ...... 12

3 The Hydrogen–Yttrium System 15

3.1 The α–phase ...... 16

3.2 The β–phase ...... 16

3.3 The γ–phase ...... 17

3.4 Electronic and optical properties ...... 20

3.5 Thin YHx–ﬁlms ...... 26

4 Experimental methods 27

4.1 X–ray diffraction ...... 27

4.1.1 Introduction ...... 27

4.1.2 Basic concepts ...... 27

4.1.3 X–ray scattering by crystals ...... 29

4.1.4 Scattering by thin ﬁlms ...... 31

4.1.5 X–ray diffraction topography ...... 34

4.1.6 Grazing incident x–ray diffraction and X–ray reﬂectivity ...... 36

i ii Contents

4.2 Neutron Diffraction ...... 40

4.2.1 Bragg scattering ...... 40

4.2.2 Neutron reﬂectivity ...... 42

4.3 Electron Diffraction ...... 43

4.3.1 Diffraction of fast electrons (RHEED) ...... 43

4.3.2 Diffraction of slow electrons (LEED) ...... 44

4.4 Instruments used ...... 47

5 Sample design 55

5.1 Molecular Beam Epitaxy MBE ...... 55

5.2 The growth process ...... 57

5.3 Sample architecture ...... 59

5.3.1 The substrate ...... 59

5.3.2 The Nb buffer layer ...... 61

5.3.3 The Y layer ...... 62

5.3.4 The cap layers ...... 64

6 Results I: The microscopic scale 67

6.1 X–ray characterization of the virgin sample ...... 67

6.2 X–ray scattering on the hydrogenated sample ...... 72

6.3 Neutron reﬂectivity and isotope exchange ...... 77

6.4 Off–specular neutron diffraction ...... 83

6.5 Conclusion ...... 87

7 Results II: The macroscopic scale 89

7.1 X–ray diffraction topography measurements ...... 89

7.1.1 The virgin sample ...... 91

7.1.2 Hydrogen loading and phase formation ...... 92

7.1.3 Lateral phase propagation ...... 97 Contents iii

7.1.4 The narrowing of the miscibility gap at elevated temperatures . . . . . 100

7.2 Optical appearance and AFM studies of a partially loaded sample ...... 101

7.3 Electrical resistance measurements ...... 103

7.4 Conclusion ...... 106

8 Summary 107

9 Zusammenfassung 111

9.1 Das Yttrium–Wasserstoff System ...... 111

9.2 Probenpraparation¨ und Experimentelle Methoden ...... 113

9.3 Ergebnisse ...... 115

List of Figures 121

Bibliography 125

Publikationsliste 131

Danksagung 133

Lebenslauf 135 iv Contents 1. INTRODUCTION

Hydrogen in metals has been investigated since Graham discovered in 1866 that palladium can absorb large amounts of hydrogen gas. Apart from Pd, there are numerous other metals which

exhibit the ability to absorb hydrogen. Within the metal, the H2 molecule is dissociated and the H atoms occupy interstitial sites in the host lattice. The hydrogen changes drastically the mechanical, electrical, magnetical and optical properties of the metal. Hydrogen also affects the crystalline structure of the specimen, often leading to complex phase diagrams. Due to the small mass of the hydrogen atom diffusion is fast. Even at room temperature jump rates of up to 1012 Hz have been observed. Therefore structural phase transitions may occur at temperatures lower than for transitions in ordinary metallic compounds.

The results of the research on metal hydride systems are reviewed in several books and review articles. The following list presents a selection of monographs which provide an overview on metal hydrogen systems. The essential theoretical and experimental aspects may be found in Hydrogen in Metals I and II, edited by Alefeld and Volk¨ el [1], followed by Hydrogen in Intermetallic compounds I and II, edited by Schlapbach [2]. Basic bulk properties have also been discussed by Fukai in The Metal-Hydrogen System [3]. The special case of rare earth hydrogen systems have been summarized by Vajda in the Handbook of Rare Earth, Vol 20, [4].

In the past, research on metal hydride has been focused on hydrogen embrittlement and on metal hydrides as hydrogen and energy storage systems. Research in this direction is still going on. Especially the ﬁeld of alternative energy sources such as hydrogen fuel cells progressed a lot.

Recent technologigal advances in thin ﬁlm deposition techniques and hydrogen loading capabilities caused renewed interest in metal–hydrogen systems. Exciting new structural and functional properties have been discovered. This has stimulated further work on thin ﬁlms and superlattices.

Hydrogen in metals turned out to be more than a structural ingredient. It can be used as a functional agent in high technology materials. Among those are hydrogen induced changes of

1 2 Chapter 1. Introduction

the magnetic exchange coupling in Fe/Nb [5] and Fe/V [6] superlattices, resulting in a hydrogen switchable giant magneto resistance effect. Hydrogen may also be used to probe mechanical properties of materials. Through the hydrogen caused lattice expansion in epitaxially grown Nb ﬁlms for example, an extraordinary adhesion of Nb on sapphire has been observed [7].

Regarding different hydrogen metal systems, the hydrogen yttrium system is outstanding. It holds the record of the highest enthalpy of solution. In other words, given the choice between all metals, the hydrogen will preferably proceed to yttrium. Together with its chemical relatives, the heavy rear earth, yttrium also holds the record of the highest possible hydrogen concentration. To reach saturation, three hydrogen atoms per yttrium atom have to introduced into the sample. Depending on the hydrogen concentration, the yttrium hydrogen system exhibits three structural phases. The structural phase transitions are accompanied by changes within the electronic configuration including a metal insulator transition in the hydrogen rich trihydride phase which also affects the optical properties of the material [4]. Starting as a shiny reflecting metal, the material becomes transparent at higher hydrogen concentrations. The discovery of these hydrogen switchable mirrors in thin rare earth hydride films challenged theoretical as well as experimental physicists to understand how the presence of hydrogen in yttrium films affects their electronic structure, determining optical attributes [8]. The influence of the dimensionality in thin film samples is still an open question. Up to now, no reliable structural data exist for epitaxially grown, single crystalline films. The crystal structure of a given material determines its physical properties. It is the starting point to discuss phase transitions, epitaxial relations and electronic band structures. In order to explain the metal–insulator transition in the Y–H system, different structural parameters have been suggested. Small changes of the arrangements of hydrogen atoms within the yttrium matrix result in different band structures and thus in different optical properties.

Within this thesis detailed structural data on epitaxially grown, single crystalline yttrium films will be presented. X–ray and neutron scattering techniques allow to study the crystal structures of the hydride phases of yttrium. Both the response of the host lattice upon hydrogen uptake as well as the order of the hydrogen atoms within the hydride phases have been investigated. Via the scattering length contrast, neuton scattering also opens an access to the hydrogen concentration within the yttrium film. Imaging techniques based on Bragg reflection also allow to study the nucleation of phases, domaine sizes and the movement of the phase boundaries. Supplemen- tary experiments like resistence measurements or microscopic techniques have been carried out to gain additional information on transport properties and on the morphology of the Y–H system. All thin film samples were manufactured in ultra high vacuum (UHV) by molecular beam Chapter 1. Introduction 3

epitaxy (MBE), a method of physical vapor deposition which guarantees chemical purity, well deﬁned and ﬂat interfaces as well as high crystalline quality. By controlled hydrogen loading

single crystalline YH2 and YH3 samples could be prepared. To perform the experiments in situ, i. e. in hydrogen atmosphere, several vacuum chambers have been build or modiﬁed within this thesis.

After introducing M–H systems in chapter 2, chapter 3 will give a detailed overview on the Y–H system. The experimental methods used to study the crystalline structure and the sample preparation will be explained in chapters 4 and 5. The results of the measurements will be presented and discussed in chapter 6 and 7. The main results and remaining open questions will be summarized in chapter 8 and an outlook will be given, suggesting further experiments. 4 Chapter 1. Introduction 2. HYDROGEN IN METALS

Many metals dissolve considerable amounts of hydrogen in an exothermic reaction. Well known prototypes of hydrogen (H) – metal (M) systems are the transition metals vanadium, niobium, tantalum and palladium as well as the rare earth metals together with their chemical relatives scandium and yttrium. They exhibit many fascinating properties in common, which make them an interesting ﬁeld of studies both from the experimental as well as from the theoretical point of view. Some of them are listed below:

The possibility of absorbing large quantities of hydrogen (up to 100 atomic % in transition metals and up to 300 atomic % in rare earth metals). In many compounds the density of the dissolved hydrogen is higher than that of solid hydrogen.At the surface of the metal,

the H2 molecule gets dissociated.

Metal–hydrogen systems can often be prepared by hydrogen gas loading or by electrolytic charging. The concentration of hydrogen in the metal may be varied continuously, allowing examination of very dilute or non–stoichiometric compositions.

Compared with other interstitials such as oxygen, nitrogen or carbon, hydrogen possesses a very high diffusion coefﬁcient.

Hydrogen offers three isotopes with mass ratios of 1 : 2 : 3, resulting in sometimes re- markable isotope effects.

As hydrogen affects the crystallographic as well as the electronic structure, very often complex phase diagrams form. Especially the reversible changes of the structural, optical and magnetic properties of metal–hydride systems are of interest. They allow the design of materials with speciﬁc properties.

5 6 Chapter 2. Hydrogen in metals

2.1. Hydrogen dissociation and hydride formation

Why do some metals dissolve hydrogen and others don’t? What are the necessary steps of hydride formation?

The process of hydride formation can be explained phenomenologically by one–dimensional

potential energy curves, as displayed in ﬁg.(2.1). Far away from the surface, the H2–molecule and the metal are in their respective ground states. Compared to molecular hydrogen, atomic

hydrogen exhibits a potential energy of ED = 218 kJ/mol H, i. e. 4.7 eV per hydrogen molecule. This energy is needed to dissociate the hydrogen molecule. Close to the metallic surface van

der Waals forces between the molecule and the metal surface result in a physisorbed state. The

¡ ¡ energy gain of this process is typically Ep 10 kJ/mol H ( 0.2 eV/H2–molecule). Closer to the surface the curves of the molecular (H2) and the atomic (H) hydrogen overlap. Thus a fur-

ther approach of the hydrogen to the surface leads to a dissociation of the molecule and results

¡ ¡ in a chemisorbed state. The energy gain of the chemisorption of about Ec 50 kJ/mol H ( 1

eV/H2–molecule) is much larger than the heat of formation of the pysisorped state. If the curves of the atomic and the molecular hydrogen intersect above the zero–energy–line, then an activation energy barrier determines the kinetics of the reaction. Once chemisorbed, the hydrogen atoms exhibit a high mobility on the surface. With increasing coverage H–H interaction occurs, leading to modiﬁcations of the adsorption probabilities and of the heat of adsorption. Finally the chemisorbed hydrogen atoms get dissolved exothermically or endothermically within the metal, where hydride phases may nucleate and grow.

The H–M bond is of electronic nature, on the surface as well as in the bulk. To understand the processes of adsorption and desorption in detail, the electronic band structure of the metal has to be known. Whenever the hydrogen atom approaches the metal, it’s 1 s electron hybridizes with the electrons of the metal. As a consequence, the band structure gets modiﬁed. Bands shift in energy and may change in energy width. New bonding and antibonding bands will form within the metal. Especially the position of the antibonding band with respect to the Fermi energy of the metal and its occupation determines the nature of the M–H bond.

The resulting hydrides can be classified by the nature of the hydrogen bond into three different principal categories, covalent, ionic or metallic. The term ”hydride” will be used to describe the binary combination of hydrogen and a metal. Within this definition the nature of the bond as well as the hydrogen concentration is not important. Especially a fixed stoichiometry is not required. Chapter 2. Hydrogen in metals 7

Figure 2.1: One–dimensional energy curves of the activated and non–activated chemisorption of hydrogen on a metal surface and of a exothermic and endothermic solution of H in the bulk, respectively [2].

¢ Covalent hydrides may be solid, liquid or gaseous. The H–M bond is of the non–polar electronsharing type. Forces between the molecules of covalent bonded hydrides are not strong, resulting in low melting points. Most of them are thermally unstable. Typical examples of covalent hydrides are aluminum hydride, tin hydride and the boron hydrides.

¢ Ionic hydrides are formed by the reaction of the strongly electropositive metals like alkali metals and hydrogen by electron transfer. Their bonds result from the strong electrostatic forces between the dissimilar electric charges of the ions. The saline hydrides are crystalline. They exhibit large heats of formation and high melting points. The face centered cubic (fcc) crystal structure of the hydrides of the alkali metals are more dense than the pure metals, which crystallize in the body centered cubic (bcc) form, due to the more efﬁcient packing of atoms.

¢ Metallic hydrides are formed by the transition metals. They possess metallic properties like thermal conductivity or hardness. Because of the wide homogeneity ranges of most of the metallic hydrides, they are often regarded as solid solutions. There are two models describing the chemical bond of metallic hydrides. In the ﬁrst model, the electrons from the hydrogen occupy the d bands of the metal, and the hydrogen therefore exists essen- tially as protons in the metallic lattice. In the second model, the hydrogen exists as anions 8 Chapter 2. Hydrogen in metals

formed by transfer of electrons from the metal to the hydrogen, forming a partially ionic bond. Yttrium forms metallic hydrides. The H–Y system will be discussed in detail in the next chapter.

2.2. The lattice gas model

The high mobility of the hydrogen atoms together with the rather rigid metal lattice leads to the lattice gas model. In this model, the hydrogen atoms are free to move through the host lattice, while the metal atoms remain immobile. The hydrogen atoms occupy interstitial sites of the metal lattice. There are two different states of an interstitial site in a dilute H–M system: Occupied or not–occupied. Consider a metallic sample, surrounded by a hydrogen atmosphere in a ﬁxed volume V. The temperature T and the pressure p can be controlled from the outside. In this situation the thermodynamics of the system can be described using the Gibbs free energy

¤ ¦ G £ E T S PV (2.1)

where E is the energy and S is the entropy of the system. Usinging the total differential of the ¤

energy from the laws of thermodynamics dE £ TdS pdV , dG takes the form:

¤ § dG £ Vdp SdT µdn (2.2)

Thus the partial derivatives of the Gibbs free energy with respect to the temperature, the pressure and the number of particles result in the entropy, the volume and the chemical potential,

respectively:

¨ ¨

¨ ∂G ∂G ∂G

¦ £ ¦ £ §

£ ¤ S V µ (2.3)

∂T © ∂p ∂n

p n T n p T

If a system consist of several components, G will change according to the mole fractions of all

the components. Thus the total differential of G is given by:

¤ § dG £ V dp SdT ∑µidni (2.4) i Chapter 2. Hydrogen in metals 9

In thermodynamic equilibrium, G has to be a minimum with respect to any of its variables. So

at constant pressure and temperature, thermal equilibrium requires:

dG ∑µidni 0 (2.5) i

In the example of the metallic sample surrounded by a hydrogen atmosphere in a ﬁxed volume, dG takes the form:

∂G ∂G

dG dn 0 (2.6) ∂ ∂ H2

n n H2 H ∂ where nH2 represents an inﬁnitesimal change of the number of hydrogen molecules in the

confined atmosphere, while ∂nH describes an infinitesimal change of the number of dissolved ∂ hydrogen atoms within the sample. As the hydrogen content in the system is fixed, nH2

2 ∂nH and thus:

µH2 2µH (2.7)

Using the deﬁnition of the Gibbs free energy and exploiting the equation of state for an ideal

gas, the chemical potential µ p T can be expressed as R T ln p p , where p is a reference H2 0 0 ∆ pressure. The chemical potential of the lattice gas, µH, contains the heat of solution, H

EB 1 2ED, i. e. the energy gain per atom solved in the metal. If the binding energy EB is

bigger than half the dissociation energy ED 4 8 eV of the hydrogen molecule, the reaction is exothermic. This class includes the alkali and alkaline–earth metals, the titanium and the vanadium subgroup metals, the rare–earth metals (including scandium and yttrium), the actinide series metals, and palladium. Most other metals (e. g. Fe, Co, Ni, Cu, Ag, and Pt) dissolve hydrogen endothermically. Together with the entropy change involved with the absorption of a

hydrogen atom, the chemical potential µH can be written as:

∆ µ H RTln (2.8) H 1 x where x = no. of H atoms/no. of interstitial sites is a measure for the hydrogen concentration

within the metallic sample. In thermal equilibrium:

µ p T 2µ p T (2.9) H2 H 10 Chapter 2. Hydrogen in metals

p x

RTln 2∆H 2RTln (2.10)

p0 1 x

" #$ ! ∆

pH2 p0exp H RT (2.11)

1 x &%

Figure 2.2: The variation of the chemical potential as a function of hydrogen concentration.

The variation of the chemical potential as a function of hydrogen concentration is depicted in ﬁg.(2.2). At constant temperature (isothermic condition) and for small concentrations this leads to Sieverts law:

∝

pH2 x (2.12) %

∝ Sieverts law applies to all H–M systems. All solubility isotherms start off with a pH2 x– behavior, giving direct evidence for the assumption of the atomic solution of hydrogen in metals. At higher pressures, the slope of the solubility isotherms exhibit deviations from this behavior,

∆ " indicating interaction. Since H EB 1 2ED and since ED is constant, EB has to change

with the hydrogen concentration x. Introducing the hydrogen–metal interaction EH ' M and the

hydrogen–hydrogen interaction u, the binding energy can be written as:

! #

EB x EH ' M ux (2.13) %

Two hydrogen atoms, dissolved into a metal lattice interact via their long range distortion ﬁelds. Chapter 2. Hydrogen in metals 11

Each hydrogen atom requires a certain amount of space in the host lattice. Metal atoms close to the hydrogen impurity are pushed apart from their equilibrium position, leading to a lattice expansion. Interstitial sites close to an hydrogen impurity are energetically more favorable for other hydrogen atoms, as the metal lattice in this region is already expanded. Therefore the H–H interaction is attractive. However, at high hydrogen concentration, a repulsive short range interaction becomes important. Taking this electronic contribution into account EB takes the form:

2 .

)* -

+ , EB ( x EH M ux bx (2.14)

Given this expression for the EB, ∆H can be written as:

2 .

- * - )

∆ )/* ∆ ∆

( , , ( H x E + ux bx E H H x (2.15) H M 2 D 0 ex

∆ )

A schematic illustration of the excess enthalpy Hex ( x is displayed in ﬁg.(2.3).

Figure 2.3: Variation of the excess enthalpy (as the sum of an electronic and an elastic contribution) with the hydrogen concentration. 12 Chapter 2. Hydrogen in metals

2.3. Phase transitions

A phase is a state of matter that is uniform throughout, in chemical composition as well as in physical state. Being a state of matter rather than a property of a single particle, a phase is characterized by its macroscopic properties like the density, the magnetization, the refractive index, the specific heat etc. Depending on external conditions like temperature, pressure, magnetic field, etc., different phases may be realized. A phase diagram visualizes the different phases of a system. It shows the regions of pressure p (or magnetic field B , or concentration c) and temperature T at which the different phases of the system are thermodynamically stable. The boundaries between regions, the phase boundaries show the values of p (B or c) and T at which two phases coexist in equilibrium. A schematic p–T diagram is shown in fig.(2.4). In thermal equilibrium, the phase with the lowest chemical potential is realized. As the temperature is raised, the chemical potential of a pure substance decreases as

∂µ ∂ S 3 (2.16)

T p 021

576 4 5 This implies that the slope is steeper for gases than for liquids, because S 4 gas S liquid . The steep negative slope of µgaseous results in its falling below µliquid when the temperature is high enough. Then the gas becomes the stable phase, the liquid evaporates. The bold line in the right panel of ﬁg.(2.4) depicts the chemical potential as a function of temperature.

Figure 2.4: Schematic p–T diagram (left panel). The arrow crossing the phase border symbol- izes the isobar phase transition in the right panel. The behavior of the chemical potential during the transition (right panel).

The thermodynamic properties of substances, in particular the chemical potential, may be used Chapter 2. Hydrogen in metals 13 to classify phase transitions into different types. If the first derivative of the chemical potential is discontinuous at the transition, the transition is classified as first order phase transition. Many familiar phase transitions, like melting and vaporization, are examples of first order transitions. First order transitions are accompanied by changes of enthalpy and volume. Also the phase transitions in the H–Y system which have been investigated in this thesis are first order transitions. A second order phase transition is one in which the first derivative of µ is continuous but its second derivative is discontinuous. A continuous slope of µ implies that the volume and entropy do not change at the transition. Second order transitions include order–disorder transitions in alloys, the onset of ferromagnetism, and the fluid–superfluid transition of helium.

The phase diagrams of M–H systems are often quite complex. The Nb–H (ﬁg.(2.5)) is a well known model for a M–H system [1]. It may serve as an example.

Figure 2.5: The niobium – hydrogen phase diagram. 8

Phases α and α9 are disordered solutions of H in bcc Nb with low and high H concentrations, respectively. While the attractive H–H interaction prefers a dense phase, entropy favors a uniform distribution of hydrogen within the crystal. Below a critical temperature

Tc, both phases may coexist. As there is no symmetry change, this transition is continu-

ous. The lattice parameter of α and α9 increase linearly with concentrations. Above Tc the hydrogen concentration and thus the lattice parameter varies steadily with the applied 14 Chapter 2. Hydrogen in metals

hydrogen pressure.

: The β–phase is an ordered interstitial solid solution of hydrogen. The structure is fc orthorhombic. Neutron diffraction studies revealed additional superlattice reﬂections from hydrogen ordering. The α–β transition is driven by the elastic interaction. The total energy of the system can be lowered by different occupation densities within the crystal. Below a critical temperature the dense, ordered β–phase nucleates. As the β–phase is no longer cubic, i. e. it crystallizes in a different symmetry as the α–phase, the α–β transition can not be continuous.

: The ζ–phase was found by transmission electron microscopy upon cooling of the β–phase to between 210 K and 230 K. It arises from β by ordering of H–vacancies. This gives rise

to an additional periodicity along the cubic [110]–direction.¯

: ; The ε–phase has the composition Nb4H3. It is described by a cell with parameters a ; b ε

2a0 <>= 2 and is completely ordered. The –phase unit cell is obtained by appropriately mixing and joining elements of the β and ζ unit cells.

: The γ–phase is a pseudocubic, high–concentration, low–temperature phase of the approx-

imate composition NbH0 ? 9. It is stable below 200 K and is visible in x–ray diffraction through the disappearance of the orthorhombic reﬂections of the β–phase.

: The λ–phase is also an ordered structure with an approximate concentration of 80 %. : The δ–phase exhibits a fcc structure corresponding to the composition NbH2. It has a

gray, metallic appearance and is very brittle. The crystal structure is of the CaF2 type, where the H–atoms occupy tetrahedral sites. A further incorporation of hydrogen could occur on octahedral sites of the lattice, which would result in compositions above H/Nb

= 2. Such structures have not been observed, i. e. there is no evidence for a phase NbH3. Such trihydride phases are indeed encountered in many RH–H systems as well as in the Y–H system, whose phase diagram will be discussed in detail in the following chapter.

Within the Nb–H system, there is no pronounced isotope effect, hydrogen and deuterium behave in a similar fashion. In other M–H systems, for instance in the V–H system, this is different. Apart from complex structural phase diagrams, many M–H systems also exhibit a great vari- ety of magnetic or optical phases. This thesis will focus on the structural phases and on the dynamics of phase formation in the Y–H system. 3. THE HYDROGEN–YTTRIUM SYSTEM

Among different hydrogen–metal systems, rare earth (RE) metals and their chemical relatives scandium, yttrium, and lanthanum are of special interest because of their ability to absorb up to three hydrogen atoms per metal atom [4]. Yttrium, like most heavy RE, at room temper-

ature has the hcp P63mmc structure [9] with lattice constants a = 3.3648 A˚ and c = 5.732 A.˚ Within this structure the metal atoms occupy places with atom co-ordinates at (0, 0, 0) and (1/3, 2/3, 1/2). Tetrahedral interstitial sites (T–sites) are located at (0, 0, 1/4-z), (0, 0, 3/4+z), (1/3, 2/3, 1/4+z), and (1/3, 2/3, 3/4-z) with z = -1/3(c/a)2. Octahedral interstitial sites (O–sites) occur at (1/3, 2/3, 1/4) and at (2/3, 1/3, 3/4).

Figure 3.1: Schematic representation of the Y–H phase diagram [4].

The phase diagram of the RE–H systems consists of three principle phases depending on the hydrogen concentration. A schematic phase diagram for RE–H systems is displayed in ﬁg.(3.1).

15 16 Chapter 3. The Hydrogen–Yttrium System

3.1. The α–phase

At low concentrations (α–phase), hydrogen in RE metals can be described as a lattice gas where the hydrogen atoms are distributed on interstitial sites of the host lattice with tetrahedral symmetry (T–sites). The site occupancy has been determined by ion–channeling experiments on

single crystals of α–LuDx [10] as well as by neutron diffraction on α–YDx [11], on α–TmDx

[12], and on α–ScDx[13]. It has been established that the hydrogen atoms occupy mostly T– sites over the entire measured temperature range between 4 K and 300 K. Quasi elastic neutron scattering experiments [14] and nuclear magnetic resonance (NMR) studies [15] at high temperatures extended the validity of T–site occupation to the whole domain of α–phase existence.

Hydrogen atoms have a tendency in several α–REHx systems to organize themselves at low

temperatures. The α–phase of yttrium, orders below 400 K. Within the ordered so called α@ – phase, second neighbor H–H pairs form along the hexagonal c–axis , surrounding a RE–atom. These pairs then condense into a quasi–linear ”zigzag” line parallel to the c–axis, which inter-

act repulsively, thus forming a three–dimensional superstructure in the metal lattice [16]. In

B A C yttrium the solubility limit of the α–phase is x A 0 24 at room temperature (x H Y). Within this solid solution phase the Y remains metallic. Addition of hydrogen above this limit causes the precipitation of the β phase hydride.

3.2. The β–phase

While most RE metals crystallize in the hcp structure, all dihydrides of trivalent RE metals

transform to a CaF2–like cubic structure Fm3m, in which all tetrahedral interstitial sites of the fcc metal lattice are ﬁlled with hydrogen. This structural transformation consists of an expansion of the metal lattice along the c–axis by typically 5 %. This phase has been well characterized experimentally from measurements on bulk samples samples [4]. It is metallic with a conductivity of a factor of 5 higher than that of the hydrogen free yttrium metal. There have also been detailed studies of the optical properties [17], which can be interpreted by conventional, self consistent one–electron band structure calculations [18]. The expansion is accompanied by a rearrangement of the stacking sequence. The formally ABAB stacked hexagonal basal planes become an ABCABC stacked cubic closed packed crystal. REH2 compounds are stable and well deﬁned from the lowest temperatures up to several hundred degrees Celsius. Inserting

β additional hydrogen atoms, O-sites become occupied until a limit 2 + x D max is reached, above Chapter 3. The Hydrogen–Yttrium System 17

which one observes the formation of the hexagonal –phase. The limit xβ E max follows the lan- G thanide contraction: It reaches x F 0 65 for Nd and decreases with increasing atomic number

down to only several percent for Lu. The limiting solubility in YH2 H x has been determined

G β from the isotherms of the lattice parameter to x F 0 10. Within the –phase a lattice contraction with increasing x has been found, caused by the interaction of the T-site atoms and the O-site atoms [19].

3.3. The γ–phase

Apart from the divalent lanthanides and from the systems La–H, Ce–H and Pr–H, which retain their cubic symmetry, all RE undergo a second phase transition at higher H–concentrations to the hexagonal γ–phase. Within the γ–phase the metal atoms regain their ABAB stacking sequence, while the closed packed planes are even further pushed apart, resulting in a c-axis expansion of about 15 %. For yttrium and the heavy RE, the dihydride phase has metallic properties which gradually disappears as the system approaches the trihydride phase. For the β– and γ–phase reliable phase boundaries are scarce. Only for Y the phase boundaries have recently been investigated using thin ﬁlm techniques.

In an early neutron powder diffraction (NPD) study of YD3, Miron et al. have determined the positions of the hydrogen atoms within the Y matrix of YD3 [20]. The structure has the space group P3c1.¯ In this structure the D atoms occupy unusual interstitial sites. hcp lattices offer two kinds of high symmetry interstitial sites with octahedral (O) and tetrahedral (T) symmetry. Per

metal atom there are two T–sites and one O–site. In YD3, the deuterium atoms occupying the O-sites are shifted parallel to the c–axis towards the basal metal plane. An additional wavelike modulation displaces one third of the O–sites above the metal plane and one third below the

metal plane, while the basal metal plane hosts the remaining third. The T–sites are also slightly

J K

displaced from their conventional positions in a correlated manner. The unit cell is a I 3

L M F F J

J 3 R30 expansion of the conventional hcp unit cell with a 3a0 and c c0. In the lower

I K L J panel of ﬁg.(3.2) the two dimensional J 3 3 unit cell is shaded dark grey. The conventional two dimensional unit cell of the hcp basal plane is shaded in bright gray, visualizing the rotation

by 30 M . The resulting distribution of D atoms parallel to the Y(0001)–axis of YD3 can be described as consisting of a regular stack of D–layers, schematically indicated in the upper panel of ﬁg.(3.2).

Between any two consecutive yttrium planes (solid lines) four deuterium planes are arranged. 18 Chapter 3. The Hydrogen–Yttrium System

Figure 3.2: The P3¯c1 structure. Along the c–axis, yttrium planes and hydrogen planes form a layered system (upper panel). The lower panel shows a top view of the hexagonal

basal planes. The conventional unit mash is highlighted in bright grey. A wavelike

O P>O Q R distribution of the hydrogen atoms leads to a N 3 3 R30 expansion. The P3¯c1 structure possesses several symetry elements: An inversion symmetry around the origin, a threefold rotation origin about the c–axis and a glide plane which is marked by the dashed line.

The two planes with tetrahedral site symmetry are fully occupied as in the YD2 phase (dashed lines). The wavelike modulation of the deuterium atoms occupying the octahedral sites close to the metal plane results in three more planes which are each ﬁlled by one third of the remaining deuterium atoms (wavy line). Later those planes will be refered to as in– and near–metal planes. Chapter 3. The Hydrogen–Yttrium System 19

The bottom panel of ﬁg.(3.2) shows a top view on a basal plane. The hydrogen modulation lies purely within the [1120]–lik¯ e directions, which will be called H later on. The perpendicular [1100]–lik¯ e directions will be referred to as K–direction when using three independent indices [HKL] to describe the lattice. This structure is characterized by an inversion symmetry about the origin, by a threefold rotation symmetry about the c–axis through the origin, and by a glide plane. In the lower panel of ﬁg.(3.2) the glide plane is indicated by the dashed line.

This experimentally determined crystal structure with its unusual arrangement of hydrogen (deuterium) atoms could be explained by theoretical models. First–principles total–energy cal-

culations carried out by Wang and Chou [21] as well as by Dekker et al. [23] for YH3 showed

that the YD3 structure as described above is the energetically more stable than a cubic or a ”sim-

ple” hcp structure. It seems that the observed YD3 structure minimizes the repulsive interaction

between D atoms. The YD3 lattice is elongated signiﬁcantly in the c–direction, leading to an in-

T U V S crease of the c0 S a0 ratio to 1.80 which is much bigger than the ideal hcp ratio of 8 3 1 633. This increase leads to a wider separation of deuterium atoms sitting on tetrahedral interstitial sites. While the vertical distance between two nearest neighbor T–sites for an ideal hcp lattice is

0.25 c, this distance increases to 0.3 c for the YD3 structure. The ﬁrst–principles calculations by Wang and Chou based on the pseudo–potential method within the local–density approximation suggest a resulting energy drop of 180 meV per YH3 unit. The driving force for the shift of the deuterium (hydrogen) atoms towards the metal plane is an energy decrease in the band–energy. Especially the stronger hybridization between the H s–electrons and the Y d–electrons which reduces the energy. In other words, the displacements of the H atoms towards the metal plane lead to a stronger hydrogen-metal interaction, reducing the energy in certain bands and hence the total energy of the system.

Apart from diffraction studies, there are alternative methods to examine the crystalline structure on an atomic scale. The electric ﬁeld gradient (EFG) tensor at a given lattice site is sensitive to the symmetry of the electric charge density surrounding. Measuring the electric quadrupole interaction (QI) between the electric ﬁeld gradient (EFG) and the quadrupole moment of a nu-

cleus on the Y site of YH3 provides information about the local environment of the Y atom. The QI can be probed via Mossbauer¨ studies. As 181Hf is known to occupy substitutionalonal lattice sites in Y, 181Ta was choosen as a suitable Mossbauer¨ isotope by Forker et al. [24] in

temperature dependant studies of the EFG at the Y site in YH3 doped with 0.5 atomic percent 181 of Hf. The results were in agreement with the YH3 structure as described above for temper-

atures below 290 K. Reversible changes in the spectra of stoichometric YH3 above 300 K were interpreted as a transition to a structure of higher symmetry. One detail is worth mentioning. 20 Chapter 3. The Hydrogen–Yttrium System

Forker et al. prepared samples of different hydrogen concentrations and characterized them at room temperature by x–ray diffraction. Spectra of substoichometric YH3 samples deviate from

those obtained on stoichometric samples. They contain contributions of YH2 spectra, refering X to phase coexistence up to at least x W 2 9, thus suggesting a larger miscibility gap than observed earlier.

More recent temperature dependant NPD characterizations of YD3 by Udovic et al. did not conﬁrm a structural phase transition at 300 K, but they revealed more details of the structure

[25]. First, they observed a considerable amount of disorder in the YD3 structure. About 16 % of the in–plane H–atoms moves out to a near– metal site, while the same amount of hydrogen moves from near–plane sites to in–plane sites, preserving the equal distribution of hydrogen on the three possible sites in and near the metal plane. This vertical displacement also leads to an additional horizontal disorder of the hydrogen atoms occupying tetrahedral interstitial sites. The presence of a hydrogen atom in the metal plane causes a slight radial expansion of the spacing between the three neighboring Y atoms. Details of this structure like the reﬁnement results for different structural models and their variation with temperature are given by Udovic et al. in reference [25].

3.4. Electronic and optical properties

Since other RE–H behave in a similar manner, this chapter will focus on the discussion of the Y–H system. The electronic and optical properties of the Y–H system depends strongly on the hydrogen concentration. The electric resistance ρ, which depends on the electronic carrier density and their mobility is a well suited example to illustrate the changes of the electronic configuration of the system. Fig.(3.3) shows the development of the resistance as well as the optical transmisson for a 5000 A˚ thick, polycrystaline Y film grown on sapphire, covered by a 200 A˚ thick Pd layer. Immediately after exposing the film to a hydrogen atmosphere of 900 mbar the sample starts to absorb hydrogen and the α–phase is formed. First, the resistance increases slightly, while the transmittivity stays constant at a low level. After about 18 s the α–phase is saturated and the sample enters the α+β coexistence region. The resistance drops

until a minimum is reached close to the stoichometric β–phase at t W 65s. At the same time, i. e. at the same hydrogen concentration, the sample becomes slightly tranparent for photons within the red part of the visible spectrum. Increasing the hydrogen concentration the γ–phase starts to precipitate. The electrical resistance increases and the ﬁlm becomes more and more Chapter 3. The Hydrogen–Yttrium System 21

transparent. Even after 150 s the equilibrium is not jet reached. In the following, both curves will be discussed in detail.

Figure 3.3: Electrical resistance (a) and optical transmission for 1.8 eV photons (b) during hy-

drogen loading (pH2 = 900 mbar) for a polycrystalline Y ﬁlm covered with Pd. The bottom panel (c) relates the measured resistance and transmission values with the structural phases [8].

In the α–phase the dissolved hydrogen atoms act mainly as impurity scattering centers and ρ increases with increasing hydrogen concentration up to the α phase limit. Concerning the optical properties, there are no signiﬁcant changes within the α phase. The sample remains shiny metallic [26].

When the Y is hydrogenated up to the β–phase, the two H–atoms per unit cell add two ex- tra electrons to the system. The 1s hydrogen bands hybridize with the Y 4d5s band leading to two bands lying several eV below the Fermi level, each containing two electrons. The remaining electron in the conduction band is responsible for the metallic character of the divalent

REH2 compounds. Although the free carrier density drops to one third, the resistance decreases 22 Chapter 3. The Hydrogen–Yttrium System

strongly. For Y, the value of the resistance drops down to 20 % in the dihydide phase. Regarding

the electrical resistance, YH2 is a better metal than pure Y. The main reason for the increased electrical conductivity is the reduced electron phonon coupling. By temperature dependant resistance measurements a very narrow gap semiconducting behavior in superstoichiometric

YH2 Y 10 was observed below 60–80 K. At higher temperatures the sample turns metallic until a further metal semiconductor transition occurs at about 235–260 K. The latter transition is driven by an order–disorder transition of the octahedral hydrogen sublattice [27]. Optical spectroscopy

studies by Kremers and coworkers [28] revealed a transmission window in polycrystalline YHx-

[ [ Z films for concentrations between 1 Z 7 x 2 1. The samples became partially transparent in the red part of the visible spectrum for photons in the energy range between 1.6 eV and 2 eV. Those results are consistent with self–consistent band structure calculations by Peterman et al. [18]. Below 1.5 eV, there is no transmission, since most of the photons are reflected by the electron gas of the metal. The onset of the interband transitions is calculated to start at slightly higher energy values [17]. Between 1.5 eV and 2 eV there is neither strong reflection nor strong

absorption. A similar behavior has been observed in many other REH2 systems. Z

Increasing the hydrogen content above the limit of the β–phase, which occurs at x \ 2 1 for Z

Y, leads to a growing volume fraction of the hexagonal γ–phase. Starting from x \ 2 75 the Z transmission increases in the whole visible spectrum. For all concentrations above x \ 2 75 the transmission decreases monotonically with increasing photon energy. This is a typical behavior for a system exhibiting a gap in the excitation spectrum, i. e. an absorption edge. The increase of the optical transmission is accompanied by an increase of the electrical resistance of several orders of magnitude. Within the trihydide phase a logarithmic divergence of the electrical resistance has been observed [29]. This behavior can be explained by assuming a layered su-

perstructure of the unstoichometric trihydride phase YH3 ] δ, where conducting sheets of lower hydrogen concentration provide metallic conduction. In other words, a 2D weak localization of conducting sheets could be responsible for this unusual temperature dependence of the electrical resistance.

The observations of the optical and electronic properties of YH3 suggest that YH3 exhibits

semiconducting properties with a bandgap of 1.8 eV. Assuming that stoichiometric YH3 is a semiconductor, a hydrogen vacancy would act as a donor. At a hydrogen vacancy level of

the order of 0.3, YH2 Y 7 should be a highly doped semiconductor and one expects a conducting donor band, which has not been observed.

The observations mentioned above demonstrate clearly, that the electronic stucture of any hy- Chapter 3. The Hydrogen–Yttrium System 23

dride is deeply affected by the presence of hydrogen. In a simple anionic picture the metallic

character of YH2 and the insulating character of YH3 can be explained by a progressive depopulation of the conduction band which is initially (at zero hydrogen concentration) ﬁlled with three electrons. A schematic picture of the depopulation of the conduction band with increasing hydrogen concentration is schematically shown in ﬁg.(3.4).

Figure 3.4: Schematic representation of the density of states for Y and its hydrides. For the trivalent Y the Fermi energy lies within the 4d5s conduction band. After adding two hydrogen atoms per unit cell, two low lying s–like bands are formed, each

containing two electrons. In YH3, a third low lying band is formed, leaving an empty conduction band.

To obtain quantitative predictions for the band gap and to explain the semiconducting state of

YH3 in detail, more sophisticated theoretical models are necessary. Numerous electronic band

structure calculations have been performed for YH3, assuming P3c1¯ structure described above. 24 Chapter 3. The Hydrogen–Yttrium System

They all do not predict a bandgap in YH3 [21, 22, 23]. Two alternative models have recently

been established to explain the semiconducting behavior of YH3.

Kelly et al. [30] have demonstrated by density functional calculations of the total energy that

symmetry breaking displacements of the deuterium atoms within the YD3 structure lead to an energy lowering and to the opening of a signiﬁcant band gap. In this suggested structure the inversion symmetry and the glide symmetry are broken. There is still one third of the close– metal–plane hydrogen atoms at approximately 0.07 c above and one third below the metal plane, but there are no longer in–plane hydrogen atoms actually in the plane. They moved slightly out of the plane and are found approximately 0.03 c above it. The three nearest Y–neighbors of such a H–atom are slightly displaced away from it. Also the hydrogen atoms on tetrahedral sites are affected by this displacement. Within the conventional P3c1¯ structure, they move inward towards the vertical displacement axis. The modiﬁcation of the positions of the in–plane atoms cause a steric hindrance of the rotational displacements of the hydrogen atoms on T–sites in adjacent planes, resulting in ”left handed” and ”right handed” single crystals.

Each additional symmetry element reduces the number of allowed Bragg reflections in scattering experiments. Therefore a lower symmetry does not only cause the opening of a gap, it would also lead to new diffraction patterns in neutron diffraction experiments. As the required deviations from the highly symmetric structure are quite small, the detection of the additional reflections is a challenging task. Up to now, neutron powder diffraction did not show any indica- tion of symmetry breaking [25]. Neutron diffraction studies carried out on thin monocrystalline films will be presented later on in this thesis. They also do not confirm the broken symmetry.

The insulating state of LaH2 ^ x, which also undergoes a metal insulator transition, has recently been described by Ng et al. [31] by strong correlation effects wich are not treated by LDA calculations. Starting point is the free hydrogen atom. The 1s electron orients its spin anti–

parallel to the spin of the proton. The stable H _ –ion possesses two electrons. Hunds rules force the second electron to be in a different spin state as the ﬁrst one when occupying the same orbital. Thus the two electrons are not equivalent, the one with the opposite spin direction with respect to the proton is tighter bound to the nucleus. It can be regarded as a localized electron close to the proton. The other electron experiences a weaker Coulomb attraction of

the nucleus due to the screening effect of the inner electron. As a result, the H _ –ion is much

bigger in diameter (1.54 A)˚ than the free atom. Within YHx each hydrogen atom forms a kind

of H _ –ion. One electron is localized at the proton’s position while the other is distributed over

the neighboring Y–atoms, leading to a strong hybridization with the Y 4d3z2 r2 orbital. The _ Chapter 3. The Hydrogen–Yttrium System 25

situation is similar to Zhang–Rice–singletts in high Tc superconductors like (La,Sr)2CuO4 or

YBa2Cu3O7. In this oxides the singlett state is formed by a hole within the Cu 3dx2 ` y2 state and a hole within one of the O 2p states. Within YH3 the electrons take the part of the holes. Fig.(3.5) visualizes this situation.

Figure 3.5: Hybridisation of the Y 4d3z2 ` r2 orbital with the H 1s orbital, leading to a singlett state. Different colors denote different signs of the wave functions.

In this picture, hydrogen has got an anionic character. As yttrium is a trivalent metal, YH3

should be an insulating ionic crystal. Unstoichiometric YH3 ` δ is characterized by H–vacancies.

Removing a neutral H–atom from YH3, i. e. creating a H–vacancy, leaves the outer electron at the place where the H ` –ion was before. This electron is not a conduction electron. The Coulomb repulsion from the other H ` –ions force it to stay on its site. Therefore a hydrogen vacancy behaves like a strongly localized donor state. Thus a high concentration of H–vacancies is necessary in order to generate an overlap of the donor wavefunctions to create a conducting

donor band. Hence YH3 ` δ stays semiconducting even in a highly doped state, while many common semiconductors become metallic at a donor concentration of about 10 ` 4. 26 Chapter 3. The Hydrogen–Yttrium System

3.5. Thin YHx–ﬁlms

All structural information available so far, has been determined from polycrystalline or powder samples, whereas most of the recent discoveries, like the switchable optical properties mentioned above have been discerned for thin films and superlattices. In epitaxially grown films the assumption of bulk symmetry is not necessarily correct. Pseudomorphic growth and clamping effects to the substrate during hydrogen uptake may change the symmetry. For a better under- standing of the structural properties and their relation to the electronic properties it is therefore necessary to study single crystalline RE films with varying hydrogen concentration. Because of the structural phase transitions mentioned above, it is not clear whether the once deposited

epitaxial RE ﬁlm would maintain its structural integrity up to x a 3. According to Vadja [4], in

the past single–crystal work on hydrides was limited to the system CeH2 b x. In all other RE–H the transformation from hcp to fcc leads to a loss of monocrystallinity. Within this thesis will

be shown that epitaxially grown Y(0001) ﬁlms on Nb/Al2O3 substrates maintain their structural coherence and their bulk symmetry during hydrogen loading. There is no loss of crystallinity

during the transition from YH2 to YH3. The transition is completely reversible and can be cycled for many times. Neutron diffraction data on the deuterated films are in agreement with NPD data, indicating matching structural properties for epitaxially grown thin films and powder samples. Furthermore it is possible to completely exchange H against D within the trihydride phase on a very short time scale. There a are no significant structural differences for the two different hydrogen isotopes. 4. EXPERIMENTAL METHODS

4.1. X–ray diffraction

4.1.1. Introduction

X–ray diffraction (XRD) allows to study the crystalline structure of condensed matter on an atomistic scale. The interaction is based on the scattering of the x–rays by the electrons of the sample. As the wavelength of the x–rays is in the order of the atomic distances within a crystal, interference effects between the x–rays scattered by different atoms become important. The resulting interference pattern depends on the structure of the sample. As the probability of a scattering process is relatively low, x–rays penetrate a given sample deep enough to give information about its internal structure. Unfortunately, a diffraction experiment does not deliver a direct image of the structure of the sample. It only reveals its reciprocal space. In a scattering experiment only the scattered intensity can be measured. All phase information is lost. Thus a transformation from reciprocal space to real space can not be done directly. To obtain information about the real structure of the sample, theoretical models have to be set up and compared with the measured intensity distribution.

Within this chapter the theory of x–ray diffraction will be developed. Special emphasis will be put on the diffraction by thin ﬁlms. Due to the small sample volume, effects like multiple scattering and extinction will be neclected. More detailed information about x–ray diffraction may be found in [32, 33].

4.1.2. Basic concepts

c d e f

X–rays are electromagnetic waves. The electric ﬁeld E c r t of a plane monochromatic electo- magnetic wave can be written as:

28 Chapter 4. Experimental methods

g g

ω mon pq i l t k r

0 n

i jk

E h r t E0e (4.1)

g g E0 is the electric vector while k0 is the wave vector and ω is the frequency. Electrons subjected to x–rays are forced to emit radiation with the same frequency. However the amplitude and the phase of this scattered radiation may differ from the incident one. The elastic scattering process

with a free electron leads to a spherical wave [32]: g

r E g

ω m p

0 0 i l t kr

h s t j i ψs k P fe k k e (4.2)

r r

2 u 2

where r denotes the distance to the observer, r0 k e mec the classical electron radius

g q

m 6 t

(0 2818 v 10 A),˚ k and k the wavevector of the incident and the scattered wave, respectively.

g g g g

t t

s j kwh s j

The scattering factor per electron fe h k k depends on the momentum transfer K k k g (see ﬁg.(4.1)). The modulus of K which is also called the scattering vector is given by:

g 4π 2θ q

K k sin (4.3)

λ 2 y

z → k'

y → 2Θ x K

→ z k Figure 4.1: The scattering triangle

The polarization factor P takes the partial polarization of the scattered wave into account. It also g

depends on the momentum transfer K. In an atom containing Z electrons the whole electron

g j cloud is involved in the scattering process. For a spherical charge distribution ρ h r the atomic

ρ g j

scattering factor is given by the Fourier transform of h r :

g g q

iKn r

jk { h j f h K ρ r e dr (4.4) Chapter 4. Experimental methods 29

For small momentum transfers K, i. e. for small scattering angles, all electrons scatter in phase

and f |~}K reaches Z. With increasing K the electrons scatter more and more out of phase and f |~}K decreases. Signiﬁcant deviations from a spherical charge distribution can be found in strong covalent bonds.

If the frequency of the incident x–rays matches a resonance frequency within the atom, the electrons can no longer be regarded as free electrons. Close to a resonance absorption of x–rays via excitations of core electrons becomes important. This can be taken into account by adding

dispersion corrections to the atomic scattering factor, so f can be expressed as:

f f0 f i f (4.5)

f and f are the real and the imaginary part of the dispersion correction. They describe a phase shift and a damping of the scattered wave. There is a proportional relation between f and the

length absorption coefﬁcient µ:

µ 2 0re f (4.6)

The angular dependence of f and f is rather small compared to f0 and can be neglected for most practical purposes. Their values and the values of f0 for the different elements are listed in tables [34].

The scattering contrast between elements with similar Z can therefore be enhanced signiﬁcantly by tuning the x–ray wavelength λ to a resonance of one element, inducing a major dispersion correction.

4.1.3. X–ray scattering by crystals

A crystal is a three–dimensional repetition of a given unit of atoms, ions or molecules. In a scattering experiment each atom will act as a scattering center. Summing up the contributions from the various atoms and taking into account their individual phases leads to the resulting diffraction pattern of the whole specimen. Only if all involved atoms scatter in phase constructive interference occurs, leading to a so called Bragg reﬂection. 30 Chapter 4. Experimental methods

The arrangement of atoms within a crystal can be described as a periodic repetition of it’s unit

cell in all directions. A unit cell can be deﬁned by three basic vectors a 1, a2 and a3. The

volume of a unit cell is than given by a1 ~ a2 a3 . Two equivalent points within two unit

cells are connected with a so called lattice vector T. It is deﬁned by the basic vectors T

ua1 va2 wa3, where u v and w are integer numbers. T expresses the translation symmetry

of the crystal. If the unit cell consists of more than one atom, the position of the n–th atom in

the unit cell is given by rn m1a1 m2a2 m3a3 0 mi 1 i 1 2 3 . The position of

an arbitrary atom involved in the scattering process can be written as Rl T rn. The scattered

Φ wave emitted by this atom is phase shifted with respect to the incident wave by K Rl. The scattered wave can be expressed as:

0 ω

i t kr K R o

Ψ s P f K e (4.7)

The whole wave ﬁeld generated by the crystal is the summation of all contributions of the involved atoms:

ω Ψ 0 i t kr iK Rl s Pe ∑ fle (4.8) r l

i t kr iK rn iK T Pe ∑ fne ∑ e (4.9)

r n u v w

The ﬁrst sum contains all information about the structural and chemical composition of one unit

cell. It is called the structure factor F K . The second sum gives a condition for constructive

interference. Only if the exponent is equal to a multiple of 2π all of the atoms of the crystalline

sample scatter in phase. This condition is fulﬁlled if K equals a reciprocal lattice vector G which

is deﬁned as G hkl hb1 kb2 lb3, where h k and l are integer numbers. The unit vectors

of the reciprocal space bi i 1 2 3 are connected to the unit vectors of direct space via the relation:

2π

bi a j ak i j k cyclic. (4.10)

The reciprocal lattice vector G hkl is normal to the scattering lattice planes which are indexed by the Miller indices h k l. It’s length is given by: Chapter 4. Experimental methods 31

2π

d hkl (4.11)

7 G

hkl

where d hkl is the distance of the lattice planes.

Combining eq.(4.3) and eq.(4.11), the scattering condition K G can also be written as:

¡ λ θ

n 2d hkl sin (4.12) This equation is known as the Bragg law.

The scattering equation can be visualized by the Ewald construction (see ﬁg.(4.2)). Given the

incident wave vector k pointing to the origin of reciprocal space, a sphere of radius k around

the initial end of k is constructed. Like a Fermi surface the so constructed Ewald sphere is £

a surface of constant energy. Any reciprocal lattice point ¢ hkl which happens to fall on the ¥

surface of the sphere, represents a set of planes ¤ hkl for which the Bragg law is satisﬁed. The ¦

direction of the scattered beam is represented by the vector k from the center of the sphere to £ the point ¢ hkl . As the Ewald sphere is by deﬁnition a sphere of constant energy, it describes

an elastic scattering process. The momentum transfer K is given by the vector connecting the £

origin of the reciprocal space and the reciprocal lattice point ¢ hkl . Therefore, the scattering condition is only satisﬁed, if K coincides with a reciprocal lattice vector G. This again is the Bragg condition as expressed in eq.(4.12).

4.1.4. Scattering by thin ﬁlms

All the calculations made so far are valid for crystals which are sufficiently extended in all three spatial directions to be regarded as infinite in size. In a single crystalline thin film one dimension is reduced, so that finite size effects become important. Considering a thin film with N lattice

planes, the intensity of the Bragg reﬂection can be calculated according to eq.(4.9) as:

2 2

N § 1 N 1

I I

ª ©

0 iK© Rn 0 iKnd

¢ £

I K 2 P ∑ fne 2 P ∑ fne (4.13)

r r

¨ ¨ n 0 n 0

if the momentum transfer is perpendicular to the stack of N lattice planes. Experimentally this is realized by altering the incident angle ω by ∆ω while the scattering angle 2θ is altered by 32 Chapter 4. Experimental methods

Figure 4.2: a)Projection of the Ewald construction as a graphical representation of the Bragg equation; b) representation of the Bragg equation in real space. [35].

2∆ω. Therefore the length of the scattering vector K« changes, but not its direction with respect to the diffracting planes. This scattering geometry results in longitudinal scans or radial scans as the scattering vector is varied along it’s direction as displayed in ﬁg.(4.4).

Equation 4.13 can be simpliﬁed to the so called Laue equation:

2 KNd

I0 sin 2

® ¬~« I ¬~«K P f K (4.14) r2 sin2 Kd 2 ¯

A plot of this equation is shown in ﬁg.(4.3) as a dotted line. In this example a ﬁlm of N =

« ® 100 lattice planes with a lattice spacing of d ® 2 A˚ was chosen. At K G all the 100 lattice planes scatter in phase. This is the position of the Bragg reﬂection, given by the Bragg equation (4.12). Like the interference pattern of an optical grating, the Bragg reﬂection is accompanied by interference fringes. Their distance is given by the number N of scattering planes. Real

systems are not perfectly ﬂat, there is a ﬂuctuation of the number of coherently scattering planes.

This ﬂuctuation can be described by a distribution function g N0 ° N which takes the variation

of N around N0 into account:

∞ 2 KNd

I0 sin 2

¬~« ® ¬~« ¬

I K P f K ∑ g N0 ° N (4.15)

r2 sin2 Kd ± N 0 2 ¯

The ﬂuctuation of N leads to a damping of the fringes, as represented by the straight line in

ﬁg.(4.3). Assuming a Gaussian distribution of N around N0, the standard deviation σ is a mea- Chapter 4. Experimental methods 33

sure of the roughness of the ﬁlm’s surface. This roughness is not necessarily the real roughness as amorphous or strained regions of the crystal do not contribute to the Bragg reﬂected intensity.

As the number of lattice planes increases the main reﬂection gets more intense and it’s FWHM θ ³ ∆ ² 2 decreases. The number of coherently scattering planes N can be calculated according to the Scherrer equation [32]:

0 µ 89 µ

N ´ (4.16)

∆ ² Θ ³ ² Θ ³ ¶

2 cos d hkl ·

´ ¶

The coherence length Dc Nd hkl · is a measure of the crystalline quality of the sample. Only if all lattice planes scatter in phase, the coherence length matches the thickness of the ﬁlm.

1000

100 ¸

Intensität (log.) 10

1 3 3.1 3.2 K / Å-1

Figure 4.3: Calculated Laue function for N=100 and a lattice parameter of d=2 A.˚ The dotted line represents a perfect film while the bold line shows the reflection curve of a rough film.

Another important property of a crystal is the so called mosaicity, namely the average tilt of different domains within the crystal with respect to each other. For a thin epitaxially grown ﬁlm, the growth direction is determined by the substrate. During the growth process small deviations (up to typically several tenth of a degree) may occur. The mosaicity is measured by turning the sample with respect to the incident beam at a ﬁxed scattering angle 2θ. This

results in transverse scans or rocking scans as the scattering vector K¹ rotates about the origin 34 Chapter 4. Experimental methods

of reciprocal space, while it’s length is kept constant. The scattering geometries of transverse

scans and longitudinal scans are compared in ﬁg.(4.4).

» º¼»

Î Ð Î Ð

Á Á

½¾½¿½¾½¾½ ½¾½¾½¿½¿½

Á Á

Å Å

Á Á ½¾½¿½¾½¾½ ½¾½¾½¿½¿½

ßàÊ É

ÉÝÜ

Å Å

Á Á

Ù Ú

Å Å

Ù Ú

Ô Ô

Â Â À Á À Á

Ç È È

Â Â À À Õ Õ

Å Å

Ç Ù Ú

Ã Â Â À À

½¾½¿½¾½¾½ ½¾½¾½¿½¿½

Ä Å Ä Å

Ä Ä

Â Â À À

Æ Æ

Ù Ú

Æ Ä Ä Æ

Â Â À À

Æ Ä Ä Ç Æ

Ã × Â Â À À Ò~Ó Ñ Ò~Ó

Ù Ú

Æ Ø Ä Ä Æ

× Â Â À À

Ã Ø

Æ Ø Ä Ä Æ

× Â Â À À

Î Ï Î Ï

Ê Ë Ì Í Ê Ë Ì

½¾½¿½¾½¾½ ½¾½¾½¿½¿½

Figure 4.4: a) Transverse scan; b) Longitudinal scan

4.1.5. X–ray diffraction topography

X–ray diffraction topography (XDT) is an imaging technique for single crystals based on Bragg diffraction. XDT exploits local variations of the direction of the diffracted beams and of the sample reﬂecting power. Thus it visualizes inhomogenities such as defects, domains or phases within the crystal under investigation. Reviews on XDT may be found in [36, 37]. When using a zero–dimensional detector (counter) as employed in most diffraction methods, this information is averaged out and consequently lost. Fig.(4.5) schematizes the main idea of the topographic methods. By using an extended beam,the radiation diffracted by a small deformed volume V within the sample impinges on the two–dimensional position sensitive detector (for example a photographic ﬁlm) in a region around the point P. Due to the, with respect to the perfect matrix, locally different direction of this diffracted beam or its locally different intensity, that region around the point P gives a different contrast on the image.

If C is a platelet shaped perfect crystal, the recorded image is uniform. A crystal which exhibits a high defect density leads to the same uniform image, but with a different exposure time. For a Chapter 4. Experimental methods 35

Figure 4.5: Principle of the x–ray diffraction topography.

non absorbing platelet shaped crystal or a thin ﬁlm illuminated by a monochromatic beam, the ω ã diffracted intensity I â is given by:

ãäæå å â ã ç I â ω F f ω y (4.17)

where ω is the rotation angle of the crystal, F is the structure factor of the considered reﬂection and y is an extinction parameter, which takes into account the modiﬁcations produced by the crystal inhomogenities on the dynamical theory.

If the crystal has two perfect regions A and B wihch are misoriented like two mosaic blocs, they do not simultaneously satisfy the Bragg condition for the same wavelength. At a fixed angle of incidence, the diffraction pattern depends on incident radiation. In plane polychromatic light, the regions A and B diffract in different directions with the same intensity. This contrast is called the orientation contrast. In plane monochromatic light, A and B diffract in the same direction, but with different intensities. The respective intensities depend on the rocking width of the two regions as well as on their misorientation. As long as the angular width of the reflection curves are larger than the misorientation, the reflections of both regions may be recorded at the same time.

In a heteroepitaxial system all lattice planes are parallel but different films exhibit different lattice spacings. The same holds true for different hydrid–phases within a c–axis grown Y–film. In this case, using monochromatic radiation, the reflections of the different materials occur at different incident Bragg–angles. Rotating the sample about an axis normal to the scattering 36 Chapter 4. Experimental methods

Figure 4.6: Scattering by a crystal consisting of two different regions A and B.

plane, the reflections of the different films (regions of different phases) will spatially separated on the photographic film, as shown in fig.(4.6). This lattice parameter contrast will be used later on to distinguish between the epilayers (Nb and Y) and the substrate and to visualize the

development of the hydrid–phases within the Y–ﬁlm. é

There are two other possible reasons for a contrast within the recorded image: First if FA è FB.

This is not a frequent case when using x–rays, but this structure factor contrast is the main one é

when investigating magnetic materials by neutron topography. Second yA è yB. Then the two regions display extinction contrast. As the samples presented in this work can be described by the kinematical theory of XRD, extinction contrast can be neglected.

4.1.6. Grazing incident x–ray diffraction and X–ray reﬂectivity

To probe the crystalline properties of a given specimen, the Bragg equation (4.12) requires

incident angles of above 5 ê for typical atomic distances of several A˚ and for typical x–ray wavelength of about 1 A.˚ Reducing the angle of incidence, the x–ray penetration depth decreases. Thus XRD becomes surface sensitive under gracing incidence. At small angles the optical properties of the sample also play an important role. The refractive index is connected

Chapter 4. Experimental methods 37

ì íî to the electron density ρe via the atomic form factor f ë Q ( Z for small angles), and the atomic

density ρat of the sample:

2πr0 µ

ë ë ìñð ∆ ò ì¼ï ï ρ n 1 2 at f K f i

k0 2k0

δ ï β ó : 1 ï i (4.18)

î λ Here k0 2π ô is the vacuum wavenumber of the incident radiation, r0 is the classical electron

radius, ρat is the atomic density of the sample, ∆ f takes dispersion corrections into account, and µ is the mass absorption coefﬁcient. Close to absorption edges ∆ f and µ are strongly wavelength 5

dependant. Since the real part δ is positive and of the order of 10 õ , total external reﬂection

of the x–ray beam penetrating into a medium of higher electron density ρe occurs. Neglecting dispersion corrections and absorption the critical angle can be calculated as :

r0ρe

î÷ö î ø α λ δ ó c π 2 (4.19)

Below αc an evanescent waveﬁeld develops which propagates parallel to the surface. Its intensity decays exponentially perpendicular to its direction of propagation. The penetration depth Λ is given by [38]:

1 1 1 î Λ Λ ð Λ (4.20)

i f ù

where:

ö 2 2 2 2 2 2

î î

ø ðûú ë ï ì ð ó α ï α β

Λ 2k0 c m am ac 4 m i f (4.21) ù m ù

This evanescent wave can be used to excite in–plane plane Bragg reﬂections, whose scattering

vector Kü lies parallel to the surface of the sample [39]. By varying the incident or the exit angle, the penetration depth may be altered, making grazing incident x–ray diffraction (GIXD) a depth sensitive technique. This scattering process combines optical and structural properties of the sample. The intensity of the diffracted wave can be calculated using the Distorted Wave Born Approximation: 38 Chapter 4. Experimental methods

2 2 £

ý~þ

ý~þ ∝

ÿ¢¡ ¡

I Kt ÿ Ti Iev Kt Tf (4.22)

¡ ¡

Ti and Tf represent the transmission functions of the incident and the reﬂected beam, respec-

tively.

þ þ Figure 4.7: Scattering geometry for grazing incidence x–ray diffraction. þ k, kS, and kG are the

wave vectors of the incoming beam, the specular reﬂected beam and the Bragg

¤ þ ¥ reﬂected beam, respectively. Kþ and K are the vectors of momentum transfer for

the out–of–plane and the in–plane reﬂected wave. αi and α f denote the incident and exit angle, respectively.

The scattering geometry is shown in ﬁg.(4.7). The incident x–ray beam þ k gets specular reﬂected

at the physical surface and induces an evanescent wave ﬁeld within the crystal. The directions þ

of the specular reﬂected and of the Bragg diffracted beams are labeled kþ S and kG, respectively. ¤

While the vector of momentum transfer Kþ of the specular reﬂection is normal to the physi- ¥ cal surface of the sample, the momentum transfer Kþ of the Bragg scattered evanescent wave lies within the surface, normal to the scattering planes. By measuring the in–plane structure of the ﬁlm and the substrate it is possible to determine the epitaxial relations between them.

Chapter 4. Experimental methods 39

¦ ¦

%'& #"$

¦ ¦

¦¨§ ¦¨§

§ §

¨ ¨

§ §

¨ !

Figure 4.8: The Parratt–formalism: Multiple reﬂections in a stratiﬁed medium

Because the in–plane component of the scattered x–ray beam has a low intensity it is necessary to perform these measurements using x–ray sources of high intensities such as rotating anodes or synchrotron storage rings.

Above αc the incident beam gets partially reflected at the surface and partially transmitted into the sample. In the case of thin films one has to deal with several interfaces. Reflection and transmission of waves occurs at all interfaces separating regions of different electron densities

in a layered material. The boundary conditions must be fulﬁlled at each individual interface. ) In ﬁg.(4.8) the two interfaces between the layers n ( 1, n, and n 1 are shown. The different

reﬂected and transmitted beams are characterized by their electric wave vectors E* .

The amplitudes of the reflected and transmitted beams have to be added to provide an overall reflectivity for a stratified sample. This may be done by the formalism developed by Parratt which uses a recursion based on the Fresnel equations. The reflected Fresnel amplitude at the

th th

( ,

interface between the n and the + n 1 layer is given by [40]:

)

0 - .

4 Rn . n 1 Fn 1 n

. / R - a (4.23)

n 1 n n - 1

)

0 - . Rn . n 1Fn 1 n 1

with

E 1 Dn 2 n - iKn

2 3

/ / 0 Rn . n 1 an an e (4.24)

En 2 40 Chapter 4. Experimental methods

The Fresnel coefﬁcients are given by:

: 7

fn 4 1 fn α2 δ β

4 5 6 6 ; 7

Fn 1 n fn i 7 2 n 2i n (4.25)

8 9

fn 4 1 fn

6 < The recursion starts at the substrate which is assumed to be infinitely thick such that Rn 5 n 1 0, and then working up to the top surface. Within the Parratt formalism no approximation is applied and absorption is taken into account. Any electron density profile can be modeled by slic- ing the material in an arbitrary number of thin layers. Fig.(4.9) compares calculated reflectivity curves. Starting from a single flat surface of a half infinitely thick sapphire substrate (fig.(4.9a)) and the calculated reflectivity curve for a 300 A˚ thick Y epilayer grown on it (fig.(4.9b)) the

basic features may be demonstrated. Below the critical angle αc the reﬂected intensity is con-

4 4 stant and equal to unity. Above αc, the reflectivity drops off approximately with K , which is usually referred to as Fresnel reflectivity. The thin film shows interference fringes, so called Kiessing fringes, originating from the interference of waves scattered from the surface and from the interface to the substrate. As the difference in electron density of sapphire and yttrium is rather small, the Kiessing fringes are not pronounced. Real interfaces exhibit some kind of roughness or interdiffusion on an atomic scale, diminishing the phase relation and hence the interference effect. More complex layer structures, lead to more complex reflectivity curves. The curves labeled (c) to (e) in fig.(4.9) are the calculated reflectivities for a Y (300 A)/˚ Nb (500

A)/˚ Al2O3 sample, for a Nb (100 A)/˚ Y (300 A)/˚ Nb (500 A)/˚ Al2O3 sample and for a Pd (100

A)/˚ Nb (100 A)/˚ Y (300 A)/˚ Nb (500 A)/˚ Al2O3 sample, respectively. Apart from the increasing complexity of the interference patterns, the increase of the critical angle with increasing electron density of the cap layer can be observed.

4.2. Neutron Diffraction

4.2.1. Bragg scattering

Neutrons are chargeless nucleons, interacting with the atomic nuclei via the strong interaction. The neutron’s spin of 1/2 implies that the nuclear scattering is spin dependent, since the strong interaction depends on the spin. The magnetic moment of the neutron couples to the magnetic moment of free or unpaired electrons, thus giving an reciprocal space image of magnetic structures. In the following only the elastic nuclear interaction of unpolarized neutrons is considered Chapter 4. Experimental methods 41

Figure 4.9: Model reﬂectivity curves of the following sample architectures:

(a) Al2O3,

(b) Y (300 A)˚ / Al2O3,

(d) for a Nb (100 A)˚ / Y (300 A)˚ / Nb (500 A)˚ / Al2O3,

(e) Pd (100 A)˚ / Nb (100 A)˚ / Y (300 A)˚ / Nb (500 A)˚ / Al2O3. All interfaces were calculated with a roughness of 1 A.˚

as magnetic ordering does not occur in Y or in the Y–H system.

Since the wavelength is similar for x–rays and neutrons, so are the Bragg angles, hence the scattering geometry and the formal description. The orders of magnitude of the scattering length for atoms are the same, with slightly smaller values for neutrons. Transferring the concepts developed for x–rays some fundamental differences have to be taken into account. Neutrons see the positions of the nuclei, thus providing complementary information to x–rays, which probe the electronic cloud surrounding the nucleus. Since the atomic nucleus is small compared to the wavelength of a neutron, it can be treated as a point scatterer. The atomic form factor is therefore constant and independent of the angle of incidence. Thus the expression for the

structure factor is:

B C

iK rB n @'A

FN =?>K ∑ bie (4.26) unit cell

where bi is the coherent scattering length, which is a constant for a single isotope. Different iso- 42 Chapter 4. Experimental methods

topes of the same element may have different scattering length. Thus neutrons can distinguish between different isotopes of the same element. In the case of hydrogen and deuterium they even have different signs, leading to a strong scattering contrast between them. Unlike x–rays, where the atomic form factor rises with the number of electrons, the neutron scattering length varies unsystematically throughout the periodic system. Thus especially for light elements like hydrogen neutrons are the ideal probes.

4.2.2. Neutron reﬂectivity

Neutron reﬂectivity is similar to x–ray reﬂectivity. For unpolarized neutrons the refractive index

is deﬁned analog to x–rays:

E δ E β F n D 1 i (4.27)

The critical angle for total reﬂection is given by:

D!I δ J α DHG λ c π 2 (4.28)

where n is the atomic density and nb is called the scattering length density. Therefore, replacing

ρatZr0 by nb all equations derived for x–ray reﬂectivity can be immediately applied for neutron scattering. Thus the critical angle is a direct measure for the average scattering length density which can be used to calculate the stochiometry of a compound. Usually for neutron scattering the dispersion correction can be neglected since for most nuclei and neutron wavelength used there is no resonance absorption close by. Furthermore, the penetration depth is much bigger for neutrons than for x–rays which is a consequence of the fact that nb is much smaller than

ρatZr0. By the same reason the critical scattering vector KK c for the total reﬂection of neutrons is a factor of 5 to 10 smaller than for x–rays. A comparison of x–ray and neutron reﬂectivity is provided in [42]. Chapter 4. Experimental methods 43

4.3. Electron Diffraction

4.3.1. Diffraction of fast electrons (RHEED)

During the sample preparation it is important to monitor the growth process in situ in order to change the growth parameters if necessary to guarantee the high quality of the sample. The crystalline quality and the ﬂatness of the single metallic layers are of particular interest. Reﬂec- tion high energy electron diffraction (RHEED) is a widely used nondestructive method to probe

the surface of the sample during the growth. Fast electrons within the energy range of 10–50 L keV hit the sample under an incident angle of 1 L'M 3 , where they get scattered elastically. Ro- tating the sample about its surface normal, different in–plane reflections may be excited. The resulting diffraction pattern can be seen on a flourescence screen, as shown in fig.(4.10).

Figure 4.10: Schematic view of a RHEED experiment. By rotating the sample about its surface normal, different reﬂections become excited and can be recorded.

As a result of the small angle of incidence, RHEED is only sensitive to the uppermost atomic layers. The growth chamber in Bochum is equipped with a RHEED 410 produced by Riber, using electrons with an energy of 30 keV. This energy corresponds to a wavelength of 0.01 A,˚ which is two orders of magnitude smaller than the x–ray or neutron wavelengths typically used for diffraction experiments, leading to huge Ewald spheres. The large distance between the electron source and the sample, as well as the large distance between the sample and the screen 44 Chapter 4. Experimental methods

Figure 4.11: Different surface structures lead to different RHEED images.

prevents any inﬂuence with the sample preparation.

A crystalline surface is defined as a two dimensional repetition of some unit of atoms, ions or molecules, called the unit mash. The reciprocal space of a crystalline surface consists of reciprocal lattice lines rather than of lattice points as in the three dimensional case. Constructive interference of the electrons occurs, if the Ewald sphere intersects the reciprocal lattice lines. The resulting diffraction pattern of perfect surface is shown in fig.(4.11). The point–like maxima of intensities lie on circles. Surface roughness broadens the reciprocal lattice lines to rods of finite thickness. As the Ewald sphere has a huge radius of curvature, the intensity maxima on the screen get smeared out along the reciprocal lattice rod and becomes a sharp line. The same effect occurs for finite energy bandwiths of the incident electrons, leading to a blurring of the Ewald sphere. Crystalline islands on the surface transmitted by electrons give rise to a three dimensional diffraction pattern. Fig.(4.11) compares the different diffraction patterns for an ideally flat surface and a rough surface.

4.3.2. Diffraction of slow electrons (LEED)

Low energy electron diffraction (LEED) is another surface sensitive method to probe the crystalline quality of the surface. Slow electrons exhibiting energies in the order of 100 eV, corresponding to wavelengths of about 1 A,˚ hit the sample under normal incidence. The arrangement of the electron source, the sample and the ﬂourescent screen is shown in ﬁg.(4.12). It gives a simple connection between the LEED image on the screen an the reciprocal space of the sam- Chapter 4. Experimental methods 45

ple. The diffraction spots on the screen represent the intersection points of the reciprocal lattice rods with the Ewald sphere. Tuning the energy of the impinging electrons, the radius of the Ewald spere can be varied to excite different surface reﬂections.

Figure 4.12: Schematic view of a LEED experiment [41]. 46 Chapter 4. Experimental methods Chapter 4. Experimental methods 47

4.4. Instruments used

As a hydrogen atom possesses only one electron, the cross section for x–rays is rather small. But x–ray scattering allows to characterize the host metal ﬁlms and to study their response to the hydrogen uptake. Structural characterizations along the growth direction as well as small angle reﬂectivity measurements were performed via high angle x–ray scattering using MoKα1–

radiation of a conventional ﬁne focus x–ray tube.

_ `

11 10 `

_a` _

5 _ 5

Y[Z

T¨U

N N

]

\^]

N N N N

VXWR¨S \

NON1 4 12

N N N 3 N

9 8 2 7

Q P P 6 13 14 14

Figure 4.13: High–resolution X–ray diffractometer in Bochum. (1) source (Mo–anode), (2) monochromator–tower, (3) turn table for the monochromator, (4) monochromator with shielding (5) slits (6) x-table, (7) turn tables for the sample and the detector, (8) tilt, (9) xy–table, (10) sample on (11) χ–circle, (12) NaJ–detector, (13) optical table with (14) shock–absorber.

Fig.(4.13) shows the setup of the diffractometer. The (220) reﬂection of a Si monochromator selects the Kα1–line from the x–ray spectrum emitted by the Mo anode of the source. After passing the primary slits the x–ray beam impinges on the sample and can be detected via a NaJ detector. The incident beam divergence is given by the ﬁnite line width of the Kα1–radiation

c d e and by the natural line width of the Si (220) reﬂection. With ∆λ b 2 766 10 A˚ the

3 f

c d e divergence is given by α b 4 21 10 . The primary slit cuts off the Kα2–line and reduces the background. A perfect crystal at the sample position would act as a mirror, conserving the 48 Chapter 4. Experimental methods beam divergence. An epitaxially grown thin ﬁlm which exhibits a certain mosaicity η increases the beam divergence by 2η. In order to have a sample independent resolution, secondary slits in

1 h

front of the detector collimate the reﬂected beam. For K g 3 A˚ , which is a typical value for g a scattering vector within the systems under investigation, the resolution is given by ∆K i K

4 3 l

k h g j k h 6 j 5 10 for longitudinal scans and ∆ω 5 2 10 [43]. In this setup, the scattering plane is ﬁxed to the plane which is deﬁned by the detector and the incident beam. Only if the scattering vector lies within this plane, the scattered beam will be detected.

Grazing incident x–ray diffraction (GIXRD) was carried out employing CuKα–radiation (λ = 1.54 A)˚ from a rotating anode x–ray generator. The diffractomter is shown in fig.(4.14). The highly oriented pyrolytic graphite (HOPG) monochromator selects a broader energy band than a silicon monochromator, increasing the flux of the incident beam at the cost of resolution. This time the divergence of the incident beam is defined by the two primary slits. The divergence of the reflected beam can be reduced by a Soller collimator or an analyzer crystal (no. 16 in fig.(4.14)) in front of the detector. The resolution of the instrument depends on the scattering vector and of the chosen slits and collimators. Typical values are about one order of magnitude lower than the corresponding values for the high resolution diffractometer. As the degree of order in a thin film is higher within the growth direction as in the film plane, the instrument resolution can be relaxed in a surface diffractometer.

Figure 4.14: Surface x-ray diffractometer in Bochum. The same labels an in ﬁg.(4.13) were

used. Additional features are: (1) source (Cu rotating anode), (15) αi-tilt, (16) turn table for the analyzer crystal or the Soller collimator. Chapter 4. Experimental methods 49

The x–ray topographic studies were performed at the imaging beamline ID19 at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The characteristics of the beamline derive from the requirement of having a spatially extended, white or monochromatic beam, a high photon ﬂux and a tunable photon energy in the range of 8–120 eV. A high–magnetic ﬁeld 2

wiggler with a variable gap delivers radiation with a small divergence (0.3 m 0.1 mrad ). The 2

requirement to provide a homogeneous beam of 45 m 15 mm which is able to illuminate also extended samples led to the choice of a 145 m long beamline. The source guarantees a high photon ﬂux at the sample position, minimizing exposure times. A double crystal, ﬁxed exit monochromator allows to select a monochromatic beam out of the wiggler spectrum.

For the experiments discussed within this thesis, a photon energy of 14 keV, close to the Mo Kα energy was chosen. The layout of the beamline is displayed in ﬁg.(4.15), further details of the beamline characteristics can be found in the beamline handbook of the ESRF.

Figure 4.15: Schematic drawing of the imaging beamline ID19 of the ESRF, Grenoble, France. A: diaphragms; B: slits; C: ﬁlters; D: dismountable section; E: shutter; F: satellite laboratory; G: monochromator hutch; H: experimental hutch [44].

All x–ray experiments were carried out in situ, i. e. in hydrogen atmosphere. Therefore a portable vacuum chamber with hydrogen loading capabilities was constructed. It is displayed in ﬁg.(4.16).

The turbo molecular pump allows to reach base pressures of about 10 n mbar regime. An oil free primary pump avoids chemical contamination. Three manometers with overlapping ranges allow to control the pressure up to 1000 mbar. The sample can be heated within the hydrogen R

atmosphere up to 500 o C. X–rays may penetrate the vacuum chamber through Kapton or Al windows. Simulteneously to the XRD experiments, the electrical resistance of the sample can be measured via a four point method. Fig.(4.17) shows the principle experimental setup: The 50 Chapter 4. Experimental methods

Figure 4.16: Portable vacuum chamber with hydrogen loading capabilities.

sample is electrically connected via four electrodes. An alternating current is passed through the sample via the outer two electrodes, labeled A and D in fig.(4.17). A voltmeter measures the voltage between the two inner electrodes B and C. This voltage is proportional to the electrical resistance between these two points. Typically an effective current of 1 mA was applied to the sample at a frequency of 480 Hz. Measuring the electrical resistance of a thin film, different geometries are possible. In the experiments presented in this thesis, the current in plane method was uesed. In this technique the current is passed along the film surface. For a sample thickness below one µm, the elecric field lines can be assumed to penetrate the whole film. Hence this method gives the integral resistance of the whole sample. Different layers within one sample can be regarded al parallel resistors. As the resistance change upon hydrogen loading is known for thin Nb films, the different responses of Nb and Y can be separated. A more direct access to the resistance of an individual layer could be achieved by passing the current perpendicular through the film. This method requires a mask technique during the sample preparation which reduces the available scattering volume.

The neutron reflectivity experiments as well as the isotope exchange were carried out at the reflectometer ADAM (Advanced Diffractometer for the Analysis of Materials) at the Institute Max von Laue – Paul Langevin (ILL) in Grenoble, France. ADAM is a fixed wavelength two circle instrument. It is connected to a liquid deuterium cold source of the ILL reactor. Chapter 4. Experimental methods 51

Figure 4.17: Scetch of the experimental setup to measure the electrical resistance. A constant currant (ac) is passed through the sample via the outer electrodes. The voltage between the inner electrodes is a measure for the resistance.

A focussing HOPG monochromator at a fixed take off angle of 82 p selects neutrons with a λ ˚ λ wavelength of 0 = 4.4 A. A Be filter may be uesd to remove 0 q 2 [45]. Higher harmonics of the wavelength are suppressed by the neutron guide delivering the neutons to the instrument. Although ADAM was primarily designed as a reflectometer in the small angle regime, it covers

1 λ r θ p ˚ a 2 range up to 140 , accessing scattering vectors Q up to 5.4 A when using 0 q 2.

ADAM offers the unique opportunity to perform small angle reﬂectivity measurements as well as high angle Bragg scattering without changing the sample environment or the alignment of the instrument. Fig.(4.18) gives a schematic view of the instrument. For the in situ hydrogen studies at ADAM another vacuum chamber was constructed, covering the same pressure and temperature range as the x–ray chamber described above.

Off–specular reﬂections were measured at the thermal triple–axis spectrometer UNIDAS at the neutron research reactor DIDO at the Forschungszentrum Julich¨ in Julich,¨ Germany. The double monochromator system, consisting of two identical, vertical focussing pyrolytic graphite (002) crystals, allows to select incident wavelength between 0.8 A˚ and 4 A.˚ After interaction with the sample the neutrons can be analyzed in energy and direction with an analyzer crystal (pyrolytic graphite (002)) and a 3He detector. During the experiments the wavelength of the incident neutrons was kept constant at 2.3558 A.˚ The analyzer was used to select the elastically scattered neutrons from the sample, reducing the background. Fig.(4.19) gives a schematic sketch of a thermal three axis spectrometer. In both neutron experiments, the sample was mounted ver- tically, i. e. the surface normal lying in the horizontal scattering plane. A vacuum chamber supplied by the Institut fur¨ Festkorperforschung¨ at the Forschungszentrum Julich¨ with an Al 52 Chapter 4. Experimental methods

Figure 4.18: Schematic drawing of the neutron reﬂectometer ADAM at the ILL, Grenoble, France. window was used for scattering experiments with in situ hydrogen loading capabilities. Chapter 4. Experimental methods 53

Figure 4.19: General layout of a three axes spectrometer. 54 Chapter 4. Experimental methods 5. SAMPLE DESIGN

5.1. Molecular Beam Epitaxy MBE

The advantages of molecular beam epitaxy (MBE) lie in the versatility and simplicity of its operating principle: In an ultra high vacuum (UHV) environment, beams of atoms or molecules are directed onto a heated substrate crystal, where they form a crystalline layer. In ﬁg.(5.1), the cross section of a basic MBE system for solid source materials is represented. The success of MBE in research and development is based on three major advantages that make it a supreme tool for the preparation of thin metallic ﬁlms:

s MBE allows a very precise control of layer thickness down to the atomic scale.

s Compared to other growth techniques, no complicated chemical reactions take place at the surface. This facilitates analysis of growth processes like surface migration, step ﬂow, etc.

s The UHV environment in the growth chamber allows the application of various in–situ measurement techniques to study the fundamental processes governing crystal growth.

The main components of an MBE system are shown in ﬁg.(5.1). The source materials in ele- mental form are evaporated from the liquid or sublimated from the solid phase. Depending on the melting point, two different methods of evaporation are in use. Materials which develop a

sufﬁciently high vapor pressure below 1400 t C are evaporated in thermal effusion cells. The source materials are contained in ceramic crucibles, e. g. made of pyrolytic boron nitride or of aluminum oxide that produce a very low impurity contamination. The sources are electrically heated with a temperature stability of typically 0.1 K. In the crucible the material and the vapor are in thermal equilibrium, allowing to control the growth gate via the temperature. The evaporation rates are very stable and the required ﬁlm thickness can be achieved by the corresponding

55 56 Chapter 5. Sample design

Figure 5.1: The MBE machine in Bochum

evaporation time. Materials which need higher temperatures to evaporate at sufﬁcient rates are evaporated by a high energy electron beam (10 keV) which can heat up the material locally

to a maximum temperature of 3000 u C. The target material is stored in a water cooled copper crucible. The growth rate is regulated electronically and controlled via an optical method based on Electron impact emission spectroscopy (EIES). EIES is a system of evaporant excitation by electrons that uses the optical intensity of the subsequent de–excitation. It has the advantage of material selectivity by wavelength discrimination. Sensors based on EIES possess a long lifetime due to the non–consumable nature of its operation. The intensity of the optical signal can then be calibrated to any known reference. The MBE machine in Bochum is equipped

with three evaporation cells which can be heated up to 1400 u C and two electron guns. Their positions with respect to the sample is also illustrated in ﬁg.(5.1).

In order to produce deﬁned chemical interfaces, the atomic beams can be switched on and off by computer controlled shutters in front of the crucibles. The substrate is attached to a heatable manipulator that allows rotation of the sample to guarantee homogeneous growth.

Fabrication of high quality materials by MBE request very low partial pressures of contaminants 10

like oxygen and hydrocarbons (below 10 v Pa). This requires the use of pure materials and the baking of the vacuum chamber prior to crystal growth. Pumping is achieved with a combination of cryopumps, ion pumps, Ti sublimation pumps and a liquid nitrogen cooled shroud that covers most of the inside chamber surface. Chapter 5. Sample design 57

Most of the solid angle in front of the substrate is barred by the sources in an MBE chamber. This restricts measurement access to lateral incidence and exit. Therefore, reﬂection high energy electron diffraction (RHEED) has become the most widely used analytical tool in MBE.

5.2. The growth process

MBE uses the ﬂat, crystalline surface of the substrate to determine the crystalline properties of the growing layer. Incident atoms originating from the evaporation sources will choose the energetically most favorable sites on the surface. As a crystalline surface exhibits a periodic potential, the growing layer will adopt the structure of the surface. Consequently, the epitaxially grown layer should exhibit the same crystal structure and the same orientation as the substrate. Three factors are important regarding the mutual relation between the substrate and the epilayer. Lattice constant matching or lattice mismatch is the ﬁrst, crystallographic orientation of the substrate is the second, and its miscut, which is the angle of deviation between the surface and the crystallographic lattice planes is the third.

The most frequent case of MBE growth is heteroepitaxy, namely the growth of a layer with a chemical composition and structural parameters different from those of the substrate. Lat- tice mismatch is usually accompanied by strain as the epilayer starts growing with a lattice parameter deviating from the equilibrium lattice parameter in the bulk. If the lattice mismatch between the substrate and the growing layer is sufficiently small, the first atomic layers which are deposited will be strained to match the substrate and a coherent epilayer will be formed. As the layer thickness increases, the strain energy becomes so large that a thickness is reached when it is energetically favorable to introduce misfit dislocations and the lattice parameter of the epilayer relaxes towards its bulk value.

As surface defects like steps often serve as nucleation centers, the miscut of the substrate strongly influences the growth mechanism. A small miscut which introduces a sufficient number of monatomic steps and perfectly flat terraces supports the growth of a well ordered and a well aligned overlayer.

A series of surface processes are involved in MBE growth. The following are the most impor-

tant:w

adsorption, sometimes dissctiative adsorption of the constituent atoms or molecules 58 Chapter 5. Sample design

reaching the surface

x surface diffusion of the adsorbed atoms, preferably towards terrace edges

x incorporation of the constituent atoms into the crystal lattice of the substrate or the epilayer already grown

x surface aggregation and island formation of migrating atoms

x thermal desorption of atoms not incorporated into the crystal lattice

These processes are schematically illustrated in ﬁg.(5.2)

Figure 5.2: Schematic illustration of the surface processes occuring during ﬁlm growth by MBE [46]. Chapter 5. Sample design 59

There are two important external parameters which govern the MBE growth, the growth rate, which is usually measured in A/s˚ and the substrate temperature. The growth rate determines the available time for an atom on the surface to ﬁnd an adsorption site and hence the length of the diffusion path for a given diffusion rate. The substrate temperature rules the mobility of the adatoms, i. e. the speed of diffusion.

5.3. Sample architecture

All samples studied within this work were designed in the same way as represented in ﬁg.(5.3).

Yttrium films within the thickness range of 300 A˚ up to 10,000 A˚ were grown on Al2O3/Nb buffers to ensure a high crystalline quality of the Y films. The Y films were all capped successively with Nb and Pd in order to prevent the yttrium from oxidation and to improve the hydrogen uptake.

Figure 5.3: Schematic illustration of the typical sample architecture.

5.3.1. The substrate

A substrate has to fulﬁll different requirements. It should not react chemically with the epilayer, even at elevated temperatures, it should provide a single crystalline surface which allows epitax-

ial growth, it should be easy to handle and it should be inexpensive. As substrate material single α ¯ z crystalline –Al2O3 y 1120 was chosen together with a Nb (110) buffer layer, which satisﬁes all the conditions mentioned above. Typical roughnesses of the high quality polished substrates were in the order of 3 A,˚ i. e. they are ﬂat on an atomic scale. The average miscut was about 60 Chapter 5. Sample design

0.5 { , leading to terrace lengths of about several 100 A.˚ The sapphire crystals were provided by

Cyocera or by CrysTec as 0.5 mm thick quadratic wafers (50 mm | 50 mm). Depending on the different experimental requirements they were cut in pieces of different size.

The α–Al2O3 structure is quasi hexagonal. It consists of an oxygen sublattice possessing the hcp stacking sequence ABAB. . . and an aluminum suplattice which exhibits the fcc stacking

sequence ABCABC. . . The Al sublattice occupies 2/3 of the octahedral interstitial sites of the

~ { oxygen lattice, leading to a rhombohedral Al lattice with α } 87 5 and a lattice constant of 3.50 A.˚

Before introducing the substrates into the loading chamber of the MBE system they were cleaned chemically, wiped with alcohol, dried with nitrogen, and ﬁxed to a molybdenum disk serving as a sample holder to allow transfer between the different chambers. Afterwards the

substrates were tempered at 400 { C for 12 h in the load lock under vacuum conditions (p = 8

10 mbar) and then transferred into the evaporation chamber where they were outgassed at { 1000 { C for 2h and annealed at 1200 C for 15 min. This treatment assures a chemically clean surface and reduces the surface roughness. Fig.(5.4) shows a RHEED image of an annealed

α–Al2O3 (1120)¯ surface.

Figure 5.4: RHEED image of an Al2O3 sample before Nb evaporation. Chapter 5. Sample design 61

5.3.2. The Nb buffer layer

The niobium buffer serves as a spacer to prevent the chemically reactive yttrium layer to react with the oxygen contained in the sapphire. It also offers a high quality crystalline surface, supporting single crystalline growth of the yttrium. Furthermore, there is no intermixing of

Y and Nb. The growth of single crystalline Nb ﬁlms on α–Al2O3 has attracted considerable interest for the study of superconductivity, epitaxial growth, hydrogen uptake, and oxidation. It also serves as a standard buffer for rare earth metals and transition metals as well as for metallic multilayers. Niobium forms a bcc lattice with a lattice constant of 3.30 A.˚ Evaporated on sapphire, Nb continues the Al lattice for all low index crystal faces. The lattice mismatch

depends on the chosen orientation of the sapphire. The epitaxial relations between α–Al2O3

and Nb have been studied in detail [47, 48, 49] and are displayed in ﬁg.(5.5).

(100)

(110)

(111)

C plane

A plane

R plane

Figure 5.5: Three–dimensional epitaxy between the sapphire substrate and the Nb layer [50].

On sapphire 112¯0 Nb grows in the (110) direction, with the in–plane orientations Nb (11¯2) Al2O3 (11¯00) and Nb (111)¯ Al203 (0001) High purity Nb (99.9 %, Goodfellow) was deposited by electron beam evaporation at a typical rate of 0.5 A/s.˚ Before starting the 10

process a background pressure well below 10 mbar was achieved. During the evaporation the substrate was constantly kept at 900 C and tempered at 950 C for 20 min afterwards. As niobium and sapphire exhibit similar coefﬁcients for thermal expansion, thermal stresses at

¯ the interface can be neglected. Fig.(5.6) shows a RHEED image along the 110 azimuth of a 62 Chapter 5. Sample design

tempered Nb layer. The sharp streaks demonstrate a long range ordered and ﬂat surface.

Figure 5.6: RHEED image of the Nb buffer.

5.3.3. The Y layer

Yttrium crystallises in a hexagonal closed packed structure with lattice parameters of 3.65 A˚ and 5.73 A˚ for the a–axis and c–axis, respectively. Evaporated on Nb (110), Y grows epitaxially in the (0001) direction [51], though it exhibits an entirely different crystal structure together with different lattice parameters than the bcc niobium crystal. The epitaxy structure

at the interface follows the so–called Nishiyama–Wassermann (NW) relation; namely, the most

densly packed row 12¯ 1¯0 of the hexagonal Y is parallel to the densly packed row 002 of bcc

Nb, and correspondingly, in the orthogonal direction, the 101¯0 axis of Y is parallel to the 1¯10 axis of Nb. The single domain growth of the NW orientation can be conﬁrmed by LEED images, which clearly show a sixfold symmetry and sharp, untwinned diffraction spots (ﬁg.(5.8)).

In the simple rigid lattice model mentioned above, epitaxial orientation occurs when the inter- atomic distances are similar in the two crystals at both sides of the interface. In the present case the situation is different. Between Nb and Y there exists a 3:4 match (within 1 %), i. e. a Chapter 5. Sample design 63

Figure 5.7: Epitaxial relation between Y(0001) and Nb (110) with a 3:4 supercellcommensura-

tion [51].

supercell commensuration between the Y 1¯210¯ (3.1587 A)˚ and Nb 002 (2.3381 A)˚ axis as illustrated in ﬁg.(5.7).

Figure 5.8: LEED image of the Y (0001) surface at an electron energy of 63 eV. The sharp, untwinned diffraction spots prove the single domain growth of the Y on Nb (110).

Chemically pure yttrium (99.9 %), also provided by Goodfellow, was deposited by electron

beam evaporation at a typical rate of 0.3–0.5 A/s˚ at a substrate temperature of 550 C. The

RHEED patterns of the Y layer exhibit the symmetry expected for a hcp (0001) surface. Diffrac-

tion pattern originating from 101¯0 –like reflections alternate each 30 with 112¯0 –like reflections. The sharp streak patterns shown in fig.(5.9) indicate a smooth and ordered surface. Within 64 Chapter 5. Sample design

Figure 5.9: RHEED images of the Y layer in the (112¯0) (upper panel) and in the (101¯0) (lower panel) azimuth. The separation of the diffraction streaks is inversly proportional to the corresponding lattice spacings.

a thickness range up to 2 µ the RHEED patterns do not change. There is no sign of pseudomorphic growth of the ﬁrst monolayers as well as no sign of surface roughening during the growth process.

The ﬂatness of the Nb/Y interface can also be seen on images gained on a transmission electron microscope (TEM). The TEM is not based on diffraction. It therefore images the direct space.

Fig.(5.10) displays a 225 nm 50 nm area of the sample. The horizontal change of the contrast marks the Nb/Y interface. On this lengthscale, the interface appears to be perfectly smooth. Indeed, small angle x–ray reﬂectivity measurements reveal a typical interface roughness of less than 0.5 nm.

5.3.4. The cap layers

The purpose of the capping is to protect the Y ﬁlm from corrosion and to enable hydrogen loading at room temperature by catalytic dissociation of hydrogen molecules at the surface. Chapter 5. Sample design 65

Figure 5.10: TEM image of the Y/Nb interface, demonstrating the ﬂatness of the layers.

Palladium meets both requirements. To guarantee a good performance of the cap layer, it has to have no grain boundaries, wich serve as channels for oxygen, thus leading to corrosion of the underlaying yttrium layer. The palladium layer should also exhibit a small roughness in order not to disturb the x–ray and neutron reﬂectivity measurements. As Pd does not wet yttrium properly, it tends to form islands. Therefore a Nb layer of 50 A˚ was always evaporated prior

to the Pd cap to achieve a homogeneous coverage. The Pd was deposited by electron beam evaporation with a rate of 0.5 A/s˚ to 1 A/s˚ at a substrate temperature of 100 C to 200 C. The face centered cubic material grows with its (111) direction normal to the surface on the Nb (110) layer. Atomic force microscope images reveal clearly the sixfold symmetry of the quasihexagonal Pd(111) surface as displayed in ﬁg.(5.11). The extended hexagonal islands are ﬂat on an atomic scale, while the ditches separating different islands exhibit a depth of up to 5 nm.

Figure 5.11: Microscopic image of the sample surface. The left panel shows a 5µ 5µ area,

the right panel a 2µ 2µ area. the hexagonal structure of the Pd(111) surface can clearly be seen. 66 Chapter 5. Sample design

On a Pd (111) surface hydrogen is adsorbed dissociatively, the heat of adsorption being 7 21 kcal/mole. Already at room temperature and at H2 pressures in the 10 mbar range considerable amounts of hydrogen dissolve into the bulk which desorb again at elevated temperatures [52]. 6. RESULTS I: THE MICROSCOPIC SCALE

This chapter deals with the microscopic structure of thin, epitaxially grown single crystalline Y

ﬁlms on Nb/Al2O3 and their behaviour upon hydrogenation. Within this discussion the crystal structure of Y and the stable hydride phases will be adressed, as well as the epitaxial relation between them and the buffer. Starting with x–ray characterization of the virgin sample, the response of the metal lattice upon hydrogen loading will be described ﬁrst. Special emphasis

will be put on the reversibility of the YH2–YH3 phase transition and on the isotope exchange. Finally, the arrangement of the hydrogen atoms in the metal lattice will be the subject of the last part of this chaprer.

6.1. X–ray characterization of the virgin sample

Prior to the hydrogen loading, all samples have been carefully characterized by x–ray diffraction and by small angle x–ray reﬂectivity measurements as explained in chapter 4. In the following a typical epitaxial single crystalline sample will be discussed in detail.

Fig.(6.1) shows an x–ray reﬂectivity scan of a representative sample before hydrogen loading. 4

The reflectivity curve shows the typical Q behaviour, decorated with finite size oscillations. Do to the complex sample design, consisting of four layers of different electron densities and thicknesses, the oscillations cannot be directly related to the different metallic layers. In order to evaluate the film characteristics, a fit to the data points using a modified Parratt formalism including interfacial roughness has been used. The solid line represents in fig.(6.1) the result of the fit. [40, 53]. Typical interface roughnesses lie below 5 A.˚ The thickness parameters resulting from the fit are shown in the inset of fig.(6.1).

A high angle radial scan of the Y(0002) reﬂection is reproduced in ﬁg.(6.2). The main Bragg

67 68 Chapter 6. Results I: The microscopic scale

Figure 6.1: Small angle x–ray reflectivity of an epitaxially grown Y film and a fit to the data points. The inset shows the sample architecture. The film thicknesses result from the fit. The interface roughnesses lie below 5 A.˚

peak is accompanied by finite size oscillations. The longitudinal width and the position of the finite size oscillations correspond to a coherently grown film thickness of 309 A,˚ which agrees very well with the layer thickness as deduced from the reflectivity data in fig.(6.2). Therefore the entire Y film is structurally coherent. The position of the Y(0002) reflection refers to an

out–of–plane lattice constant of 5.75 0.005 A,˚ which is about 0.3 % larger than the bulk value of 5.73 A.˚

A conventional two circle diffractometer cannot be used to measure absolute values of 2θ, hence it does not directly provide reliable lattice parameters. The measured 2θ value depends on the position of the sample with respect to the center of rotation of the instrument. Nevertheless, a two cirle diffractometer measures angular distances accurately. Therefore all 2θ positions were compared with the position of the known substrate reﬂection and calibrated accordingly. The error bars of the lattice parameter are estimated from the resolution of the instrument used and from the accuracy of the stepper motors. Also the point density and the count rate may diminish the actual resolution. The effective resolution leads to an uncertenty or the lattice parameter of Chapter 6. Results I: The microscopic scale 69

Figure 6.2: Radial scan of the Y(0002) reflection. The Bragg peak is accompanied by finite size oscillations, proving the high quality of the film. The inset shows the corresponding rocking scan. It exhibits a two component line–shape indicating long range lateral order within the Y(0001) planes. Both scans were carried out using MoKα1 radiation, λ = 0.709 A.˚

about ¡ 0.01 A.˚

The rocking curve of the Y(0002) reflection exhibits a two–component line shape with a narrow component superimposed on a broader one. Two component line shapes have been observed in other heteroepitaxial systems as well [54, 55, 56, 57] and are a sign for high quality epitaxial growth. The sharp component indicates a long range structural order of the film induced by a flat and monocrystalline substrate, while the broad component reflects short range order fluctuations of individual growth domains. Due to a miscut between the Y layer and the buffer, the sharp component is not centered with respect to the broad one. In reciprocal space the sharp component and the substrate reflection occur in the same radial scan.

The in–plane epitaxial relation of the Y(0001) film to the Nb(110) buffer layer has been exam- ined using surface scattering techniques with glancing incident and exit angles to the surface [38, 58]. The incident angle was kept constant and equal to the critical angle for total external reflection from the surface. The intensity of the exit beam was integrated over a wide range of exit angles via a broad detector window. With this set–up the structural information is averaged over the entire thickness. The in–plane detector angle 2θ was fixed to the scattering vector of 70 Chapter 6. Results I: The microscopic scale

¯ the Y(1120) Bragg peak and the sample is rotated (ω–axis) by 360 ¢ around the surface nor-

mal. This scan reveals six Bragg reﬂections equally separated by 60 ¢ , reﬂecting the six–fold

symmetry of the (0001) zone axis of Y, as seen in the lower panel of ﬁg.(6.3).

£ ¤ Figure 6.3: 360 ¢ in–plane rocking scans of the Nb[002] (top) and the Y 112¯0 (bottom) reflections, showing that both materials grow with their in–plane crystal axis parallel to each other. The different intensities of the Y reflections have geometrical reasons. The strong Nb(002) reflections are due to planes of the Nb buffer layer. The weak Nb(002) reflections originate from the Nb cap layer, showing a sixfold symmetry, due to a Nishiyama–Wassermann epitaxial relationship between Nb(110) and Y(0001). The scans are superimposed on each other for clarity.

The varying intensities are due to different geometrical factors such as a tilt of the yttrium planes

with respect to the physical surface because of a miscut of the substrate by about 0.5 ¢ , which is on the order of the critical angle for total reflection. This leads to different incident angles of the x–ray beam with respect to the crystal planes and causes intensity fluctuations. Keeping the scattering vector constant at the value of the Nb(002) reflection and rotating the sample,

two strong Bragg reflections 180 ¢ apart can be seen (upper panel of fig.(6.3). They originate from the Nb buffer, confirming the twofold symmetry of the Nb(110) layer. The weaker re- Chapter 6. Results I: The microscopic scale 71

ﬂections separated by 60 ¥ originate from the Nb cap layer. One can distinguish between the buffer and the cap layer by performing x–ray scans at different incident angles of the x–ray beam, probing different depths. With increasing incident angle the intensity of the Nb buffer reﬂection increases, whereas the intensity of the cap layer remains constant. The different symmetries for the Nb buffer and the Nb cap can be explained by the different materials they were

grown upon. While the Al2O3(112¯0) substrate deﬁnes a unique in–plane growth direction for the Nb(110) buffer layer, the sixfold Y(0001) surface offers three equivalent directions for the

Nb(110) growth. As a result, the cap layer consists of three domains, separated by 120 ¥ . Tak- ing into account the different 2θ values of the Y(12¯ 1¯0) and the Nb(002) reﬂections by plotting

the intensity versus ω = θ - 2θ ¦ 2, the niobium reflections coincide exactly with the yttrium reflections, confirming the alignment of the Y(12¯ 1¯0) and the Nb(001) planes (fig.(6.3)).

Figure 6.4: In–plane radial scans. All equivalent Y[11¯ 20] reﬂections peak at the same position, demonstrating the isotropic growth of Y on Nb. The Nb buffer layer exhibiting a

twofold symmetry causes the strong Nb[002] reﬂection at 55.71 ¥ (solid line). The weak Nb[002] reﬂections originate from the Nb cap layer.

Fig.(6.4) shows in–plane radial scans along threee quivalent Y[112¯0] directions. All three equivalent Y[112¯0] reﬂections peak at the same 2θ position, indicating that the Y–lattice spacings are isotropic. This is surprising since only one crystallographic axis coincides between Y and Nb, which might have caused an anisotropic pseudomorphic growth of the yttrium layer. 72 Chapter 6. Results I: The microscopic scale

¯ The Y[1120] in–plane reﬂections exhibit a transverse width of about 0.55 § , referring to an in– plane coherence length of about 135 A.˚ This is a typical value for epitaxial growth of Nb on

Al2O3 substrates. Thus the yttrium in–plane domain size is limited by the Nb island size. From

the position of the Y peaks an in–plane lattice parameter of 3.63 ¨ 0.01 A,˚ can be deduced, which is slightly smaller than the bulk value of 3.65 A.˚ This slight distortion may be attributed to the fact that the 3:4 supercell commensuration between Y and Nb is not perfect, as explained above. Note again, that the observed compression of the a–axes is isotropic, though the Nb buffer exhibits a strong uniaxial structural anisotropy. The solid line in fig.(6.4) represents a scan through the Nb(002) buffer layer peak and the Y(12¯ 10)¯ peak. Along the Y(1120)¯ and the Y(21¯10)¯ directions no Nb reflection exists from the buffer. The two weak reflections accompanying these Y reflections originate from the Nb cap layer.

6.2. X–ray scattering on the hydrogenated sample

All hydrogenation experiments were carried out in the hydrogen chamber described in chapter 4.4. At room temperature, the sample starts absorbing signiﬁcant amounts of hydrogen at hydrogen pressures above 1 mbar. The loading process can be monitored by measuring the out– of–plane lattice constant. The lattice expands with increasing hydrogen pressure and with time.

At pH2 of about 1 mbar to 2 mbar it takes several days to reach the phase boundary. The time needed to enter the β–phase depends on the amount of hydrogen offered. In order to follow the hydrogen uptake in a reasonable time, the scans in ﬁg.(6.5) were measured with increasing hydrogen pressures from bottom to top. From solubility isotherms measured by electrochemical β methods at room temperature the equilibrium pressure for the α © coexistence is known to 30 lie at 10 ª mbar [59]. Therefore, the scans in ﬁg.(6.5) are far away from thermal equilibrium. Below 1 mbar no change in the lattice parameter has been observed. Obviously there is a kind of activation energy needed to start the loading process.

However, these measurements allow a precise measure of the critical lattice parameter cα « c above which the α–phase becomes unstable. Within the measured thickness range of 100 A˚ to

¨ ˚

several µm cα « c = 5.80 0.005 A. Within the accessible temperature range between room § temperature and 500 C this value is constant. The absolute value of cα « c as well as the absence of a temperature dependence is in full agreement with literature values obtained from bulk samples [4].

Hydrogen loading at room temperature up to the phase limit degrades slightly the structural Chapter 6. Results I: The microscopic scale 73

Figure 6.5: Radial scans of the Y(0002) reﬂection within the α–phase. The vertical lines indicate the positions of the reﬂection of the virgin sample and of the sample loaded up to the limit of the α–phase. The hydrogen concentration increases from bot-

tom to top. During hydrogen uptake the c–axis expands from 5.73 ¬ 0.005 A˚ to

5.80 ¬ 0.005 A.˚ The coherence length remains constant. At the phase boundary the β–phase precipitates, reducing the intensity of the reﬂection.

long range order of the Y(0001) planes, causing the narrow component in the rocking scan of

the unloaded sample to vanish. The initially sharp transverse width broadens to typically 0.65

at cα ® c while the transverse width does not change, indicating a constant coherence length. Si- multaneously, the peak intensity drops by a factor of 6, conserving the integrated intensity under the Bragg peak. No additional diffuse scattering from structural disorder could be observed.

Further hydrogen loading causes the precipitation of the YH2 phase which can be identiﬁed by

θ a Bragg reﬂection at 2 = 13.536 ¬ 0.005 , corresponding to the (111) reﬂection of a cubic α lattice with a lattice constant of 5.21 ¬ 0.005 A.˚ Already within the phase coexistence of – and β–phase, the γ–phase begins to form. The coexistence of three phases within one sample demonstrate clearly, that thermodynamic equilibrium is not reached. The time needed to form the trihydide is governed by the hydrogen pressure, i.e. the amount of hydrogen offered. At 74 Chapter 6. Results I: The microscopic scale

10 mbar the transition takes about 1 h or more, whereas it takes typically 15 min at 250 mbar.

The peak position corresponds to a c–axis lattice parameter of 6.62 ¯ 0.005 A˚ [60]. Within the trihydride phase, the c–axis lattice parameter does not depend on the external hydrogen pressure, i. e. on the hydrogen concentration.

While the ﬁrst transition is accompanied by a loss in the quality of crystallinity, the second transition causes no further change neither of the width nor of the shape of the x–ray peaks.

Figure 6.6: Radial scans of the YH2 (111) reflection. Dark symbols refer to the first hydrogen loading, open symbols to the fifth cycle. The inset shows the corresponding rocking scans through the (111) reflection. Corresponding curves overlap, proving the total reversibility of the dihydrid phase.

7 ± Expelling the hydrogen atoms in an environment of 10 ° mbar at 200 C results again in the

YH2 phase. Even after several cycles, no loss in the structural coherence is observable. Figures

(6.6) and (6.7) compare the radial scans and the rocking curves for the YH2 (111) and the

YH3 (0002) reflections in the first and in the fifth cycle, respectively. Within the statistics, the corresponding curves overlap perfectly.

Thus starting from the hydrogen rich trihydride phase, single phase YH2 samples can be pre-

pared. The protecting Pd cap layer prevents the chemically reactive YH2 from corrosion in air. The sample can be transported through ambient air for further examination. Apart from

single phase ﬁlms it is also possible to stabelize the phase coexistence between YH2 and YH3

within a sample. As mentioned above, at 200 ± C YH3 decays to YH2 under vaccum conditions. Chapter 6. Results I: The microscopic scale 75

Figure 6.7: Radial scans of the YH3 (0002) reflection. Dark symbols refer to the first hydrogen loading, open symbols to the fifth cycle. The inset shows the corresponding rocking

scans through the (0002) reﬂection. As in the case of YH2 corresponding curves overlap, proving the total reversibility of the trihydrid phase.

In a hydrogen atmosphere of at least 30 mbar, however, YH3 remains stable even at 200 ² C. At lower pressures stable phase coexistences form. Depending on the amount of hydrogen offered, the fractional scattering volumes of both phases can be shifted continously between them. At higher temperatures higher hydrogen pressures are needed to stabelize the trihydride

phase. Fig.(6.8) shows a series of θ ³ 2θ scans at different hydrogen pressures, visualizing the

controlled transition from YH2 to YH3.

As known from polycrystalline and powder samples, the transition to the hydrate phases affects mainly the c–axis. While the c–axis expands by about 15 %, the change of the basal plane lattice parameter is only about 0.5 %. Epitaxially grown c–axis Y ﬁlms behave similarly.

The trihydride phase is ﬁrst observed at room temperature at a hydrogen pressure of 4 mbar with ´ an in–plane lattice constant of 3.646 ´ 0.01 A,˚ corresponding to an expansion of 0.015 0.01 A˚ compared to the hydrogen free case. In contrast to the c–axis, the in–plane lattice parameter in the trihydride phase changes with hydrogen pressure. Increasing the hydrogen pressure up to

250 mbar, the in–plane lattice constant expands by 0.55 % up to 3.65 ´ 0.01 A.˚ The different response of the host lattice along the c–axis and basal plane directions indicate that the hydrogen sites in the host metal plane are ﬁlled last. Within the resolution of the instrument no in–plane anisotropy of the lattice expansion could be detected.

In the literature different values for the lattice constants are given. While there is good agree- 76 Chapter 6. Results I: The microscopic scale

Figure 6.8: Controlled transition from YH2 to YH3 at 200 µ C. With increasing hydrogen pres-

sure, the YH3 contend increases.

ment on an a–axis value of 3.666 ¶ 0.008 A,˚ the c–axis value is determined less precisely to

6.629 ¶ 0.030 A˚ [61, 25, 4]. The measured values for the lattice constants lie within the error bars of the published data.

The development of the in–plane radial Bragg reﬂections with increasing hydrogen pressure is represented in ﬁg.(6.9).

The Y in–plane peak shifts only slightly to lower angles while at the same time the Nb in– plane peak shows a large shift due to hydrogen loading. We therefore make the surprising observation that the Y film and Nb buffer expand independently upon hydrogen uptake. The increase of the Nb in–plane lattice parameter by 3.8 % within the Nb buffer layer is about 7 times as big as the in–plane lattice expansion of the Y film. The Nb expansion observed here is conform with the recently reported expansion of Nb(110) films on sapphire substrates having comparable thickness [62]. Moreover, the highly anisotropic in–plane expansion of the Nb buffer layer and its uniaxial structural anisotropy have no effect on the hydrogen uptake in the yttrium film, which expands isotropically in–plane. Thus, the trihydride maintains a sixfold symmetry irrespective to the twofold symmetry of the niobium buffer. There is no sign of a lattice distortion. These two observations indicate weak adhesive forces or an easy glide plane between the two metals. Chapter 6. Results I: The microscopic scale 77

Figure 6.9: In–plane radial scans during hydrogen loading at room temperature, measured with λ = 1.54 A˚ (CuKα radiation). The different scans are offset along the y axis for clarity. The hydrogen concentration increases from the bottom to the top. The stronger in–plane expansion of the Nb buffer layer does not effect the Y symmetry, which is grown on top of it.

The in–plane mosaicity and coherence length remain unchanged during the dihydride to trihydride phase transition. Thus the β–γ transition is reversible in all spartial directions without any loss of srtuctural coherence.

6.3. Neutron reﬂectivity and isotope exchange

The neutron scattering experiments carried out at the instrument ADAM were performed on a 2400 A˚ thick Y sample, grown in the same way as the sample mentioned above. The bigger sample volume was chosen to obtain more scattered intensity. Small angle neutron reﬂectivity measurements can be used to determine the deuterium concentration within the yttrium trihydride phase. The critical angle of total reﬂection is determined by the refractive index of the sample. The refractive index itself depends on the number density n of the material under investigation and on the coherent scattering length b of the involved nuclei within the sample. In the small angle regime, i. e. at low momentum transfer, neutrons probe the average scattering 78 Chapter 6. Results I: The microscopic scale

length density nb of the sample. Changing the average scattering length density by introducing hydrogen into the sample causes a modification of the refractive index and thus a shift of the critical angle of total reflection. The amplitudes of the finite size oscillations also change, because the scattering length density determines the neutron optical contrast. Additionally, the film expands during hydrogenation and the interface roughnesses may be affected. The critical

angle for total reﬂection θc of the YH3 ﬁlm is related to the hydrogen / yttrium ratio x via:

¸ ¸ λ ·

n · x b x θ ¸º¹H»

c · x (6.1)

π ¼

¸ ¸'¹ ½ ¸

· ·

where the particle density, n · x , is given by n x 1 x nY and the effective scattering length

¸º¹ ½ ¸ ¾ ½ ¸

· · by b · x bY xbH 1 x . Here bY and bH are the coherent scattering lengths for Y and H, respectively, and nY is the yttrium particle density (atoms per volume) within the sample. Thus the critical angle θc depends on the hydrogen concentration x. In reﬂectivity scans the measured edge is determined by the layer with the highest scattering length density nb within the sample.

As the scattering length density nb for Al2O3 is larger than for Y, the critical angle of the virgin sample is determined by the sapphire substrate. Since hydrogen has a negative scattering length, adding hydrogen to the Y ﬁlm results in a further decrease of nb. Hydrogen in Y is therefore not a suitable isotope for observing changes close to the critical angle as a function of the hydrogen concentration. This can, however, be achieved by replacing hydrogen with deuterium, which has a positive scattering length. Concerning the structure there is no difference between H and D in yttrium, except a slight difference in the lattice constants, which will be discussed later.

The reflectivity curve of the virgin sample together with a fit to the data is compared with the reflectivity curve of the deuterium loaded sample in fig.(6.10).

The reflectivity curve of the as prepared sample clearly shows high frequency oscillations which originate from the 2380 A˚ thick Y layer, as well as oscillations stemming from the 540 A˚ thick Nb buffer. The fit to the data gives interface roughnesses of about 4 A.˚ Exposing the sample to a deuterium atmosphere of 100 mbar, the high frequency oscillations vanish and the lower frequency oscillations become damped out quickly as the thickness fluctuations increase strongly. As the fit routine based on the Parratt formalism cannot handle thickness fluctuations, it fails under these conditions. The deuterium concentration can still be measured via the critical angle. The edge of total reflection shifts to higher angles with increasing D content (see inset of fig.(6.10)). The shift of the critical edge stops when the concentration of deuterium within the sample is in equilibrium with the atmosphere surrounding it. A further increase of the pres- Chapter 6. Results I: The microscopic scale 79

Figure 6.10: Small angle reflectivity scans for the sample as prepared (top) and the deuterated sample (bottom), measured with 4.4 A˚ neutrons. The solid line is a fit to the scan from the virgin sample, where the critical angle is determined by the sapphire substrate. As the scattering length density increases with increasing deuterium concentration, the critical angle is a measure for the deuterium content of the sample. The inset compares the edges of total reflection in detail. sure has no effect on the position of the critical edge for total reflection, indicating saturation. Longitudinal scans through the Bragg peak assure that the sample has completely converted to YD3. The small angle reflectivity scans for the as prepared sample and for the deuterated sample, measured with 4.4 A˚ neutrons are displayed in fig.(6.10). The solid line is a fit to the scan from the virgin sample, where the critical angle is determined by the sapphire substrate. As the scattering length density increases with increasing deuterium concentration, the critical angle is a measure for the deuterium content of the sample. The inset compares the edges of

total reflection in detail. From the measured position of the critical edge of total reflection, a À deuterium concentration of x = 2.94 ¿ 0 03 can be deduced. Thus the trihydride exhibits a substoichometric composition. Expelling the deuterium at 472 K, the critical edge of total reflection completely moves back to its initial, sapphire determined position. Simultaneously, the (111) reflection of the stable YD2 reappears in high angle Bragg scans. The critical angle of Al2O3 is still larger than for YD2. Therefore it is not possible to determine the deuterim concentration in the dideuteride phase by neutron reflectivity when using sapphire substrates.

Stability of hydride phases 80 Chapter 6. Results I: The microscopic scale

With neutron scattering and using the different isotopes the stability of the hydrides can be

tested. It is well known that YH2 is a very stable compound even under vacuum conditions.

The heat of formation for YH2 is relatively high (-114 kJ/mole H) [63], indicating a strong hydrogen–metal bond for the hydrogen atoms occupying tetrahedral interstitial sites. In comparison, YH3 is much less stable and decomposes to YH2 after removing the hydrogen pressure.

If a YD3 sample is exposed to a hydrogen atmosphere, two different reactions may occur. Either all deuterium atoms will be exchanged by hydrogen atoms (model 1), or only deuterium atoms occupying the in and near metal planes with octahedral symmetry (model 2).

Neutron diffraction can distinguish between these two cases. The sensitivity of neutrons to the different scattering lengths of the hydrogen isotopes results in distinguishable structure factors. Using the structural parameters determined recently by Udovic et al. [25], the structure factor for the YH3(0002) Bragg reﬂection can be calculated as:

2πi

α α Ä È S0002 ÁÃÂ ∑a b exp bY (6.2)

α rα ÅÇÆ

where aα describes the relative occupation of plane α, bα the average scattering length of the species occupying this plane and rα the relative position of the α plane in units of the distance between two adjacent Y planes. In the case of a stoichometric composition of YH3 the occupa-

tion number is 1 for the tetrahedral planes and 1 É 3 for each in and near metal plane. In model

1, bα was varied continuously from bD to bH for all layers simultaneously. In model 2, bα was kept constant at the value of bD for those planes containing the tetrahedral interstitials. Only bα for the in and near metal planes was varied continuously from bD to bH. The ﬁrst model predicts a decrease in scattered intensity by 20 %, while the second model predicts an increase by a factor of four, making the decision between both cases easy. In ﬁg.(6.11) the experimental results are reproduced.

First, the intensity at the center of the YH3(0002) Bragg reﬂection was measured under equilibrium hydrogen pressure conditions. Then the hydrogen atmosphere of 100 mbar was exchanged by a deuterium atmosphere of the same pressure at room temperature. The intensity of the Bragg peak stays constant. Obviously there is no interchange taking place with the hydrogenated sample and the deuterium atmosphere at this temperature and during the observation time. Increas- ing the temperatire from room temperature to 472 K, the neutron count rate starts to decrease and reaches a new stable plateau of about 78.5 % of the initial value. Radial scans through the

YH3(0002) reﬂection before isotope exchange and the YD3(0002) reﬂection after completion Chapter 6. Results I: The microscopic scale 81

Figure 6.11: Comparison of the YH3 reflection (open symbols) with the YD3 reflection (solid symbols) measured with a neutron wavelength of λ = 4.4 A.˚ Exchanging the hydrogen isotope, the integrated intensity drops to 78.5 % of the starting value. The inset shows the development of the peak intensity of the (0002) reflection during

the transition from YH3 to YD3. At t = 0 s the temperature was set to 372 K, at t = 1050 s the temperature was increased to 472 K. Note also the isotope effect of slightly different peak positions.

of the isotope exchange show two respective peaks which coincide in position and width but which differ in integrated intensity by 21.5 %. The same behavior can be observed in transverse scans. The exchange of deuterium and hydrogen is fully reversible, the intensity change could be reproduced several times. After each exchange, the concentration of deuterium and hydrogen was checked by small angle neutron reﬂectivity to assure that the isotope exchange has indeed

taken place. Within the YH3 phase the critical angle of total reﬂection is always determined by the sapphire substrate, obscuring the sensitivity for the hydrogen content. On the other hand, the sensitivity to the deuterium concentration is not limited and always a deuterium concentration

of x = 2.94 Ê 0.03 has been measured, even after several hydrogen–deuterium cycles, hinting at a complete isotope exchange.

As the intensity difference of the (0002) Bragg peak between YD3 and YH3 is very sensitive to 82 Chapter 6. Results I: The microscopic scale

x, the observed difference in intensity is a measure of the hydrogen (deuterium) concentration. While the shift of the critical angle is a direct measure of the average concentration, the structure factor, and thus its change, depend on the spartial arrangement of the hydrogen (deuterium)

atoms. To be specific, the intensity of the YH3 (0002) or the YD3 (0002) reflection is determined by the different scattering lengths of the hydrogen isotopes. The relative distances of the H (D) planes from the Y planes and their occupation also influence the scattering factor. In order to calculate the the hydrogen (deuterium) concentration from the relative intensities of the

two reﬂections, the crystallographic structures of YH3 and YD3 have to be known in advance.

Assuming the same P3¯c1 structure for YH3 and for YD3 and assuming the same occupation

(i. e. the same, still unknown concentration for YH3 and for YD3), the hydrogen content can be calculated.

While a stoichometric composition leads to an intensity decrease by 20 % upon isotope exchange, for a substoichometric composition of x = 2.8 the intensity drops down to 49 % of the initial value. From the measured decrease from 100 % to 78.5 % a deuterium concentration of

x = 2.99 Ë 0.03 can be deduced, which is a higher concentration than calculated from the small angle reﬂectivity curve. This difference may be attributed to various effects.

Ì There is a non–homogeneous distribution of hydrogen and deuterium in the sample. In this case the critical angle for total reﬂection, being sensitive to the average concentration in the yttrium ﬁlm, would give a different result than the Bragg peak intensity, which probes only the ordered, crystalline part of the sample.

Ì The isotope exchange is not quite complete.

Ì The crystal structures differ for YH3 and for YD3, or the concentration of hydrogen is different than the concentration of deuterium.

At the present time no distinction can be made between one or the other model, and further experiments such as hydrogen proﬁling measurements are necessary.

In any case, exploiting the scattering contrast of the different hydrogen isotopes offers an independent method to determine the hydrogen concentration if the structure is known. Vice versa, if the concentration is known, the structural model can be reﬁned.

There is another effect which is worth mentioning. The YD3(0002) Bragg peak is slightly

shifted towards higher angles with respect to the YH3 Bragg reﬂection, indicating a smaller Chapter 6. Results I: The microscopic scale 83

lattice spacing within YD3 as compared to the YH3 structure. This isotope effect agrees well with the lattice constants published in ref.[4]. Again, the epitaxially grown ﬁlm shows no difference in the structural properties than polycrystalline or powder samples.

6.4. Off–specular neutron diffraction

While the previously discussed measurements along the specular direction provide information about the layered structure of the sample, they are not sensitive to the lateral arrangement of the atoms within the individual layers. In order to study the change of the stacking sequences during the phase transitions as well as the in–plane deuterium ordering, scans along reciprocal lattice directions containing in–plane components are necessary. All measurements discussed in this section have been carried out at the three–axis neutron spectrometer UNIDAS at the DIDO reactor in Julich.¨

The sample used in this experiments was prepared in the same manner as the samples used in the previous experiments. Because the Pd cap layer was rather thin and did not completely cover the underlying Y ﬁlm, parts of the sample were oxidized. Below the uncovered parts of the sample almost no deuteration takes place as the natural oxide layer prevents the direct uptake of deuterium. Deuteration of these parts of the sample requires lateral diffusion of deuterium entering at Pd covered parts. During the time the experiment was carried out, deuteration by lateral diffusion was negligible. Thus the phase transition was not complete. This sample composition allows during the whole measurement to observe Bragg reﬂections emerging from deuterium free yttrium, which serve as markers in reciprocal space.

The bottom panel in fig.(3.2) shows schematically the real space of the hexagonal basal plane of Y. To simplify the description of the following measurements, three perpendicular axes were chosen to characterize the hexagonal lattice. In this description the Y(112¯0) axis is called the H–axis, and the perpendicular in–plane direction (1100)¯ is called the K–direction. The specular c–axis coincides with the L–axis. The first allowed in–plane reflections will be denoted as (100) and (010), respectively. As demonstrated by the grazing incident x–ray diffraction (GIXRD) measurements, the basal plane maintains its sixfold symmetry during hydrogenation. In the cubic co–ordinates of the YD2–phase, the H direction coincides with the (110¯ direction, the K– direction with the (112¯) direction and the L–direction with the closed packed (111) direction.

As a consequence of the structural changes during the transition to the β–phase, the reciprocal 84 Chapter 6. Results I: The microscopic scale space changes as well. Fig.(6.12) shows the K–L plane in reciprocal space.

Figure 6.12: Reciprocal lattice of the K–L plane. Allowed hexagonal reﬂections are represented by bold hexagons and indexed in italics. Bold and open squares mark the allowed positions of the two possible fcc domains, of which only one (bold symbols) is indexed. Common reﬂections are represented by circles.

Reflections which are only allowed in the hexagonal lattice are marked with hexagons, reflections which are only allowed in the fcc lattice are indicated by squares. Common reflections are represented by circles. Due to the ABCABC. . . stacking, the reciprocal space of a fcc lattice in the K–L plane is not symmetric with respect to L or K. Domains which are rotated by

180 Í against each other will produce two sets of reflections which are distinguished by open and solid squares in fig.(6.12). There is a priori no reason for preferring one orientation. Thus scans along (01L) do not only show the different stackings, they are also sensitive to different domains as well. The relative intensities of the fcc reflections along this rod are a measure for the scattering volume of the two possible domain orientations [64, 65].

To follow the phase transitions during deuteration, aditional scans along (00L) were carried out. In reciprocal space units of the hydrogen free Y lattice, the reﬂections of Y, YD2 and YD3 appear at L= 2, L= 1.91 and L= 1.74, respectively. Thus scans along (01L) should display reﬂections at L= 1 (=1/2 of 2) for the α–phase, at L= 0.64 (=1/3 of 1.91) and at L= 1.28 (=2/3 of 1.91) for the two different cubic domains for the β–phase and at L= 0.87 (= 1/2 of 1.74).

Neutron scans along the (01L) direction are shown in ﬁg.(6.13). The virgin sample exhibits a strong reﬂection at (011) which slightly shifts to lower L values during deuteration in the α Chapter 6. Results I: The microscopic scale 85

phase. A further increase of the gas pressure leads to a drastic decrease of its intensity.

Figure 6.13: Scans along (01L) for Y (top), YD2 (middle), and YD3 (bottom).

However, it does not vanish completely as the phase transition does not take place in the entire sample as described above. At the same time two new reflections occur at L= 0.64 and L= 1.28. The strongly reduced intensity of the hexagonal peak and the appearing cubic reflections clearly show that the lattice expansion during the α–β transition is accompanied by a rearrangement of the stacking sequence. Furthermore, the occurrence of both fcc reflections indicates that within the sample both possible stackings ABC. . . and BAC. . . are realized. The intensity ratio of 1 : 3 of these two reflections agrees well with the intensity ratio of calculated powder spectra. There seems to be no preferred orientation of the fcc stackings. Obviously, as the sample undergoes the hcp–fcc transition, the probability for the formation of either domain is equal. This observation agrees with recent x–ray photoelectron diffraction measurements on Y films grown on tungsten. [66].

A further increase of the deuterium pressure causes the fcc reﬂections to drop in intensity as

the sample reaches the YD3 phase. Again, the phase transition is not complete. Within the

YD3 phase a weak Bragg reﬂection at L= 0.87 (= 1.74/2) can be observed, originating from the

YD3 (011) reﬂection. In contrast to the P3 structure of the virgin metal, YD3 crystallizes in the higher symmetry P3c1¯ structure, for which only even L reﬂections exhibit strong intensity. 86 Chapter 6. Results I: The microscopic scale

Expelling the deuterium, the reﬂection at L= 0.87 vanishes and the reﬂections at L= 0.64 and L= 1.28 reappear. The sample was cycled three times without any measurable loss of structural coherence.

Like the transition from Y to the dihydride phase, the transition from the dihydride phase to the trihydride phase is accompanied by a rearrangement of the stacking sequence along the closed

packed axis. The hexagonal c–axis of YD3 coincides with the c–axis of the virgin metal. This

is however by no means obvious. The fcc structure of YD2 has four equivalent [111]–axes, and

single crystals of YD3 develop domains along all four directions. This is because the six–fold

symmetry of the Y c–axis does not provide a template for a particular [111]–axis in the YD2

phase. Then one would expect four different YD3 domains with their c–axis align along the [111]–directios of the fcc structure. In thin ﬁlms the situation is different. A thin ﬁlm can easily relax along the growth direction which in this case coincides with only one of the four [111]– directions. This direction will be the direction of choice if a structural phase transition requires an uniaxial lattice expansion.

Figure 6.14: Scans along (H00) for YD2 (open symbols) and YD3 (bold symbols). The peaks at H=1/3 and 2/3 in the trihydride phase show that the deuterium distribution exhibits a wavy like modulation about the Y basal planes in the [100] directions corresponding to the hexagonal [112¯0] directions.

Within the trihydride phase, scans along (H00) and (H02) exhibit Bragg reﬂections at H= Î 1/3

and H= Î 2/3, as shown in ﬁg.(6.14). They do not occur in x–ray diffraction measurements, Chapter 6. Results I: The microscopic scale 87

indicating that those reflections are indeed deuterium related. Since those reflections are also absent in the virgin sample as well as for YD2, they clearly show the ordering of the deuterium atoms within the metal. As there are no additional reflections along K or L, we conclude that thin single crystalline films, like powder samples exhibit an uniaxial deuterium modulation along the H–direction. This modulation is commensurate with respect to the metal lattice. The modulation length equals three times the distance of the yttrium atoms in this direction. Like in previously measured neutron powder diffraction spectra, superstructure reflections appear only

at (H0L) where L Ï 2n for integer values of n.

Since band structure calculations based on this structure do not predict the metal insulator tran-

sition, Kelly et al. [30] suggested a low–energy, broken–symmetry P3 structure for thin YD3 films. In this assumption the P3 structure would be stabilized by epitaxial strain in thin films [67]. The symmetry lowering would result in additional Bragg reflections which are forbidden in the high symmetry structure. In contrast to the P3c1¯ structure, in which the c–glide symmetry restricts the allowed Bragg reflections to (H0L) for even values of L, the absence of this element of symmetry in the P3 structure abolishes this restriction. We could not find any (H0L)

reﬂection for odd values of L, indicating that the P3c1¯ is preserved for epitaxial YD3 ﬁlms. For all structural measurements carried out so far, a contradiction to the P3¯c1 structure could nor be observed

6.5. Conclusion

Epitaxial single crystalline Y(0001) ﬁlms with perfect six–fold symmetry have been grown on

Nb(110)/Al2O3(112¯0) buffer/substrate systems with uniaxial structural symmetry. This system has often been grown in conjunction with rare–earth superlattices [68, 69].

Here a complete structural analysis of the in–plane epitaxial relation between the different layers has been presented. Moreover, for the ﬁrst time it was possible to prepare single epitaxi-

ally grown single crystalline samples of YH3 by controlled ex–situ hydrogen loading of MBE grown Y ﬁlms from the gas phase. More surprising then the hexagonal symmetry of the virgin Y(0001) layer is the fact that the symmetry and epitaxial relation are maintained during hydro-

gen uptake and lattice expansion to the bulk value of YH3. Admittedly, the lattice expansion is highly anisotropic and takes mostly place in the out–of–plane direction. Nevertheless, the 0.5 % in–plane lattice expansion of Y is surprisingly isotropic irrespective of the simultaneously expanding Nb buffer layer to a much larger value of 3.8 %, and irrespective of the different 88 Chapter 6. Results I: The microscopic scale in–plane structural symmetries. Thus the basal plane of Y is very robust.

The structural transition from the pure Y to the YH2 phase causes some degradation of the structural coherence, indicated, for instance, by the loss of the sharp component in the transverse scan across the (0002) peak. Between the YH2 and the YH3 phase no further loss in structural coherence is observed and the phase transition is completely reversible.

With small angle neutron reﬂectivity measurements as well as high angle neutron scattering experiments the isotope exchange in YH3 and possible preferential occupation sites with stronger binding energies have been investigated. The results show that there is no doubt that all hydrogen atoms are being exchanged by deuterium (and vice versa) within the sample by changing the surrounding gas atmosphere. The position of the critical angle for total reﬂection of neutrons as well as the intensity of the (0002) Bragg peak can be shifted continuously between the two limiting values of YH3 and YD3 depending on the relative H/D ratio in the sample. Entropy requires a complete isotope exchange. Surprising is the fact that this isotope exchange takes place on a rather short time scale of only a few minutes and that it effects all H atoms in the same way.

Off–specular neutron diffraction demonstrates nicely the reorientation of the stacking sequence of the yttrium atoms during the phase transition. It also shows the wavelike modulation of the deuterium atoms in the basal plane of YD3. All Bragg reflections are in agreement with the P3c1¯ structure found in powder samples. No additional reflections, indicating a broken symmetry, could be found. There seems to be no structural difference between thin epitaxial films and bulk samples. 7. RESULTS II: THE MACROSCOPIC SCALE

Within this chapter, the macroscopic structure of thin epitaxially grown single crystalline Y ﬁlms and the effect of hydrogen on it will be discussed. The focus of this discussion lies on the question of domain size, domain formation and domain mobility. Again x–ray diffraction methods will be used, but this time as an imaging tool for obtaining spatial information. Sub- sequently the results of the diffraction experiments will be related to atomic force microscope (AFM) measurements and to electrical resistance measurements.

7.1. X–ray diffraction topography measurements

The x–ray and neutron scattering experiments described so far deliver detailed information about the crystalline structure of a given material on an atomic scale. They do not yield any information about the phase nucleation, the domain size, the spatial distribution of domains during phase coexistence or about the lateral hydrogen diffusion within a sample. All these questions may be investigated by x–ray diffraction topography. In the experiments presented in this chapter, the height of the beam was limited to 7 mm by the windows of the vacuum chamber. 2

The 10 Ð 20 mm big sample was mounted horizontally, i. e. with the short side parallel to the ﬂoor. Due to large horizontal width of the beam, covering the whole width of the sample, an 2

area of 10 Ð 7 mm of the sample can be illuminated. The angle of incidence of the parallel and monochromatic beam can be varied by rotating the sample about an axis perpendicular to the incident beam. A photographic film was employed as a detector with a large image field (open detector). The Kodax Professional Industrex SR used for this experiment allows to record all specular Bragg reflections of the sample within one exposure. The exposure times were adjusted according to the scattering volume of the constituencies of the sample. For the sapphire substrate an exposure time of one second was chosen, the reflections of the epilayers

89 90 Chapter 7. Results II: The macroscopic scale were recorded in about 100 s. Different lattice parameters of the different metals evaporated onto the substrate allow to separate their images spatially on the photographic film by their different Bragg angles. The topographic images were recorded in two different ways. First, in order to visualize the orientations of the structural domains within the sample, images were taken at several fixed positions on the rocking curve. Second, the sample was rocked during the exposure to collect all the reflected intensities from the differently oriented domains. Due to the high collimation of the incident beam, spatial resolution of method is only limited by the grain size of the photographic film which is 1 µm. But one has to bear in mind that the diffraction process itself provides additional limitations, which are in general below that value.

Fig.(7.1) is a typical topographic image of the virgin sample. From left to right, corresponding to an increase of the scattering angle, the reflections of the yttrium layer, the sapphire substrate and the niobium layer can be seen. The trace of the wire used to fix the substrate during the growth process can clearly be observed on the recorded images of the two metallic layers. As in fig.(7.1) all samples discussed in this chapter were mounted such that the wire is horizontal and in the upper part of the sample. For the interpretation of the images it is important to take the horizontal compression into account. As described in chapter (4.1.5), the images are compressed by the sine of the Bragg angle, which results in a factor of about 10.

Figure 7.1: Topographic image of the virgin sample. From left to right the reﬂections of the yttrium layer, the sapphire subsrtrate and the niobium buffer are displayed. During the exposure time, the incident angle was continuously changed by rocking the sample. Chapter 7. Results II: The macroscopic scale 91

7.1.1. The virgin sample

The topographic images of the metal layers exhibit many details. Images taken at different fixed incident angles illustrate which domains contribute to the reflected intensity at a specific point of the rocking curve.

Figure 7.2: Topographic images of the Nb buffer layer prior to hydrogen loading. The images ’A’ and ’B’ were recorded at different incident angles, corresponding to positions on the ﬂank of the rocking curve (A) and on the center of the rocking curve (B) as indicated on the schematic rocking curve.

Fig.(7.2) displays two topographic images of the niobium buffer layer recorded at the flank (image A) and at the center of the rocking curve (image B), respectively. At first glance both images appear almost uniform, indicating a homogeneous film. An optical microscope was employed to obtain more details from the exposed and developed photographic film. An enlarged section of fig.(7.2 A) is shown in fig.(7.3). Single mosaic blocs become visible. Their shape is well defined by sharp borders and an abrupt change of contrast to the background. The size of these mosaic blocks is in the order of up to 10 µm. This appearance may be explained by assuming an incoherent composition of the Nb film. Each block has its own orientation, independent from its surrounding. Two neighboring blocks are separated by a sharp border where the orientation changes discontinuously. Such a mosaic bloc is not necessarily a tiny, perfectly crystalline volume element of the sample. As known from GIXRD (see chapter 6.1), the in–plane coherence length is much smaller than the topographically detected mosaic blocs. Also measurements carried out by transmission electron microscopy show a dislocation density which require de- 92 Chapter 7. Results II: The macroscopic scale fect free domain sizes in the order of about 20 nm. Thus a mosaic bloc has to be considered as to be composed of several single crystalline domains of the same orientation, separated by dislocation lines.

Figure 7.3: Details of ﬁg.(7.2 A)

The yttrium layer has a different appearance. Unlike the Nb layer, the Y film appears to be coherent. The topographic images show smooth changes of the contrast, suggesting a continuos modulation of the orientation. As expected by the independent in–plane expansion of Nb and Y, there is no influence of the buffer on the Y film. While the Nb–layer shows well defined structures in the µm range, the Y–film exhibits much larger structures in the mm range. The two topographic images displayed in fig.(7.4) demonstrate nicely the ”negative effect”. Those volume elements which fulfill the Bragg condition at the center of the rocking curve do not contribute to the intensity in the flanks of it. As a result, one topography appears to be the negative image of the other one.

7.1.2. Hydrogen loading and phase formation

In order to study the different stages of hydrogenation, the sample structure was modiﬁed as displayed in ﬁg.(7.5). As all samples discussed before, the Y layer is grown on a Nb/sapphire substrate, but unlike the others only one half of it was covered with Nb and Pd. In ambient air, the uncovered part of the sample oxidizes on the surface. After the formation of an oxide layer of a typical thickness of several nm, the oxidation process stops. Chapter 7. Results II: The macroscopic scale 93

Figure 7.4: Topographic images of the Y layer prior to hydrogen loading. The images were recorded at different incident angles, corresponding to positions on the ﬂank of the rocking curve (A) and on the certer of the rocking curve (B). A’ and B’ are enlarged areas of A and B, respectively.

Figure 7.5: Sample architecture and scattering geometry used in the XDT experiments.

The body centered cubic oxide Y2O3 grows along its closed packed (110) direction. Y2O3 is known to be protective. Therefore the natural oxide layer of yttrium is often been used to cover rare earth ﬁlms and superlattices [68]. The following hydrogenation experiments prove, that

Y2O3 is also an effective barrier for hydrogen. Exposing a sample designed like this to a hydrogen atmosphere, leads to fast hydrogen loading of the yttrium and of the niobium beneath the palladium covered part. Thermal equilibrium with the surrounding atmosphere is achieved within several minutes. Afterwards lateral hydrogen diffusion starts, accompanied by the structural phase transitions discussed in the previous chapter. A series of topographs at increasing pressures, showing the hydrogenation of the initially virgin sample is displayed in ﬁg.(7.6). All

images were taken at 300 Ñ C. Each topographic image depicts a 7 mm long part of the sample, limited by the trace of the wire. Due to geometrical effects mentioned earlier, the image of the 94 Chapter 7. Results II: The macroscopic scale

10 mm wide sample is compressed to about 1 mm on the photographic film. In order to record all domains of a given phase in all the thin films irrespective of their orientations, the sample was rotated about the axis normal to the diffraction plane during the exposure. Therefore no details are visible in the images, they appear uniformly grey. The exposure times were on the order of 100 s for the epilayers and 1 s for the substrate. The actual exposure times were adjusted to the intensity of the reflections. At pressures below 1 mbar, hydrogen dissolves in the palladium covered part of the yttrium layer, forming a lattice gas. The expansion of the lattice causes a decrease of the scattering angle. Therefore the image of the yttrium reflection shifts to the left side in the upper part of the image of the yttrium layer. The precipitation of YH2 starts at about 1 mbar. The nucleation of the β–phase starts simultaneously at arbitrary places in the Pd covered part of the sample. This process may be compared with the wetting of the floor as it starts raining. Starting from the ”dry phase”, rain drops fall on arbitrary places on the floor. Between the two states ”dry” and ”wet” both ”phases” coexist lateraly. There is no spatial separation of the phases. In the case of the Y–YH2 system the domains of both phases must be smaller than 1 µm (film resolution). The intensity of both reflections is distributed almost homogeneously. At this stage of the hydrogenation the Y film consists of YH2 domains embedded into a matrix of the lattice gas phase. Between the reflections of the α–phase and the β–phase no scattered x–rays were detected by the photographic film, indicating again that the transition between these two phases is discontinuous. Up to 1 mbar, there is no effect to the Nb buffer layer, all hydrogen is absorbed by the yttrium.

At a pressure of 5 mbar, the transition to the β–phase is completed below the Pd covered part

of the sample. Also the Nb buffer underneath the YH2 is saturated with hydrogen. Unlike the Y, Nb does not cross a phase boundary between the hydrogen free state and the saturated state as the experiments were carried out well above the critical temperature. There is a continuos shift of the lattice parameter along the hydrogen concentration gradient within the sample. As a result, the topographic images of the hydrogen free part of the Nb film and of the hydrogen loaded part are not isolated as in the case of Y. They are connected, indicating that the gradient in lattice parameter is caused by a gradient of the hydrogen concentration. A further increase of the hydrogen pressure forces the lateral diffusion of hydrogen. The diffusion fronts in the Y and in the Nb layer move together. There is no sharp front in the Y film. A region of coexisting α– and β–phase can be observed. Like the coexistence of both phases at 1 mbar, their domains are smaller than the film resolution and both phases are totally mixed up. The γ–phase starts to nucleate at a pressures of 80 mbar. Like the occurrence of the β–phase at 1 mbar, both phases coexist underneath the Pd cap layer before the hydrogen rich phase starts Chapter 7. Results II: The macroscopic scale 95

Figure 7.6: Series of x–ray diffraction topographies of the ﬁrst hydrogenation.

diffusing along the sample at higher pressures. During the diffusion process, the YH3 front

behaves similar to the YH2 front. There is no visible change in the domain size. Again a region

of phase coexistence goes ahead of the YH3 phase. Hydrogen diffusion within the investigated

sample is slow, especially in the YH3 phase. Even after 36 hours in a hydrogen atmosphere of 265 mbar the hydrogen front just moved 2 mm while the rest of the Y ﬁlm changed completely

to YH2. Due to the low velocity of the diffusion, thermal equilibrium has not been achieved in any of the topographic images in ﬁg.(7.6). 96 Chapter 7. Results II: The macroscopic scale

An investigation of the YH3, the YH2 and the Nb reﬂection at different points of their respective rocking curve does not provide any details. The topographic images appear to be uniformly grey. Hydrogen loading destroys all the structural features which could be seen in the virgin state of the sample and averages out all the details of the domain structures.

Removing the hydrogen atmosphere completely and keeping the temperature constant at 300 Ò C expels the hydrogen partially from the sample as shown in ﬁg.(7.7).

Figure 7.7: Series of XDT images during dehydrogenation at 300 Ò C. First, the Pd covered

part switches to the YH2 phase, than the hydrogen within the remaining YH3 phase diffuses towards the Pd limit, where it leaves the sample. This process is illustrated by the two scetches representing the phase distribution within the sample in the ﬁrst and in the last image.

The exposure times were kept constant at 300 s for the YH3 and the YH2 reﬂections together Chapter 7. Results II: The macroscopic scale 97

and at 500 s for the Nb reﬂection, summing up to a total time of 800 s for the whole image of the sample. Immediately after ﬁnishing one exposure, the next one of the series was started. Des- orption of the hydrogen takes place through the Pd cap layer. First the hydrogen gets expelled

from the Pd covered part. On the second and third exposure a coexistence of YH3 and YH2 can clearly be seen. As a result, the yttrium underneath the Pd cap layer as well as in the bottom part of the sample exists in the β–phase. Between these two regions of the sample, the yttrium is still loaded up to the hydrogen rich γ–phase. On the topographic image, the YH2 reﬂection consists of two spots which are related to the Pd covered part (top) and the bottom part of the sample which has not been reached by the hydrogen diffusion front during the loading process.

The middle part of the sample is still in the YH3–phase. Later on the hydrogen from this region diffuses towards the Pd window, where it leaves the sample. This process causes the γ–phase to vanish gradually. The Nb reflection behaves differently as the lattice paramer is allowed to change continuously at different hydrogen concentrations. On the first topographic image, exposed under hydrogen atmosphere, the Nb reflection is inclined, demonstrating a lattice parameter gradient. Under the Pd covered part the lattice parameter is higher than at the bottom of the sample. Immediatly after removing the hydrogen atmosphere, the hydrogen starts leaving the Nb layer via the Pd window. Now the hydrogen concentration and the lattice parameter rises toward the bottom of the sample. As time passes on and more hydrogen gets expelled, the Nb reflection moves back towards its initial position without completely reaching it during this experiment.

7.1.3. Lateral phase propagation

Exposing a partially Pd covered Y layer to a hydrogen atmosphere leads to the fast formation of the YH3–phase underneath the Pd cap layer while the rest of the Y layer is still hydrogen free. The resulting steep hydrogen concentration gradient in the Y layer close to the Pd border is the driving force behind the lateral phase propagation in the sample. Due to the large miscibility gaps in the H–Y system the hydrogen concentration can not vary continuously within the sample. The lateral hydrogen progression therefore requires two mechanisms. First, the hydrogen atoms have to diffuse from the Pd covered part to the phase boundary. Then new domains of the hydrogen rich phase have to nucleate. The phase boundary moves through the sample by the continuous precipitation of new domains. This heterogeneous seed formation consumes energy which is nesessary to plastically deform the crystal lattice and to build up domain walls. During the α–β transition as well as during the β–γ transition, the heterogeneous seed formation is the 98 Chapter 7. Results II: The macroscopic scale

process that limits the velocity of the phase propagation.

Generally, the net ﬂux J of impurity atoms is related to the gradient of the impurity concentra-

tion c by a phenomenological relation called Fick’s ﬁrst law:

Õ Öº× J Ó!Ô D grad c (7.1)

Within this relation the diffusion coefﬁcient D is a measure for the mobility of the impurity Ö

atoms. D may be explicitly concentration dependent, symbolized by D Õ c . Particle conservation ÓÙÔ requires ∂c Ø ∂t divJ, leading to Fick’s second law:

∂c

Õ Õ Ö Õ Ö Öº× Ó div D c grad c (7.2) ∂t

In the present diffusion situation, only one spatial dimension has to be considered. Fick’s second law then takes the form:

∂c ∂ ∂c

Õ Ö

Ó D c (7.3) ÛÝÜ ∂t ∂z Ú ∂z

where z is the diffused distance. Boltzmann showed that Fick’s second law can be transformed ØßÞ into a relation of only one variable λ Ó z t, if the boundary conditions can be transformed accordingly [70]. This transformation still holds in multiphase systems [71, 72].

dc d dc

Õ Ö ×

λ ÓÙÔ 2 D c (7.4) Û dλ dλ Ú dλ

The validity of this Boltzmann scaling in the Y–H system has been demonstrated by F. J. A. den

Broeder and coworkers [73] on a 3000 A˚ thick Y layer by optical transmission measurements.

Ö Õ Ö To deduce the diffusion coefﬁcient D Õ c , the concentration as a function of λ, c λ has to be known. Those data could be obtained mapping the concentration by nuclear proﬁling methods or, in the case of H in Y, by optical methods. However, the effective mobility of the phase

2 Ø boundary Me Ó z t, where z denotes the position of the diffusion front of the phase boundary can directly be measured. F. J. A. den Broder et al. investigated the temperature dependence

of Me and obtained an Arrhenius behavior between room temperature and 140 à C and at a

Chapter 7. Results II: The macroscopic scale 99

â ã å ä hydrogen pressure of 1000 mbar. Me can then be expressed as Me á M0exp Ea kT . The

4 2 ç activation energy and the M0 were determined to be 0.369 eV and 1.4 æ 10 cm /s, respectively.

As the motion of the phase boundary can clearly be seen, Me is also easily accessible in XDT

measurements. To obtain a value for the mobility of the YH3–YH2 phase boundary, a second

loading experiment has been carried out at a constant temperature of 300 è C and a constant

hydrogen pressure of 800 mbar. The progression of the YH3 front as a function of time is represented in fig.(7.8). Due to the rather large coexistence area, the position of the diffusion front has to be defined for all topographic images in the same way. For the calculation of the phase mobility the front of the coexistence region has been chosen. The error bars in fig.(7.8) originate from the uncertainty of determinig this border line.

Figure 7.8: Progression of the YH3 front at a T = 300 è C in a hydrogen atmosphere of 800 mbar (left). The right ﬁgure displays the square of the diffusion length as a function of time and a linear ﬁt to the data.

The motion of the diffusion front of the trihydride follows a é t law, indicating the validity of the

6 2

æ ç

Boltzman scaling. A ﬁt to the data points reveals an effective mobility of Me á 5 10 cm /s.

Extrapolating the results of den Broeder et al. [73] to 300 è C results in a effective mobility of

4 2

æ ç 7 ê 7 10 cm /s, which is about two orders of magnitude faster than in the present experiment. There are several reasons for this huge difference: The slightly higher hydrogen pressure used by den Broeder or different performances of the Pd capping. However, the main reason for the different velocities lies in the different sample preparation. The samples used by den Broeder et al. were directly evaporated to the sapphire substrate without the use of a buffer layer. In order to keep chemical reactions between the Y ﬁlm and the sapphire as small as possible, the substrate was not heated during the evaporation process. The absence of an absorbing buffer is 100 Chapter 7. Results II: The macroscopic scale

advantageous for optical transmission experiments. On the other hand, the crystalline quality is different. Yttrium films prepared in this way still show c–axis growth, but they are highly textured and polycrystalline. Therefore the diffusion of hydrogen is governed by the diffusion along grain boundaries, which is indeed faster than the diffusion through a single crystal. More- over, the initial domain size in polycrystalline films is smaller than in epitaxially grown films. Thus the structure has not to be broken in smaller domains during the hydrogen loading. Unfor- tunately a single value of the effective mobility measured at one specific temperature and one specific hydrogen pressure does not allow to determine the activation energy. Thus additional experiments are necessary to determine the kinetics of hydrogen in single crystalline Y films.

7.1.4. The narrowing of the miscibility gap at elevated temperatures

After 20 h at 300 ë C in a hydrogen atmosphere of 800 mbar, the lower half of the Y ﬁlm still shows no trace of the γ–phase. It is completely in the β–phase. On the other hand, after removing the hydrogen atmosphere and cooling the sample to room temperature, the topographic

image of the lower part of the sample clearly shows the appearance of YH3 (Fig.(7.9)). The sudden nucleation of the γ–phase can be explained by the Y–H phase diagram (see ﬁg.(3.1)). At elevated temperatures the miscibility gap between the β– and the γ–phase becomes narrower. In other words, the hydrogen content of the saturated β–phase increases with temperature. As the diffusion of hydrogen is very slow, the surplus of hydrogen has to precipitate in the hydrogen rich γ–phase as the temperature is lowered. This should have occured as well without removing the H atmosphere.

Figure 7.9: Comparison of the saturated β–phase at 300 ë C and at room temperature, showing the precipitation of the γ–phase. Chapter 7. Results II: The macroscopic scale 101

7.2. Optical appearance and AFM studies of a partially loaded sample

The different diffusion fronts as well as the coexistence regions can be identiﬁed in the optical appearance of the sample. In ﬁg.(7.10) a photograph of the sample is shown. The image was recorded using an optical microscope and a black and white video camera. The sample itself was illuminated from the top with white light. The upper third of the sample is covered with Pd. The trace of the wire as well as the sharp change of contrast at the Pd border are clearly

visible. The YH3 diffusion front coincides with another change in the reﬂected intensity about 8 mm away from the trace of the wire. Comparing the different grey scales, the region of phase coexistence can be distinguished from the homogeneous phases, as marked in ﬁg.(7.10). Within the lower part of the sample parallel stripes of up to 4 mm length and of 0.1 mm width are

visible. Those stripes may be attributed to the precipitates of YH3 which have been discussed in the previous paragraph. Their shape, their inclination with respect to the sample edges as well as their parallelity are not understood.

Apart from the basic features described above, the sample exhibits lots of details like cloudy stains or streaks. Without further studies, explanation of those details are subject of speculation. They may be due to hydrogen density ﬂuctuations or due to chemical impurities.

Although the sample is covered by an oxide layer, the surface topology of the partially hydrogenated sample also reﬂects the different stages of hydrogenation. As the out–of plane lattice

parameter of YH2 and YH3 differ by 10 %, the overall thickness of the sample varies as well. Within the region of phase coexistence the thickness variations should be on the order of about 20 nm, as the thickness of the Y ﬁlm is 200 nm.

Since the expected domain size is on the order of 1 µm, an atomic force microscope (AFM) is 2

the ideal tool for recording the surface profile of the sample. Fig.(7.11) shows a 5 ì 5 µm area of the sample within the region of phase coexistence. The surface reminds hilly landscape with gentle slopes. Typical sizes of the hills match the expected domain proportions. The height difference between the lowest and the highest point of the displayed area equals 15 nm. This is five times more than the original height fluctuations from the surface roughness of the oxide layer. AFM images taken in single phase regions show an average roughness of about 2–3 nm. While the lateral extension of the surface structures as well as their heights correspond to the expected values, their shape does not. Assuming columns of YH2 and of YH3 wizh respective 102 Chapter 7. Results II: The macroscopic scale

Figure 7.10: Optical photography of the partially hydrogen loaded sample.

Figure 7.11: AFM image of the partially hydrogen loaded sample. The surface proﬁle was measured in the phase coexistence region of the sample (compare ﬁg.(7.10)). Chapter 7. Results II: The macroscopic scale 103

ﬁlm thickness, surface topology with sharpcontours would have been expected. The YH3–YH2 border line should result in a steep surface step, separating ﬂatter areas. But it is important to recall that the AFM scans the actual surface of the sample, which in this case is covered by

Y2O3. The oxide layered may smoothen the discontinuities of the surface.

7.3. Electrical resistance measurements

In order to relate the structural data gained in scattering experiments to transport properties, the electrical resistance has been recorded during the x–ray scattering experiments in Bochum. Monitoring the resistance together with the diffracted x–ray intensity offers the opportunity to follow the structural aspects of the phase transition as well as the electronic aspects simultaneously.

The electrical resistance was measured in a conventional four probe method as described in chapter 3. The current in plane (cip) geometry averages the resistance of the whole sample. As all samples contain a niobium buffer as well as a palladium cap layer, the change of the electrical resistance due to hydrogen loading is affected by the response of all materials in the sample. Fortunately the energy gain per hydrogen atom solved into the sample is smaller in

YH2 than in Nb. In a hydrogenation experiment in a thin ﬁlm Y/Nb system the transition from

YH2 to YH3 starts only after the niobium is saturated with hydrogen. As the XDT experiments show, the yttrium layer remains in the β–phase as long as the niobium buffer is not saturated with hydrogen.

All resistance measurements presented in this chapter were performed at 200 í C. This temperature was chosen because the behavior of Nb ﬁlms has been extensively studied at this temperature, allowing to separate the resistance changes of both materials. In order to distinguish between the different materials, the sample was prepared to be in the dihydride phase as regards the yttrium while the niobium was almost hydrogen free.

Fig.(7.12) shows the development of the electrical resistance as a function of time. At a time t = 300 s, 5 mbar of H2 gas were introduced into the chamber. The Nb buffer is immediatly saturated with hydrogen, while the Y is still in the YH2 phase. The sudden increase of the electrical resistance at this point is related to elevated resistance of the hydrogen saturated Nb ﬁlm. Both the time scale as well as the absolute change of resistance are the same as for a single Nb layer of the same thickness under the same conditions [62]. Later on the hydrogen 104 Chapter 7. Results II: The macroscopic scale

6 25 mbar 17 mbar

] 5 . 10 mbar u . a [

y 5 mbar

it 4 v

ti s i s e

r 3 . l e

2 YH2 YH2 + YH3 YH3

0 250 500 750 1000 1250 1500 1750 2000 time [s]

Figure 7.12: Electrical resistance of a typical sample as a function of time. Starting from YH2,

the hydrogen pressure was successively increased up to the YH3 phase. First the Nb saturates, then the Y enters the two phase region. pressure was increased step by step up to a pressure of 25 mbar. All additional resistance changes originate from the Y layer. Each time the electrical resistance reached equilibrium, a radial x–ray scan was performed. The increase of the electrical resistance is accompanied by the structural phase transition. Plotting the fractional scattering volume of YH3, i. e. the area under the (0002) x–ray reﬂection curve, versus the resistance results in an exponentially increasing curve. This curve is represented in ﬁg.(7.13) together with the corresponding radial x–ray scans.

This result can be modeled by two parallel resistors. The YHx layer is represented by a tunable resistor, the resistance of the Nb buffer remains constant. Assuming an electrical conductivity

close to zero for the pure YH3 state, the conductivity of the whole system may be written as

ó σ ô σ σ ò ïñð total î Nb 1 x YH2 ; (7.5)

where x is the fractional volume of YH3. The conductivity of the buffer, σNb, and of the YH2 Chapter 7. Results II: The macroscopic scale 105

Figure 7.13: Plot of the electrical resistance versus the fractional scattering volume. The inset shows the corresponding radial x–ray scans (compare ﬁg.(6.8).

σ film, Y H2 , can be deduced from the initial conductivity (x = 0) and from the final conductivity (x = 1). A sketch of this model is given in fig.(7.14).

Figure 7.14: Model of two parallel resistors.

What makes this naive model so appealing is the fact that it fits very accurately to the measured data. This experiment first shows that YH3 is a bad conductor or even an insulator. As the Y layer is parallel to a metallic conductor, the cpp geometry does not allow to obtain an accurate value of its electrical conductivity. Moreover this experiment proves that during the phase coexistence the Y film is composed of two structurally distinct phases possessing distinct electrical resistivities. A change of the resistance is only possible together with a change of the fractional σ volumes of the participating phases. Within this experiment it is possible to measure Y H2 for

106 Chapter 7. Results II: The macroscopic scale õö

0 õ÷ö x 1 only because of the presence of the Nb buffer layer. Otherwise the conductivity ø

measurement would be limited to the percolation threshold of x ö 0 6, i. e. experiments would

õö ø only be possible for 0 õö x 0 6.

7.4. Conclusion

On the macroscopic scale, thin layers of Nb and Y appear quite different. Nb shows distinct mosaic blocks of several µm in diameter, indicating an incoherent composition of the crystalline layer. Y on the other hand shows larger structures with smoothly varying orientation, suggesting a coherent structure. No inﬂuence of the structural details of the buffer could be observed on the structure of the epilayer.

Exposing a Pd covered Y ﬁlm to a hydrogen atmosphere of a few mbar, domains of YH2 nucle-

ate at random places. With increasing hydrogen pressure the number of YH2 domains increase until the whole ﬁlm has changed to the β–phase. At higher pressures, the formation of the

YH3 phase starts in the same way. Typical sizes of the domains are on the order of one micron. Within the hydride phases, the topographic pictures show no more details. The structural features of the virgin sample are averaged out.

Atomic force microscope images show enhanced thickness ﬂuctuations in regions of phase coexistence, originating from the different lattice spacings of the distinct phases, leading to different layer thicknesses. However, no sharp contours could be detected.

Hydrogen diffusion can be observed by the lateral progression of the phase boundary. At pH2

6 2

ú û = 800 mbar and at 300 ù C, the YH3 front moves with an effective mobility of 5 10 cm /s. This is two orders of magnitude slower than the diffusion in polycrystalline ﬁlms. The reason for this difference may lie in the fast diffusion of hydrogen along grain boundaries which are absent in single crystalline ﬁlms.

Measuring the electrical resistance of the sample together with the x–ray diffraction curves, allow to relate the metal–insulator transition to the structural information. Starting with a pure

YH2 ﬁlm, the electrical resistance increases with the amount of the nucleated hydrogen rich γ–phase. The sample may be seen as a hydrogen tunable potentiometer. 8. SUMMARY

The intention of this thesis work is to understand the structural phase transitions within the Y–H system. Studies in this field are driven by the spectacular optical properties of thin, polycrystalline Y films. Conventional band structure calculations of YH3 based on bulk data fail to predict the electronic and optical phenomena observed in this material. Therefore it is essential to provide data on the crystal structure of YH3 in thin films. The assumption of bulk lattice parameters and symmetries for thin films is not necessarily correct. Due to epitaxial stress the arrangement of atoms may differ from the structure found in bulk or powder samples.

Several diffraction techniques have been successfully employed to study epitaxially grown, single crystalline yttrium and yttrium hydride films. Special attention has been paid to the crystal structure of YH3 and to the epitaxial relation between the Y film and the Nb/Al2O3 buffer system. Surprisingly, neither deviation from the bulk structure nor an influence from the niobium buffer could be found.

Though the niobium buffer exhibits an uniaxial structural anisotropy, yttrium ﬁlms evaporated on it crystallize with a perfect sixfold symmetry. During the uptake of hydrogen from the gas phase stable yttrium hydrides form. The two hydrides show distinct lattice parameters. They do not vary with the surrounding hydrogen pressure, leading to straight lines as solubility

isotherms. While the pure metal crystallizes in a hcp structure with lattice constants of a = 3.63

ü ü

0.01 A˚ and c = 5.57 0.005 A˚ YH2 forms a CaF2 type fcc lattice with a unit cell size of 5.21 ü 0.005 A˚ in which the hydrogen atoms occupy all available tetrahedral interstitial sites. YH3

again crystallizes in a hexagonal crystal in which the metal atoms form a hcp lattice with lattice ü constants of a = 3.65 ü 0.01 A˚ and c = 6.62 0.005 A.˚ By neutron diffraction the arrangement

of the deuterium atoms within YD3 could be detected. All these measurements confirm the P3c1¯ structure which has been found for powder samples. Neither the epitaxial relation to the buffer layer nor its non isotropic response upon hydrogen loading influences the Y film.

In contrast to bulk Y crystals which decompose during hydrogen uptake, in c–axis grown thin ﬁlms maintain their structural coherence. The phase transition between the cubic dihydride and

107 108 Chapter 8. Summary

the hexagonal trihydride phase is completely reversible without any loss of crystalline quality. This involves especially the rearrangement of the stacking sequence of the host metal.

Apart from delivering detailed structural information, which are a snapshot in space and time, diffraction techniques can be employed to study the domain structure and the dynamics of the system. By means of x–ray diffraction topography the phase formation and the hydrogen diffusion could be visualized. Exposed to a hydrogen atmosphere, the nucleation of the hydride phases starts at arbitrary places in the sample. The typical domain size is about 1 micron. The motion of the diffusion front in single crystalline ﬁlms turned out to be much slower than in polycrystalline ﬁlms.

Additionally, neutron scattering can be used to determine the hydrogen concentration within the sample. Exploiting the different scattering lengths of the different hydrogen isotopes, the angle of total reﬂection as well as the intensities of the structural Bragg reﬂections are sensitive to the hydrogen content. Within the γ–phase the H/Y ratio is close to 3, indicating a stoichometric trihydride. Neutron scattering also allows to verify the isotope exchange within the sample.

In order to study the crystal structure of yttrium and its hydrides in thin films, it is nessecary to prepare samples of high structural quality. Molecular beam epitaxy is a powerful tool to evaporate chemically pure metallic layers. Due to the high hydrogen affinity of Y, it is especially difficult to grow hydrogen free samples. The samples used in this thesis exhibit an initial hydrogen contamination of about two atomoc percent. By the choice of suitable buffer systems and growth parameters single crystalline films may be achieved. For the investigation of thin film metal–hydride systems a catalytic Pd layer on top of the sample is advantageous to purify the hydrogen gas and to enhance the hydrogen uptake. As the natural yttrium oxide layer is impermeable with respect to hydrogen, partially palladium covered films may be employed to study the lateral diffusion of hydrogen.

Most scattering experiments have been carried out in situ, i. e. in hydrogen atmosphere. There- fore it was necessary to build or to modify vacuum chambers which allow the control of the

temperature between room temperature and 500 ý C as well as of the hydrogen pressure up to 1000 mbar. Essential requirements of x–ray and neutron experiments are of course windows which do not absorb the probing radiation signiﬁcantly. All materials used in the vacuum chambers had to be chosen according to the requirements mentioned above. Especially hydrogen embrittlement had to be avoided.

The major challenge in applying diffraction techniques is the low scattering volume of the sam- Chapter 8. Summary 109

ples. Only the development of third generation synchrotron sources made techniques like XDT available for thin ﬁlms. The topographic images presented in this work demonstrate the possibility to apply XDT to investigate the structure and the dynamics of structural phase transitions in metallic ﬁlms in the thickness range of 100 nm.

Apart from the studies presented in this work, lots of other techniques have been used to study the hydrogen–yttrium system, especially in thin ﬁlms. The attention paid to this systems is caused by the unique physical properties of the rare earth hydrides, of which the Y–H system serves as a model, as well as by possible technological applications. The optical properties may be used to build windows with tuneable optical transparency, to build large area displays or may be employed in optical instruments. Also the electronic properties of thin yttrium hydride ﬁlms may be used. The metal–insulator transition within the Y–H system may be used to change the exchange coupling reversibly by hydrogen loading. In contrast to the hydrogen tuneable exchange coupling in Fe/V or in Fe/Nb multilayers, where the non–magnetic spacer material

stays metallic upon hydrogen loading, YH3 is insulating. Thus the insulating state of YH3 additionaly opens the possibility of the hydrogen switchable tunneling magnetoresistence effect. Together with lithographic techniques it seems also possible to build laterally structured yttrium and yttrium hydride ﬁlms on the nanometer scale. Therefore yttrium hydrides may be used as switchable elements in electronic devices. Future work will involve metallic multilayers like Ho/Y or Fe/Y to study these effects.

Within this thesis, single crystalline YH2 and YH3 films have been prepared and the reversibility of the structural phase transition accompanying the electrical transition has been proven. During this transition the structural coherence remains maintained. As regards the crystal structure, no difference between thin epitaxially grown films and bulk samples could be found. This thesis provides essential crystallographic data as well as information about the morphology and the dynamics in the rapidly growing field of the research on rare–earth hydrides. 110 Chapter 8. Summary 9. ZUSAMMENFASSUNG

9.1. Das Yttrium–Wasserstoff System

Seit Grahams im Jahre 1866 die Loslichk¨ eit von Wasserstoff in Palladium entdeckte sind Metall–Wasserstoff Systeme Gegenstand der Forschung. Neben Palladium gibt es viele Metalle welche die Eigenschaft besitzen Wasserstoff zu absorbieren. In dem Wirtsmetall ist das H2 Mo- lekul¨ dissoziiert und die Wasserstoffatome nehmen Zwischengitterplatze¨ ein. Der Wasserstoff ist dabei mehr als eine Verunreinigung. Er vermag die mechanischen, elektronischen, magnetischen und optischen Eigenschaften drastisch zu verandern.¨ Die Anwesenheit von Wasserstoff beeinﬂußt weiterhin die Kristallstruktur des Systems, was oft zu komplexen Phasendiagram- men fuhrt.¨ Bedingt durch die hohe Diffusionsgeschwindigkeit des leichten Wasserstoffatoms, ﬁnden strukturelle Phasenumwandlungen oft bei Temperaturen statt, die weit niedriger sind als in gewohnlichen¨ metallischen Verbindungen.

In der Vergangenheit standen Metallhydridspeicher im Mittelpunkt der Forschung. Insbeson- dere im Bereich der alternativen Energien wurden hierbei Fortschritte erzielt. Technologische Entwicklungen im Bereich der Dunnschichttechnik¨ sowie im Bereich der Ultrahochvakuum- technik verstarkten¨ das Interesse an dunnen¨ Metall–Wasserstoffschichten. Dabei wurden au- ßergewohnliche¨ und neue strukturelle und funktionelle Eigenschaften entdeckt. Herausragende Beispiele sind die Steuerung der magnetischen Kopplung in Fe/Nb und Fe/V Uber¨ gittern und die extreme elastische Dehnung in Mo/V Uber¨ gittern. Wasserstoff kann daruber¨ hinaus auch als Sonde verwandt werden, um mechanische Eigenschaften von dunnen¨ Metallschichten zu studieren. Anhand der wasserstoffbedingten Gitterdehnung in dunnen¨ Nb Filmen konnte so z. B. die außerordentliche Haftung von Nb auf Saphir nachgewiesen und untersucht werden.

Unter den verschiedenen Wasserstoff–Metall Systemen zeichnet sich das System Wasserstoff– Yttrium (H–Y) durch die hochste¨ Loslichk¨ eitsenthalpie aus. Das heißt, Wasserstoff zieht Yttri- um allen anderen Metallen als Wirtsmetall vor. Zusammen mit seinen chemischen Verwandten,

111 112 Chapter 9. Zusammenfassung

den schweren Seltenen Erden, halt¨ Yttrium auch den Rekord bezuglich¨ der großtm¨ oglichen¨ Wasserstoffkonzentration unter den reinen Metallen. In Sattigung¨ betragt¨ das maximale Wasserstoff–Yttrium Verhaltnis¨ 3:1. Abhangig¨ von der Wasserstoffkonzentration besitzt das H– Y System drei strukturelle Phasen. Die Wasserstoffarme α–Phase ist bis zu einer Konzentration von 20 Atomprozent Wasserstoff stabil. In dieser Phase besetzen die Wasserstoffatome Zwi- schengitterplatze¨ mit tetragonaler Symmetrie im Gitter des in hcp Struktur kristallisierenden Yttriums. Erhoht¨ man die Wasserstoffkonzentration uber¨ die kritische Konzentration hinaus, so bildet sich Ausscheidungen der β–Phase YH2. YH2 kristallisiert in der kubischen CaF2– Struktur. Dabei bilden die Y Atome ein kubisch ﬂachenzentriertes¨ Gitter, die Wasserstoffatome

nehmen die Zwischengitterplatze¨ mit tetragonaler Symmetrie ein. Die β–Phase existiert im þ Konzentrationsbereich von YH1 þ 8 bis YH2 1. Bei noch hoheren¨ Wasserstoffkonzentrationen nu- kleiert die wasserstoffreiche γ–Phase. Beim Uber¨ gang von der β zur γ–Phase andert¨ sich erneut die Stapelfolge des Yttriums. Es ordnet wieder in der hcp Struktur. Innerhalb der γ–Phase nehmen die Wasserstoffatome ungewohnliche¨ Zwischengitterplatze¨ ein. Das hcp–Gitter bietet zwei verschiedene Arten von Zwischengitterplatzen¨ mit symmetrischer Anordnung der umgebenden Gitterplatze¨ an. Pro Gitterplatz gibt es zwei Zwischengitterplatze¨ mit tetragonaler Symmetrie

(T–Platze)¨ und einen mit oktaedrischer Symmetrie (O–Platze).¨ In YH3 sind die Platze¨ oktaedrischer Symmetrie zur Basalebene des hcp–Gitters hin verschoben. Eine zusatzliche¨ sinusformige¨ Modulation versetzt ein Drittel der O–Platze¨ oberhalb und ein Drittel unterhalb der Basalebe- ne. Somit verbleiben ein Drittel der O–Platze¨ in der Basalebene selbst. Bedingt durch die Umgruppierung der O–Platze¨ sind die T–Platze¨ ebenfalls leicht aus ihrer symmetrischen Posi- tion versetzt. Die so resultierende Kristallstruktur hat die Raumgruppe P3c1;¯ Prototyp dieser

Struktur ist HoD3. Die Große¨ der Mischungsluck¨ e zwischen der β– und der wasserstoffreichen γ–Phase ist immer noch Gegenstand aktueller Diskussion.

Die strukturellen Phasenuber¨ gange¨ werden von Anderungen¨ der Elektronenkonﬁguration ein- schließlich eines Metall–Isolatoruber¨ gangs in der wasserstoffreichen Trihydridphase begleitet. Besonders augenfallig¨ ist dabei der optische Uber¨ gang bei hohen Wasserstoffkonzentrationen

in dunnen¨ Yttriumschichten. Wahrend¨ Y und YH2 metallischen Charakter haben und sicht-

bares Licht reﬂektieren, ist YH3 optisch transparent. Unter geeigneten Bedingungen vollzieht sich dieser Uber¨ gang innerhalb von Sekundenbruchteilen, so daß sich dieser Vorgang fur¨ das menschliche Auge abrupt vollzieht. Die Reversibilitat¨ dieses Effekts macht ihn fur¨ technologische Anwendungen interessant.

Die Anderungen¨ der elektronischen Konﬁguration sind auch anhand des elektrischen Wider- stands zu verfolgen. In der α–Phase tritt der Wasserstoff zunachst¨ als Verunreinigung in Er- Chapter 9. Zusammenfassung 113 scheinung. Der elektrische Widerstand steigt mit steigender Konzentration bis zum Erreichen der Phasengrenze an. Oberhalb der kritischen Konzentration fallt¨ er dann mit steigender Was- serstoffkonzentration bis zum Erreichen der β–Phase. In der β–Phase betragt¨ der Widerstand nur noch ein funftel¨ seines ursprunglichen¨ Wertes. Vom Standpunkt des elektrischen Wider- standes ist YH2 somit das bessere Metall als das reine Yttrium. Die γ–Phase ist dagegen ein sehr schlechter elektrischer Leiter. Zwischen dem Valenzband und dem Leitungsband wurde eine Bandluck¨ e 1.8 eV gefunden. Trotzdem verhalt¨ sich YH3 nicht wie ein klassischer Halblei- ter. Bei gegebener Wasserstoffkonzentration zeigt der Widerstand ein logarithmisches Tempe- raturverhalten. Außerdem ist YH3 auch unterstochiometrisch,¨ also bei hoher Dotierung, noch transparent. Klassische Halbleiter wie Silizium oder Germanium sind bei gleicher Dotierung langst¨ metallisch.

Bis jetzt sind die optischen und elektronischen Eigenschaften des H–Y Systems nicht vollstandig¨ verstanden. Bandstrukturrechnungen, die auf der P3¯c1 Struktur basieren, ergeben keine Bandluck¨ e fur¨ YH3. Da das wasserstoffbedingte, optische Schalten bisher nur an dunnen¨ Yttriumschichten, nicht jedoch an Volumenproben beobachtet wurde, ist es denkbar, daß die optische Tranzparenz der YH3–Phase eine Dunnschichteigenschaft¨ ist. Ein wesentliches The- ma dieser Arbeit war somit die Frage nach der Kristallstruktur dunner¨ Yttriumhydridschichten und die Suche nach moglichen¨ Abweichungen von der Volumenstruktur.

9.2. Probenpraparation¨ und Experimentelle Methoden

Alle untersuchten Proben wurden mittels Molekularstrahlepitaxie (MBE) hergestellt. MBE ist eine Methode der physikalischen Dampfdeposition, bei der das aufzudampfende Materi- al thermisch verdampft und auf einem geeigneten Tragermaterial,¨ dem Substrat, abgeschieden wird. Hohe Reinheit der Ausgangsmaterialien sowie Ultrahochvakuumbedingungen in der Auf- dampfkammer sind unerlaßliche¨ Voraussetzungen fur¨ chemisch reine Proben. Der Abscheide- prozeß selbst laßt¨ sich uber¨ die Substrattemperatur und die Aufdampfrate steuern. Wahrend¨ des Wachstums lassen sich mit Hilfe eines Manometers und eines Massenspektrometers die Vakuumbedingungen einschließlich einer Restgasanalyse uberpr¨ ufen.¨ Die Kristallqualitat¨ der wachsenden Probe kann mittels Elektronenbeugung in situ, also wahrend¨ des Aufdampfpro- zeßes uberw¨ acht werden. 114 Chapter 9. Zusammenfassung

Die Yttriumﬁlme wurden auf Nb/Al203 Substraten aufgedampft. Niob wachst¨ epitaktisch auf

Al2O3. Es bildet eine einkristalline Unterlage und ermoglicht¨ so das epitaktische Wachstum von Yttrium, welches eindomanig¨ in der Nishiyama–Wassermann Orientierung auf dem Niob auffwachst.¨ Weiterhin dient das Niob als Barriere zum Saphir und verhindert so eine chemi- sche Reaktion zwischen dem Yttrium und dem Substrat. Niob selbst bildet keine Legierung mit Yttrium, so daß man das Yttrium, um eine hohe Kristallqualitat¨ zu erziehlen, bei hohen Tempe- raturen aufdampfen kann, ohne daß es zu chemischen Reaktionen oder zur Legierungsbildung kommt. Um die Proben vor Korrosion zu schutzen¨ und um die Wasserstoffaufnahme aus der Gasphase zu ermoglichen¨ wurden die Proben mit einer Palladiumschicht abgedeckt. Palladium vermag H2 Molekule¨ katalytisch zu spalten und den so entstehenden atomaren Wasserstoff zu adsorbieren. Die Palladiumdeckschicht wirkt somit zusatzlich¨ als Filter fur¨ den Wasserstoff.

Die Proben wurden zumeist mit Rontgen–¨ und Neutronenbeugung untersucht. Um die Mes- sungen in Wasserstoffatmosphare¨ durchfuhren¨ zu konnen¨ wurden mehrere Vakuumkammern gebaut bzw. umgebaut. Die Anforderungen an die Kammern waren hoch. Sie sollten wasser- stoffdicht sein, die Probentemperatur und der Wasserstoffdruck sollten regelbar sein. Keines der verwandten Materialien durfte unter Wasserstoffversprodung¨ leiden. Um die Beugungsver- suche durchzufuhren¨ mußten Fenster fur¨ die jeweilige Strahlung eingebaut werden, die einen moglichst¨ großen Winkelbereich abdecken sollten. Außerdem sollte optional die Moglichk¨ eit vorhanden sein, den elektrischen Widerstand der Probe zu messen. Um die Kammern an verschiedenen Diffraktometern einzusetzen mußten sie transportabel sein. Da an verschiedenen Diffraktometern verschiedene Streugeometrien realisiert wurden, mußte es außerdem moglich¨ sein, die Probe in verschiedenen Lagen einzubauen.

Die strukturellen Untersuchungen wurden im Wesentlichen mittels Rontgen–¨ und Neutronen- beugung durchgefurt.¨ Rontgenbeugung¨ basiert auf der elektromagnetischen Wechselwirkung der Rontgenstrahlung¨ mit den Elektronen des zu untersuchenden Materials. Sie ist somit ge- eignet die Kristallstruktur des Yttriums zu bestimmen und die strukturellen Phasenuber¨ gange¨ zu verfolgen. Da Wasserstoff nur ein Elektron pro Atom besitzt, ist die Wechselwirkung von Rontgenstrahlung¨ mit Wasserstoff sehr gering. Fur¨ Neutronen, welche uber¨ die starke Wechselwirkung an den Atomkernenpotentialen gestreut werden, ist dies anders. Wasserstoff und Deuterium besitzen jeweils einen relativ großen Wirkungsquerschnitt fur¨ die Neutronen- beugung. Die Tatsache, daß die Streulange¨ fur¨ beide Isotope verschiedene Vorzeichen hat, laßt¨ sich z. B. zur Bestimmung der Wasserstoffkonzentration uber¨ den Strukturfaktor bestimmen. Neben der Bragg–Beugung wurden auch Reﬂektivitatskurv¨ en zur Schichtdickenbestim- mung, und im Falle der Neutronen auch zur Bestimmung der Wasserstoffkonzentration genutzt. Chapter 9. Zusammenfassung 115

Die Rontgenbeugungse¨ xperimente wurden an verschiedenen Diffraktometern an der Ruhr– Universitat¨ in Bochum sowie an der europaischen¨ Synchrotronquelle (European Synchrotron Radiation Facility, ESRF) in Grenoble, Frankreich durchgefuhrt.¨ Die Neutronenbeugungsex- perimente erfolgten am europaischen¨ Hochﬂuß–Reaktor des Instituts Max von Laue – Paul Langevin in Grenoble sowie am Reaktor des Forschungszentrums in Julich.¨ Das kleine Streu- volumen und die damit verbundenen langen Zahlzeiten¨ stellten oft eine große Herausforderung dar. So sind die Messungen an der Imaging Beamline ID19 der ESRF die ersten Messungen an Phasenuber¨ gangen¨ in dunnen¨ metallischen Schichten uberhaupt.¨

9.3. Ergebnisse

Ausgehend von einkristallinen, epitaktisch auf Nb(110)/Al2O3 Substraten aufgedampften Yt- triumfilmen gelang es mittels Wasserstoffadsorption aus der Gasphase erstmals einkristalline Yttriumhydridfilme herzustellen. Bedingt durch die epitaktische Fehlanpassung zwischen Y und Nb und durch Wassertoffverunreinigungen wahrend¨ des Aufdampfens, weichen die atomaren Abstande¨ der unbeladenen Yttriumfilme leicht von den Literaturwerten fur¨ Volumenkristalle ab. So ist der Gitterparameter fur¨ die c–Achse um 0,3 Prozent auf 5,75 A˚ gedehnt, wohingegen der Gitterparameter der a–Achse um 0,5 Prozent auf 3,63 A˚ gestaucht ist.

Obwohl sich die Niob Pufferschicht durch eine uniaxiale strukturelle Asymmetrie auszeichnet, besitzt der Y Film die volle sechszahlige¨ Symmetrie des Volumenkristalls. In plane haben alle equivalenten Gitterebenen denselben Gitterparameter, unabhangig¨ davon, wie sie im Bezug zu dem Niobgitter orientiert sind.

Unter Wasserstoffbeladung dehnt sich der Y Film entlang der c–Achse innerhalb der α–Phase bis zum erreichen der Phasengrenze um bis zu 1,22 Prozent aus. Weiteres Beladen fuhrt¨ zur Nu-

kleation der β–Phase. Der Gitterparameter von YH2 betragt¨ dabei 5,21 A,˚ was einem c–Achsen Abstand von 3,01 A˚ entspricht. Dieser Phasenuber¨ gang beeintrachtigt¨ die Kristallqualitat¨ des Yttriumﬁlms. Die Halbwertsbreite der Rockingkurve, einem Maß fur¨ die mittlere Verkippung einzelner Kristalldomanen¨ untereinander, erhoht¨ sich um einen Faktor funf¨ bis sechs. Gleichzei- tig nimmt die maximale Intensitat¨ der gebeugten Rontgenstrahlung¨ um denselben Faktor ab. Die Halbwertsbreite des radialen scans, ein Maß fur¨ die Anzahl der koharent¨ streuenden Netzebe- nen, bleibt jedoch konstant. Somit bleibt auch die integrierte Streuintensitat¨ erhalten. Fuhrt¨ man dem System noch mehr Wasserstoff zu, so dehnt sich der Kristall weiter entlang der c–Achse aus. Die Anderung¨ des Gitterparameters erfolgt wiederum diskontinuierlich. Die γ–Phase be- 116 Chapter 9. Zusammenfassung

sitzt schließlich eine out of plane Gitterkonstane von 6,62 A.˚ Gegenuber¨ dem unbeladenen Git- ters ist dies eine Expansion von 15,5 Prozent. Beim Uber¨ gang von der β– zur γ–Phase erfolgt keine weitere Beeintrachtigung¨ der Kristallqualitat.¨ Daruberhinaus¨ ist dieser Phasenuber¨ gang unter Beibehaltung der vollen strukturellen Koharenz¨ vollig¨ reversibel. Bei einem Uber¨ gang von einer hexagonal dichtesten Kugelpackung zu einer kubisch dichtesten Kugelpackung, also beim Uber¨ gang der Stapelfolge ABABAB... zu ABCABC..., geht die hexagonale c–Achse in eine kubische (111)–Achse uber¨ . In diesem Fall ist die Beibehaltung der strukturellen Koarenz¨ nicht verwunderlich, da die Zuordnung eindeutig erfolgt. Das kubische Gitter verfugt¨ jedoch uber¨ 4 aqui¨ valente (111)–Achsen, die bei einem erneuten Phasenuber¨ gang jeweils zu einer neu- en c–Achse werden konnten.¨ Somit ware¨ zu erwarten, daß die Probe beim Uber¨ gang von der β– zur γ–Phase in vier Domanen¨ zerfallt.¨ Dies ist jedoch offensichtlich nicht der Fall. Yttrium Einkristalle verhalten sich jedoch wie erwartet. Die mit den Phasenuber¨ gangen¨ verbundenen Anderungen¨ der Stapelfolge in Verbindung mit der Volumenexpansion zerstoren¨ den Kristall- verband. Die Frage, ob in epitaktisch aufgedampften, einkristallinen dunnen¨ Yttriumfilmen die Anderung¨ der Stapelfolge unterdruckt¨ wird oder nicht, konnte ebenfalls mit Beugungsmetho- den beantwortet werden. Durch die Auswahl bestimmter, auf die Stapelfolge sensitiver Reflexe konnte gezeigt werden, daß sich auch in dunnen,¨ einkristallinen Filmen die Stapelfolge bei den Phasenuber¨ gangen andern.¨ Offensichtlich reicht die Haftung des Yttriums auf dem Niob aus, um diejenige der aqui¨ valenten (111)–Achsen auszuzeichnen, welche senkrecht zur Grenzflache¨ steht und somit mit dem geringsten Energieaufwand expandieren kann.

Die Modulation der Wasserstoffatome in der Basalebene konnte durch Neutonenbeugung in der Trihydridphase ermittelt werden. Aufgrund der hoheren¨ koharenten¨ Streulange¨ wurden diese Versuche an deuterierten Proben durchgefuhrt.¨ Die Modulation liegt ausschließlich in den [1120]¯ Richtungen. Sie macht sich durch zusatzliche¨ Reﬂexe bemerkbar, die einzig entlang

diesrer Richtungen auftreten. Diese Reﬂexe tauchen nur in der YD3–Phase auf und sind mit Rontgenbeugung¨ nicht sichtbar. Sie stammen also eindeutig von der Deuteriumordnung in der γ–Phase. Die Modulation ist kommensurabel mit dem Metallgitter und fuhrt¨ zu einer Verdrei- fachung der Einheitszelle. Die Amplitude der Modulation ist durch den Intensitatsk¨ ontrast zwi-

schen dem YH3 (0002) Reflex und dem YD3 (0002) Reflex bestimmbar. Durch die unterschiedliche Streulange¨ der verschiedenen Wasserstoffisotope reagiert der Strukturfaktor sehr empfind- lich auf den Isotopenaustausch. Dabei bestimmt die Lage der Wassetstoffatome bezuglich¨ der Yttriumebenen und die Wasserstoffkonzentration die Differenz der Strukturfaktoren. Das heißt, sobald es gelingt, die Wasserstoffkonzentration zu bestimmen, kann man uber¨ den Struktur- faktor die Kristallstruktur bestimmen. Andrererseits laßt¨ sich so die Wasserstoffkonzentration Chapter 9. Zusammenfassung 117

bestimmen, wenn man die Kristallstruktur kennt. Die gemessenen integrierten Intensitaten¨ der beiden Reﬂexe unterscheiden sich um 21,5 %. Modellrechnungen, die auf der P3¯c1 Struktur

basieren, ergeben ebendiesen Wert, wenn man eine Wasserstoffkonzentration von x = 2,98 ÿ 0,02 zu Grunde legt.

Zur Konzentrationsbestimmung in der Trihydridphase kann ebenfalls die Wechselwirkung der Probe mit Neutronen benutzt werden. Im Kleinwinkelbereich bestimmt die mittlere Streulangendichte¨ die Lage der Totalreﬂexionskante. Mit den bekannten Werten fur¨ die Streulangen¨ von Yttrium und Deuterium ist somit die Position des kritischen Winkels ein di- rektes Maß fur¨ die Deuteriumkonzentration. Dabei spielt die Kristallstruktur keine Rolle, so daß mit dieser Information die angenommene Kristallstruktur uberpr¨ uft¨ werden kann. Die so

ermittelte Wasserstoffkonzentration liegt bei x = 2,96 ÿ 0,03.

Alle hier prasentierten¨ Messungen zur Kristallstruktur sind selbstkonsistent. Es sind keinerlei

Abweichung zur P3c1¯ Struktur aufgetaucht, derjenigen Struktur in der YH3 Volumenproben kristallisieren. Offenbar gibt es keine abweichende Kristallstruktur gegenuber¨ dunnen¨ epitaktischen Schichten. Somit ist die beobachtete Bandluck¨ e und die mit ihr verbundene optische Transparenz in der γ–Phase nicht auf eine Symmetriebrechung im Kristallgitter zuruckzuf¨ uhren.¨

Fur¨ die technologische Anwendung wasserstoffschaltbarer Yttriumschichten muß die Schalt- zeit optimiert werden, d. h. neben dem Verstandniß¨ des Prozeßes auf atomarer Ebene ist die geschwingidkeitsbestimmende, makroskopische Struktur des Systems von besonderer Bedeu- tung. Das Gefuge¨ des Materials, die Domanenstruktur¨ , sowie die Kinetik der Keimbildung und die damit verbundene Mobilitat¨ der Phasengrenze wurde mit Hilfe der Rontentopographie¨ studiert. Rontgentopographie¨ ist ein bildgebendes Verfahren, daß auf Rontgenbeugung¨ basiert. Dabei erhalt¨ man die Ortsauflosung¨ uber¨ das homogene Ausleuchten der Probe mit einem ausgedehnten, monochromatischen Strahl geringer Divergenz. Die reflektierte Strahlung wird dann mit einem photographischen Film, der als offener Detektor wirkt, aufgenommen. Das Auflosungsv¨ ermogen¨ dieser Methode ist im Wesentlichen durch die Divergenz des Strahls und die Kornung¨ des Films gegeben. Die topographischen Aufnahmen des Yttriumfilms zei- gen großflachige¨ Strukturen mit sanften Konturen und Kontrastwechseln. Dies deutet auf ein koharentes¨ Kristallgefuge¨ hin, in dem die einzelnen Domanen¨ zusammenhangende¨ Netzebe- nen besitzen und sich die Fehlorientierung stetig andert.¨ Die Große¨ der einzelnen Domanen¨ liegt dabei unterhalb der Auflosung¨ des photographischen Films von ca. einem Mikrometer. Zusammen mit den gemessenen in–plane Koharenzl¨ angen¨ von typischerweise 150 A˚ laßt¨ sich eine mittlere Domanengr¨ oße¨ von 15 bis 1000 nm abschatzen.¨ Nach der ersten Wasserstoff- 118 Chapter 9. Zusammenfassung

beladung erscheint das Topogramm einformig¨ grau. Die vorher beobachteten Strukturen sind zerstort.¨ Wahrend¨ der Wasserstoffaufnahme bilden sich Keime der Hydridphase an statistisch verteilten Platzen¨ unterhalb der Pd Deckschicht. Unter weiterer Wasserstoffzufuhr bilden sich neue Keime, ein Wachstum der vorhandenen konnte nicht beobachtet werden. Die topographischen Aufnahmen illustrieren dabei eindrucksvoll das unterschiedliche Verhalten des diskreten Phasenuber¨ gangs des Yttriumfilms und des kontinuierlichen Phasenuber¨ gangs des Niobfilms. Wahrend¨ die diskreten Gitterparameter der verschiedenen Phasen im Yttrium in raumlich¨ ge- trennten Beugungsreflexen auf dem photographischen Film resultieren, fuhrt¨ der kontinuierli- che Konzentrationsgradient im Nb zu einem zusammenhangenden,¨ gebogenen Reflex. Bedingt durch die diskreten Phasenuber¨ gange¨ des Y–H Systems erfolgt das laterale Fortschreiten der Wasserstfffront uber¨ heterogene Keimbildung. Innerhalb der wasserstoffarmeren¨ Phase mussen¨ entlang der Front neue, wasserstoffreiche Domanen¨ entstehen um in einem Beladungsexpe- riment mehr Wassertoff aufzunehmen. Diese heterogene Keimbildung ist in einkristallinen, epitaktischen Schichten der geschwindigkeitsbestimmende Schritt. In polikristallinen Filmen ist die Mobilitat¨ der Phasengrenze um zwei Großenordnungen¨ schneller. In ihnen sind die zu schaltenden Domanen¨ deutlich kleiner als in einkristllienen Schichten. Dazu kommt im Fall polikristalliner Schichten die verstarkte¨ Wasserstoffdiffusion entlang der Korngrenzen. Somit sind einkristalline Schichten ideale Modellsysteme zum Studium der Kristallstruktur, sie sind jedoch aufgrund ihres aufwendigen Praparationsv¨ erfahrens und ihrer langsameren Kinetik po- lykristallinen Filmen unterlegen.

Die Messungen an Yttriumhydridschichten demonstrieren erstmalig die Moglichk¨ eit die Struk- tur dunner¨ Filme sowie die Kinetik von strukturellen Phasenumwandlungen in dunnen¨ Schich- ten mit Hilfe der Rontgentopographie¨ zu untersuchen. Bedingt durch das geringe Streuvolu- men der Schichten und die relativ schlechte Kristallordnung war Rontgentopographie¨ bisher im Bereich dunner¨ Schichten im Dickenbereich von wenigen 100 A˚ auf Halbleiterschichten be- schrankt.¨ Erst die hohe Brillianz moderner Synchrotronquellen macht dieses Forschungsgebiet zuganglich.¨

Neben den Untersuchungen auf dem Gebiet der Kristallstruktur, die in dieser Arbeit prasentiert¨ wurden, gibt es viele andere aktuelle Arbeiten im Bereich der Dunnschichthydride.¨ Die Auf- merksamkeit, die diesem Gebiet zu Teil wird liegt an den außergewohnlichen¨ physikalischen Ei- genschaften und deren technischen Anwendungsmoglichk¨ eiten. So bieten sich Yttriumhydride aufgrund ihrer optischen Eigenschaften als Fenster variabler Transparenz oder als großﬂachige¨ Anzeigetafeln an. Der reversibel regelbare Metall–Isolator Uber¨ gang ermoglicht¨ ihren Einsatz im Bereich elektronischer Bauelemente. Zukunftige¨ Arbeiten auf diesem Gebiet werden metal- Chapter 9. Zusammenfassung 119 lische Multilagen wie Ho/Y oder Fe/Y einbeziehen. Auch werden lithographische Techniken dazu Beitragen, laterale Nanostrukturierung an Yttriumhydridsystemen vorzunehmen.

Diese Arbeit hat gezeigt, daß es moglich¨ ist, mittels Wasserstoffbeladung aus der Gasphase einkristalline YH2 und YH3 Schichten zu praparieren¨ und ohne Verlust der Kristallqualitat¨ reversi- blel zwischen beiden Phasen zu schalten. Die Kristallstruktur selbst zeigt keine Abweichungen von der bekannten Struktur von Volumenproben. Sie hat weiterhin die Moglichk¨ eit gezeigt, diese Proben mittels verschiedener Beugungsmethoden zerstorungsfrei¨ zu untersuchen. Sie hat somit einen nicht unwesentlichen Beitrag zum Verstandniss¨ dunner¨ Yttriumhydridschichten ge- leistet. 120 Chapter 9. Zusammenfassung LIST OF FIGURES

2.1 One–dimensional energy curve ...... 7

2.2 The chemical potential ...... 10

2.3 The excess enthalpy ...... 11

2.4 Schematic p–T diagram ...... 12

2.5 Nb-H phase diagram ...... 13

3.1 The Y–H phase diagram ...... 15

3.2 The crystal structure of YH3 ...... 18

3.3 The electrical and optical properties of YHx ...... 21

3.4 Schematic representation of the density of states of Y, YH2, and YH3...... 23

3.5 Hybridisation of the Y-4d3z2 r2 -orbital with the H–1s orbital ...... 25

4.1 The scattering triangle ...... 28

4.2 The Ewald–Sphere ...... 32

4.3 Graphic representation of the Laue function ...... 33

4.4 Scattering geometries in reciprocal space ...... 34

4.5 Principle of x–ray diffraction topography (XDT) ...... 35

4.6 XDT image of a crystal consisting of two different phases ...... 36

4.7 Principle of grazing incident x–ray diffraction (GIXS) ...... 38

4.8 The Parratt–formalism ...... 39

121 122 List of Figures

4.9 Model x–ray reﬂectivity curves ...... 41

4.10 RHEED scattering geometry ...... 43

4.11 Inﬂuence of the surface roughness on the RHEED image ...... 44

4.12 Principle of LEED measurements ...... 45

4.13 High-resolution X-ray diffractometer in Bochum ...... 47

4.14 Surface x-ray diffractometer in Bochum ...... 48

4.15 The imaging beamline ID19 of the ESRF ...... 49

4.16 The hydrogen chamber ...... 50

4.17 The 4–point-method to measure the electrical resistance ...... 51

4.18 The neutron reﬂectometer ADAM at the ILL ...... 52

4.19 Principle of a three axes spectrometer ...... 53

5.1 The MBE machine ...... 56

5.2 Surface processes during ﬁlm growth ...... 58

5.3 Sample architecture ...... 59

5.4 RHEED image of Al2O3 ...... 60

5.5 The epitaxial relations between α–Al2O3 and Nb ...... 61

5.6 RHEED image of the Nb buffer ...... 62

5.7 Epitaxial relation between Y(0001) and Nb (110) ...... 63

5.8 LEED image of the Y layer ...... 63

5.9 RHEED image of the Y layer ...... 64

5.10 TEM image of the cross section of the Nb/Y interface ...... 65

5.11 AFM image of the sample surface ...... 65

6.1 Small angle reﬂectivity scan ...... 68 List of Figures 123

6.2 The Y(0002) reﬂection ...... 69

6.3 360 ¡ in–plane rocking scans of Y and Nb ...... 70

6.4 In–pane radial scans ...... 71

6.5 Radial scans of the Y(0002) reﬂection within the α–phase ...... 73

6.6 Reversibility 1: Scans of the YH2 (111) reﬂection ...... 74

6.7 Reversibility 2: Scans of the YH3 (0002) reﬂection ...... 75

6.8 Radial scans during the β–γ transition ...... 76

6.9 In–plane radial scans during hydrogen loading ...... 77

6.10 Neutron reﬂectivity curves ...... 79

6.11 Isotope exchange ...... 81

6.12 Reciprocal lattice of the K–L plane ...... 84

6.13 Scans along (01L) of all three phases ...... 85

6.14 Deuterium modulation along (H00) ...... 86

7.1 Topographic image of the virgin sample ...... 90

7.2 Topographic images of the Nb layer ...... 91

7.3 Details of the topographic image of the Nb layer ...... 92

7.4 Topographic images of the Y layer ...... 93

7.5 Sample design used in XDT experiments ...... 93

7.6 XDT during H–loading ...... 95

7.7 XDT during dehydrogenation ...... 96

7.8 Motion of the YH3 front ...... 99

7.9 Precipitation of the γ–phase ...... 100

7.10 Photography of the partially hydrogenated sample ...... 102 124 List of Figures

7.11 AFM image of the partially hydrogenated sample ...... 102

7.12 Electrical resistance during hydrogenation ...... 104

7.13 Fractional scattering volume versus electrical resistance ...... 105

7.14 Model of two parallel resistors ...... 105 BIBLIOGRAPHY

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¢ Reversible loading of epitaxial Y (00.1) ﬁlms with hydrogen A. Remhof, G. Song, K. Theis-Brohl,¨ and H. Zabel, Physical Reviev B 56, R2897, 1997.

¢ Anisotropy of hydrogen induced lattice expansion in epitaxial metal ﬁlms G. Song, A. Remhof, K. Theis-Brohl,¨ and H. Zabel, ECASIA 97, ed. I. Olefjord, I. Ny- borg, D. Briggs, John Wiley & Sons, p.635, 1997.

¢ Extraordinary adhesion of niobium on sapphire substrates G. Song, A. Remhof, K. Theis-Brohl,¨ and H. Zabel, Physical Review Letters 79, 5062, 1997.

¢ Hydrogen and deuterium in epitaxial Y(0001) ﬁlms: Structural properties and isotope exchange A. Remhof, G. Song, Ch. Sutter, A. Schreyer, R. Siebrecht, H. Zabel, F. Guthof¨ f, and J. Windgasse, Physical Reviev B 59, 6689, 1999.

¢ Hydrogen in thin epitaxial metal ﬁlms and superlattices: Structure, magnetism, and transport A. Remhof, D. Labergerie, G. Song, Ch. Sutter, K. Theis-Brohl,¨ H. Zabel and B. Hjrvars- son, J. Magnetism and Magnetic Materials, 198-199 (1-3), 264, 1999.

Danksagung

Mein Dank gilt an erster Stelle Herrn Prof. Dr. Hartmut Zabel fur¨ die interessante Aufgaben- stellung. Seine Offenheit und seine stete Gesprachsbereitschaft¨ haben wesentlich zum Gelingen dieser Arbeit beigetragen. Dank dem von ihm entgegengebrachten Vertrauen und der damit verbundenen Freiheit, hatte ich das Privileg viele Arbeiten in großer Selbstandigk¨ eit ausfuhren¨ zu konnen.¨

Den Mitgliedern der Wasserstoffgruppe, Herrn Arnold Abromeit, Herrn Michael Hubener¨ , Frau Dr. Danielle Labergerie, Herrn Gang Song und Herrn Dr. Christoph Sutter, gilt mein besonderer Dank fur¨ die Unterstutzung¨ bei der Durchfuhrung¨ vieler Experimente, insbesondere am ESRF sowie am ILL. Ohne ihren Einsatz und ihre kritischen Anmerkungen waren¨ viele Ergebnisse nicht erzielt worden.

Insbesondere mochte¨ ich mich bei Herrn Dr. Patrick Bodeck¨ er, Herrn Dr. Thomas Koll, Herrn Jur¨ gen Podschwadeck sowie bei Frau Dr. Katharina Theis–Brohl¨ fur¨ die Einweisung in die MBE Anlage sowie die technische Unterstutzung¨ bei der Probenpraparation¨ bedanken.

Herrn Dr. Thomas Koll, Herrn Dr. Peter Sonntag und Herrn Dr. Christoph Sutter danke ich fur¨ die Einfuhrung¨ in die Geheimnisse der Rontgenbeugung.¨

Herrn Dr. Jur¨ gen Hartwig,¨ Herrn Michael Hubener¨ , Frau Dr. Danielle Labergerie und Herrn Andreas Walter danke ich fur¨ die sorgfaltige¨ Durchsicht des Manuskripts.

Fur¨ die kompetente technische Unterstutzung¨ bin ich insbesondere Frau Sabine Erd–Bohm,¨ Herrn Peter Stauche, Herrn Jur¨ gen Podschwadeck und den Mitarbeitern der Feinmechanikw- erkstadt zu Dank verpﬂichtet.

Im Kampf mit der Burokratie¨ ware¨ ich ohne die Hilfe von Frau Ingrid Bickmann und von Frau Christine Kramer¨ oft unterlegen.

Mein Dank gilt auch Herrn Cristoph Gerharts, Herrn Olav Hellwig und Herrn Gang Song, die es stets verstanden in unserem gemeinsamen Buro¨ ein angenehmes und streßfreies Klima zu schaffen. Allen anderen Mitarbeitern des Lehrstuhls danke ich fur¨ das herzliche und stets konstruktive Arbeitsumfeld.

Viele wichtige Experimente wurden extern an Großforschungseinrichtungen durchgefuhrt.¨ Fur¨ die ausgezeichnete Unterstutzung¨ und Betreuung ’vor Ort’ mochte¨ ich mich bei Herrn Ralf Siebrecht und Herrn Dr. Andreas Schreyer (ILL Grenoble), Herrn Dr. Friedrich Guthof¨ f (FZ Julich)¨ sowie bei Herrn Dr. Jur¨ gen Hartwig¨ (ESRF Grenoble) bedanken.

Den Mitgliedern des TMR–networks ’Metal-hydride ﬁlms with switchable physical properties’, insbesondere Herrn Prof. Dr. Ronald Griessen und Herrn Dr. Bjor¨ gvin Hjorv¨ arsson danke ich fur¨ viele anregende Diskussionen.

Diese Arbeit wurde vom Bundesministerium fur¨ Bildung und Forschung im Rahmen der Pro- jekte ZA4BC1 und ZA4BC2 sowie durch das EU–TMR Projekt ’Metal-hydride ﬁlms with switchable physical properties’ (ERB FMRX–CT98–187) gefordert.¨

Abschließend mochte¨ ich mich herzlich bei meinen Eltern dafur¨ bedanken, daß sie mir das Studium der Physik und die Doktorarbeit ermoglicht¨ haben. Lebenslauf

Name Arndt Remhof Geburtsdatum 17.03.1969 Geburtsort Bochum Familienstand ledig

1975 - 1979 Besuch der Gemeinschaftsgrundschule Oberwinzerfeld in Hattingen 1979 - 1985 Besuch der Hugo–Schulz Realschule in Bochum 1985 - 1988 Besuch der Goethe Schule in Bochum Mai 1988 Abitur

1988 - 1990 Zivildienst

1990 - 1992 Studium der Physik an der Ruhr-Universitat¨ Bochum Oktober 1992 Diplom-Vorprufung¨ 1993 - 1994 Jahresstipendium fur¨ die University of Kent in Canterbury, Großbritannien im Rahmen des European mobility schemes for physics students 1994 - 1995 Studium der Physik an der Ruhr-Universitat¨ Bochum Juni 1995 Diplom Facherpr¨ ufung¨ 1995 - 1996 Diplomarbeit uber¨ Neutronen– und Rontgenstreuung¨ an Ideal– kristallen im Ultraschallfeld am Institut Laue–Langevin in Grenoble, Frankreich bei Prof. Dr. Andreas Magerl Marz¨ 1996 Studienabschluß Diplom seit 1996 Wissenschaftlicher Mitarbeiter am Institut fur¨ Experimentalphysik/ Festkorperphysik¨ bei Prof. Dr. Hartmut Zabel. Sommer 1999 Gastaufenthalt an der Universidade Sao˜ Francisco, Itatiba (Sao˜ Paulo), Brasilien