Studies of local order in apparently disordered hydrides of Laves phases YFe2Dx, YMn2Dx, ZrV2Dx and of La(Ni4.5Sn0.5)D3.85

Thesis

Reference

Studies of local order in apparently disordered hydrides of Laves phases YFe2Dx, YMn2Dx, ZrV2Dx and of La(Ni4.5Sn0.5)D3.85

ROPKA, Joanna

Abstract

Le sujet principal de la thèse présentée est une étude de l'ordre locale de l'hydrogène (deutérium) dans les phases de Laves sélectionnées: YFe2Dx, YMn2Dx, ZrV2Dx et un composant de AB5 type: LaNi4.5Sn0.5Dx. La thèse se compose de trois parties:

l'Introduction, la Méthodologie et les Composants investigués. La première partie définie les différents aspects de la thèse. Dans la partie Méthodologie, il y a une description de toutes les méthodes et techniques utilisées, en commenant par la préparation des échantillons et en terminant par l'analyse des données. Enfin, les résultats et la discussion ont été mis dans la partie Composants investigués.

ROPKA, Joanna. Studies of local order in apparently disordered hydrides of Laves phases YFe2Dx, YMn2Dx, ZrV2Dx and of La(Ni4.5Sn0.5)D3.85. Thèse de doctorat : Univ. Genève, 2011, no. Sc. 4349

URN : urn:nbn:ch:unige-220830

DOI : 10.13097/archive-ouverte/unige:22083

Available at:

http://archive-ouverte.unige.ch/unige:22083

Studies of local order

in apparently disordered hydrides of Laves phases YFe ₂ D _x , YMn ₂ D _x , ZrV ₂ D _x

and of La(Ni _4.5 Sn _0.5 )D _3.85

TH`ESE

Pr´esent´ee `a la Facult´e des sciences de l’Universit´e de Gen`eve pour obtenir le grade de Docteur `es sciences, mention cristallographie

par Joanna Ropka

de

Cracovie (Pologne)

Th`ese N<sup>◦</sup> 4349 Gen`eve 2011

I owe my deepest gratitude to Dr Radovan ˇCern´y who was incessantly helpful and offered invaluable assistance, support and guidance.

I am grateful to Dr Val´erie Paul-Boncour for conversations that clar- ified my understanding of Laves phase hydrides and to Prof. Dr Reinard Neder for introduction to PDF analysis.

I also would like to thank the staff of the Laboratory of Crystallogra- phy, without whose knowledge and assistance the experimental part of this study would not have been successful.

A few samples of alloys and hydrides were provided by Dr Val´erie Paul-Boncour (CNRS, Thies) and Dr R. C. Bowman Jr (Caltech, Pasadena). I appreciate their support.

Last but not least, I would like to thank my family members, especially my husband Micha l, for supporting and encouraging me to pursue this degree.

R´ esum´ e

Le sujet principal de la th`ese pr´esent´ee est une ´etude de l’ordre locale de l’hydrog`ene (deut´erium) dans les phases de Laves s´electionn´ees:

YFe₂D_x, YMn₂D_x, ZrV₂D_xet un composant de AB₅type: LaNi_4.5Sn_0.5D_x. La th`ese se compose de trois parties: l’Introduction, la M´ethodologie et lesComposants investigu´es. La premi`ere partie d´efinie les diff´erents aspects de la th`ese.

Dans la partie M´ethodologie, il y a une description de toutes les m´ethodes et techniques utilis´ees, en commenant par la pr´eparation des ´echantillons et en terminant par l’analyse des donn´ees. Enfin, les r´esultats et la discussion ont ´et´e mis dans la partie Composants investigu´es.

Il est g´en´eralement connu que de petits changements de structure cristalline peut influeer fortement sur les propri´et´es physiques ou chim- iques - un bon exemple est l’acier dont les propri´et´es sont d´etermin´ees par l’introduction d’unee tr`es petite quantit´e de carbone au r´eseau de fer. ´Evidemment, la pr´esence d’hydrog`ene dans la structure cristalline a un effet sur les hydrures cr´e´es. Il passe soit par des phases dites ”or- donn´ees” dans lesquelles des positions des atomes d’hydrog`ene sont enti`erement occup´ees, ou ”d´esordonn´ees” qui contient des sites par- tiellement occup´es. Pour les compos´es ´etudi´es dans ce projet, la quan- tit´e particulaire de l’hydrog`ene la phase devient ordonn´ee (au-dessous de la ”temp´erature d’ordre” T_OD) ou d´esordonn´ee (au-dessus de la T_OD). Il faut souligner que la transformation entre ces deux phases

temp´erature ´elev´ee (apparemment d´esordonn´ee).

En outre, la phase de Laves et les structures AB₅ sont g´en´eralement connus et tr`es bien d´ecrits. Leur g´eom´etrie simple facilite l’analyse de l’arrangement de l’hydrog`ene et permet de trouver la relation (si elle existe) entre le m´etal et les atomes d’hydrog`ene.

Malheureusement, l’hydrog`ene n’est pas d´etect´e par les rayons X. Les mesures neutroniques donnent un bruit de fond ´elev´e (en raison de significative diffusion incoh´erente). Dans le contexte de cette th`ese, l’hydrog`ene a ´et´e remplac´e par le deut´erium - l’isotope de l’hydrog`ene.

Il est g´en´eralement admis que le deut´erium tient la m`eme relation structurale que l’hydrog`ene (`a l’exception de cas rares), tout en ´etant plus pratique pour la mesure neutronique (plus petit signal de la dif- fusion incoh´erente). Par cons´equent, tous les ´echantillons ont ´et´e pr´epar´es comme deuterides au lieu d’hydrures.

Les r´esultats des mesures de rayons X (XRD) et de diffraction de neutrons (NPD) des ´echantillons s´electionn´ees sont des diagrammes de poudre qui montrent un bruit de fond ondul´e. Ce ph´enom`ene peut

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etre reconnu comme ce qu’on appelle ”diffusion diffuse” qui indique l’existence de l’ordre locale dans les phases d´esordonn ´etudi´ees. Les informations cach´ees dans le fond ont ´et´e examin´e grce `a l’analyse de Fonction de distribution des pairs (PDF). Cette m´ethode a ´et´e utilis´ee pendant des ann´ees pour les liquides et les mat´eriaux en verre.

R´ecemment, le d´eveloppement de techniques de diffraction XRD and NPD permet d’appliquer l’analyse PDF pour les ´echantillons de poudre.

Entre toutes les phases de Laves, trois groupes de deuterides ont ´et´e choisis: YFe₂D_x (x = 1.2, 1.9, 2.6, 4.2), YMn₂D_x (x=2.0, 3.4, 4.5) et ZrV₂D_x (x=2.8, 4.9). Ces compos´es r´ev`elent de tr`es int´eressantes propri´et´es structurales et magn´etiques. La d´ecouverte de l’ordre local de deut´erium peut compl´eter la description de leurs structures.

Le fait que l’information la plus importante doit ˆetre extraite de fond de diagramme de poudre, d´etermine la proc´edure de pr´eparation des ´echantillons ( plus grande puret´e) et des mesures de diffraction (donn´ees `a haute r´esolution du NPD).

Tout d’abord, chaque ´echantillon a ´et´e pr´epar´e aussi pur que possible.

Tous les m´etaux initiaux ont ´et´e fondus sous atmosph`ere d’argon, les alliages ont ´et´e recuits sous vide pour obtenir une grande homogn´eit´e de r´eseaux m´etallique, et ensuite, ils ont ´et´e broy´es sous atmosph`ere d’argon `a nouveau. Le processus de deut´eration a aussi ´et´e effectu´e sous vide. L’appareil Sievert (disponible `a l’Universit´e de Cristal- lographie `a Gen`eve ou le CNRS, Thi`es) a ´et´e utilis´e pour contrˆoler la quantit´e pr´ecise de deut´erium absorb´e. Les ´echantillons ont ´et´e stockes dans l’azote liquide pour ´eviter tout les changements struc- turel.

L’analyse de PDF r´eclame des donn´ees de NPD et XRD recueillies dans une ampleur tr`es large (angle ou d’´energie) `a haute r´esolution.

Comme nous nous int´eressons `a l’ordre local du deut´erium, l’´el´ement qui est invisible pour les rayons X, il ´etait n´ecessaire de r´ealiser des exp´eriences de diffusion de neutrons, en particulierTemps de vol neu- trons (ToF selon l’acronyme anglais Time of Flight), ce qui peut garantir le bon assemblage de donn´ees pour le PDF. Par cons´equent, chaque ´echantillon a ´et´e mesur´e par des neutrons avec ToF IPNS (Argonne Laboratory, Etats-Unis) ou avec NPDF (Lujan Center, le LANL, Etats-Unis).

Ces efforts ont apport´e l’effet attendu. Presque tous les ´echantillons, en particulier les phases les plus riches en deut´erium (YFe₂D_4.2, YMn₂D_4.5, ZrV2D4.9) montrent une diffusion diffuse significative dans le fond des diagrammes de poudre ce qui avait donn´e l’espoir de trouver l’ordre local des atomes de deut´erium.

Comme il a ´et´e mentionn´e ci-dessus, la relation entre l’ordre `a courte distance dans les phases `a haute temp´erature et de l’ordre `a longue port´ee dans les basses temp´eratures est tr`es int´eressant. Les structures

La d´etermination de la structure cristalline a ´et´e faite en deux ´etapes.

Tout d’abord, le r´eseau m´etallique a ´et´e trouv´e en utilisant des rayons X et des informations pr´eliminaires trouv´ees dans la litt´erature. En- suite, en fonction des diagrammes de NPD, les positions des atomes de deut´erium ont ´et´e d´etermin´ees par l’algorithme d’optimisation glob- ale (FOX application) et affin´e par la m´ethode de Rietveld (Full- Prof, GSAS). En cas de YFe₂D_4.2, un r´esultat int´eressant a ´et´e con- stat´e: tous les atomes de fers sont coordonn´es par 4 ou 5 atomes de deut´erium (en faisant les t´etra`edres et les bipyramides trigonale) avec des distances entre 1.630 - 1.875 ˚Ace qui indique une liaison entre les deux. Tous les sommets de la coordination polyhadra sont partag´es, de sorte qu’il ´etait impossible d’´ecrire la r`egle des 18 ´electrons. Par cons´equent on ne devrait pas l’appeler hydrure complexe. Toutefois, YFe₂D_4.2 ne peut pas ˆetre plus trait´ee comme un hydrure pur inter- stitiel.

Les phases `a haute temp´erature ont ´et´e analys´ees par PDF. La com- paraison de diagramme de PDF (obtenu par logiciel PDFgetX et PDFgetN) conduit `a dire qu’il ya une certaine similitude entre les arrangements d’atomes de deut´erium des phases les plus riche en deu- terium dans les temp´eratures basses et ´el`eves. En cas de ZrV2D4.5, le rayon de similitude est `a 5 ˚A, YMn2D4.5 `a 4 ˚Aet pour YFe2D4.2

`

a 8 ˚Ace qui permet de s’attendre `a des SRO dans ces faisceaux. La r´eponse a ´et´e trouv´ee grce `a la mod´elisation de PDF par le logiciel Discus (l’algorithme RMC) et le PDFgui (la m´ethode des moindres carr´es). Les calculs ont ´et´e faits dans une maille ´el´ementaire cubique (petite cube) ou 8 mailles ´el´ementaires cubiques (2x2x2 - grande cube) sur syst`eme de traitement par lots avec 100 processus parall`eles.

Malheureusement, le syst`eme ZrV<sub>2</sub>D<sub>x</sub> est apparu comme un com- posant tr`es complexe, et finalement la mod´elisation de PDF n’a pas

´

et´e possible. Les calculs obtenus pour le YMn₂D_4.5 ´etaient promet- teur pour le petit cube, mais ils doives encore ˆetre poursuivi pour le grand. Les tr`es bons r´esultats obtenus pour le YFe2D4.2 (les 2 cubes) permettent de confirmer la forte pr´ef´erence d’arrangement de deut´erium comme 4 et 5 atomes autour des atomes de fer.

Dans le cas d’un exemple de composant autre que phase de Laves - LaNi_4.5Sn_0.5D_3.8 - la question scientifique pos´ee est si l’ordre de deut´erium est ”saddle-like ” ou non. L’analyse de PDF n’a pas donn´e la r´eponse directe - il n’est pas sˆur que l’entourage est du type ”saddle- like”.

The main subject of presented thesis is investigation of local hydro- gen (deuterium) order in selected Laves phases: YFe₂D_x, YMn₂D_x, ZrV₂D_x and one compound of AB₅ type: LaNi_4.5Sn_0.5D_x.

The thesis falls to three parts: Introduction,Methodology and Investi- gated compounds. First of them contains wide introduction to particu- lar aspects of the thesis. Methodology part it is description of all used methods and techniques beginning from sample preparation, ending on data analysis with the newest approach to diffraction experiment.

Finally, results and discussion is put to Investigated compounds.

It is generally known that small changes of crystal structure can in- fluence strongly physical or chemical properties - the famous example is steel which properties are determined by introduction of very little amount of carbon to iron lattice. Obviously, the hydrogen presence in crystal structure has an effect on the created hydride. It can make so-called ’ordered’ phases in which fully occupied hydrogen atoms positions are localized, or ’disordered’ which contains sites partially occupied. For compounds studied within this project for given hy- drogen content the phase becomes ordered (below so-called ’ordering temperature’ T_OD) or disordered (above T_OD). Importantly, transfor- mation between these phases is completely reversible. Therefore, it is very interesting if it is possible to describe some local order of low temperature phase in apparently disordered high temperature phase.

Additionally, the Laves phase and AB₅structures are generally known and very well described. Their simple geometry makes analysis of hydrogen arrangement easier and allows to find relation (if it exists) between metal and hydrogen atoms.

Unfortunately, the hydrogen is not detected by X-rays and in case of neutron measurements gives high background (because of significant incoherent scattering). For purposes of this thesis, hydrogen has been replaced by deuterium - the isotope of hydrogen. It is generally as- sumed that deuterium keeps the same structure relation as hydrogen (with the exception of rare cases), but it is more convenient for neu- tron measurement (definitively smaller incoherent scattering signal).

Therefore, all samples have been prepared as deuterides instead of hydrides.

The results of X-ray (XRD) and neutron (NPD) powder diffraction measurements of selected deuterides are powder patterns which show a wavy background. It can be recognized as so-called ’diffuse scattering’

which indicates existence of a short range order in studied disordered phases. Information hidden in the background was examined thanks to the Pair Distribution Function (PDF) analysis. This method has been used for years for liquid and glass materials. Recent development of techniques for big synchrotron XRD and NPD facilities allows to apply PDF analysis for powder samples.

Between all Laves phases three groups of deuterides have been chosen:

YFe₂D_x (x=1.2, 1.9, 2.6, 4.2), YMn₂D_x (x=2.0, 3.4, 4.5) and ZrV₂D_x (x=2.8, 4.9). These compounds reveal very interesting structural and magnetic properties. Learning of deuterium local order can complete description of their structures.

The fact, that the most important information has to be extracted from powder pattern background, determines the procedure of sample preparation (high purity) and diffraction measurements (high resolu- tion of NPD data) - it requires the Total Scattering experiment.

nealed under vacuum to obtain the high homogeneity of metal lattice.

Next, they were ground again under argon atmosphere. The deutera- tion processes was performed without air, as well. The Sievert appa- ratus (available in University of Crystallography in Geneva or CNRS, Thi`es) was used for controlling the precise amount of absorbed deu- terium. Ready samples were stored in liquid nitrogen to avoid any structural changes.

PDF analysis requires a high resolution XRD and NPD data collected in a very wide range (angle or energy). As we are interested in a local deuterium order, the element which is invisible for X-ray radiation, it was necessary to perform neutron scattering experiments, especially Time-of-Fligt neutrons, which can guarantee the proper data sets for PDF. Therefore, each sample was measured by ToF neutrons in IPNS (Argonne Laboratory, USA) or in NPDF (Lujan Center, LANL, USA).

These whole efforts have brought expected effect. Almost all sam- ples, especially the most deuterium rich phases (YFe₂D_4.2, YMn₂D_4.5, ZrV₂D_4.5) show a significant diffuse scattering in background of pow- der patterns which had given a hope to figure out some local order of deuterium atoms.

As it was mentioned above, interesting is the relation between a short range order in high temperature phases and a long range order in low temperature ones. The crystal structures of ordered LT phases have been taken from the literature or solved ourselves.

The crystal structure solving has been done in two steps. First, the metal lattice has been found using the X-ray results and in some cases preliminary information read from literature. Next, based on NPD patterns, the position of deuterium atoms have been determined by a global optimization algorithm (FOX application) and refined by the Rietveld method (FullProf, GSAS). In case of YFe₂D_4.2 a fantastic result has been found: all irons are coordinated by 4 or 5 deuterium

atoms (making the tetraedra and trigonal bipiramides) with distances between 1.630 - 1.875 ˚A what indicates a directional bounding be- tween them. All vertices of coordinating polyhadra are shared, so it was impossible to write the 18-electron rule and consequently should not be named a complex hydride. However, YFe₂D_4.2 cannot be any more treated as a pure interstitial hydride.

The high temperature phases have been analyzed by PDF. Compari- son of PDF chart (obtained by the PDFgetX and PDFgetN software) allowed to say that there is some similarity between arrangements of deuterium atoms of the most D rich LT and HT phases. In case of ZrV₂D_4.5 the corresponding range is up to 5 ˚A, YMn₂D_4.5 up to 4 ˚A and for YFe₂D_4.2 up to 8 ˚A what allows to expect SRO within these ranges. The answer has been found thanks to the PDF modeling by DISCUS (RMC algorithm) and PDFgui (least-squares) applications.

Calculations have been done in one cubic unit cell (small box) or eight cubic unit cells (2x2x2 - big box) on a batch computing service as 100 parallel jobs.

Unfortunately, the ZrV₂D_x system came out as a very complex com- pound, and the PDF modeling has not been possible. The YMn₂D_4.5 calculation has given a promising result for the small box but should be still continued for the big box. The very good results obtained for YFe2D4.2 (small and big box) allow to confirm the strong preference of deuterium arrangement of 4 and 5 atoms around irons.

In case of one example of non Laves phase compound - LaNi_4.5Sn_0.5D_3.8 - the scientific question had been asked, whether the deuterium order is ’saddle-like’ or not. The PDF analysis has not given any straight answer - the site is not necessarily of ’saddle-like’ type.

I Introduction 1

1 What is this thesis about? 2

1.1 Motivation . . . 2

1.2 Hydrogen as energy carrier . . . 5

1.3 Hydrogen storage materials for chemical storage . . . 9

1.4 Why local order? . . . 10

1.5 The goal of this project . . . 11

2 Investigated metal hydrides 12 2.1 Structure and stability of Laves phases . . . 12

2.2 Hydrides and deuterides of Lave’s phase compounds . . . 17

2.2.1 Hydrogen absorption . . . 18

2.2.2 Maximal hydrogen capacity . . . 22

2.2.3 Hydrogen diffusion . . . 22

2.2.4 Hydrogen ordering . . . 24

2.2.5 Hydrogen influence on properties of formed hydrides . . . 25

2.2.6 Hydrogen or Deuterium . . . 26

2.3 General description of investigated compounds . . . 28

2.3.1 The YFe₂-H system . . . 28

2.3.2 The YMn₂-H system . . . 30

2.3.3 The ZrV₂-H system . . . 33

2.3.4 The LaNi₅-H system . . . 35

CONTENTS

II Methodology 37

3 General approach to long and short range order studies 38

4 Sample preparation 40

4.1 Synthesis of intermetallic compounds . . . 40

4.1.1 Arc melting . . . 40

4.2 Synthesis of metal hydrides . . . 42

4.2.1 Hydrogen line . . . 42

4.2.2 Sievert apparatus . . . 43

5 Powder diffraction 45 5.1 Diffraction principles . . . 45

5.2 Total Scattering experiment . . . 46

5.2.1 When is it worth performing the total scattering experiment? 46 5.2.2 General Considerations . . . 47

5.2.2.1 Background definition . . . 51

5.2.2.2 Diffuse scattering . . . 51

5.2.3 Obtaining S(Q) in theory and in practice . . . 52

5.2.4 General corrections . . . 53

5.2.4.1 Corrections for X-rays . . . 57

5.2.4.2 Correction for ToF . . . 60

5.2.4.3 Correction applying in practice . . . 61

5.2.5 The best diffraction facility for the Total Scattering Exper- iment . . . 61

5.3 X-ray Diffraction . . . 63

5.3.1 X-rays for structure determination . . . 63

5.3.2 X-ray diffraction facilities . . . 63

5.3.2.1 Laboratory devices . . . 63

5.3.2.2 Synchrotron facility . . . 64

5.4 Neutron scattering . . . 66

5.4.1 Neutrons for structure determination . . . 66

5.4.2 Neutron sources . . . 68

5.4.3 Neutron diffraction experiment . . . 69

5.4.3.1 Constant wavelength neutron scattering . . . 70

5.4.3.2 Time-of-Flight Facility . . . 71

6 Data analysis - structure solution 76 6.1 Profile Matching . . . 77

6.1.1 Figures of merit . . . 78

6.2 Global optimization method . . . 79

6.2.1 Simulated Annealing . . . 80

6.2.2 Parallel Tempering . . . 81

6.3 Rietveld refinement . . . 81

6.4 Total Scattering analysis . . . 82

6.4.1 PDF analysis . . . 82

6.4.1.1 General principles . . . 82

6.4.2 Reverse Monte Carlo method . . . 84

6.4.3 Available software . . . 87

III Investigated compounds - results and discussion 89

7.1.1 Sample preparation . . . 90

7.1.2 X-ray and neutron diffraction . . . 92

7.2 YFe₂D_4.2 - the most deuterium rich phase under normal conditions 93 7.2.1 Structure solution of ordered low temperature phase . . . . 93

7.2.1.1 Lattice description . . . 93

7.2.1.2 Structure solution . . . 95

7.2.1.3 Rietveld refinement . . . 96

7.2.1.4 Group-subgroup relation . . . 103

7.2.2 Structure solution of disordered high temperature phase . 108 7.2.2.1 Time of Flight NPD experiment . . . 108

7.2.2.2 Rietveld refinement . . . 111

7.2.2.3 PDF analysis and modelling . . . 114

7.2.3 Amorphous YFe₂D_4.2 phase . . . 131

CONTENTS

7.2.3.1 Sample preparation . . . 132

7.2.3.2 PDF analysis . . . 132

7.3 YFe2Dx (x = 1.3 - 2.5) - unsaturated deuterides . . . 136

7.3.1 YFe2D1.2 . . . 136

7.3.2 YFe₂D_1.9 . . . 137

7.3.2.1 Structure solution . . . 137

7.3.2.2 Group-subgroup relation . . . 148

7.3.3 YFe₂D_2.6 . . . 154

8 YMn₂ - system 155 8.1 Sample preparation . . . 155

8.2 YMn₂D_4.5 - the most deuterium rich phase . . . 156

8.2.1 Synchrotron measurement results . . . 156

8.2.2 Neutron scattering results . . . 156

8.2.3 PDF analysis and modelling . . . 160

8.3 YMn₂D_x (x = 0.5 - 3.4) - unsaturated deuterides . . . 166

8.3.1 YMn₂D_0.5 and YMn₂D_1.0 . . . 166

8.3.2 YMn₂D_2.0 and YMn₂D_3.4 . . . 166

9 ZrV₂ - system 176 9.1 Sample preparation . . . 176

9.2 ZrV₂D_4.9 - the most deuterium rich phase . . . 176

9.2.1 Synchrotron measurement results . . . 176

9.2.2 Neutron scattering results . . . 180

9.2.3 PDF analysis . . . 183

9.3 Deuterium poor sample ZrV₂D_2.8 . . . 186

9.3.1 Synchrotron measurement results . . . 186

9.3.2 ToF neutrons scattering results . . . 188

9.3.3 PDF analysis . . . 189

10 LaNi₅ - system - NOT a Laves phase 192 10.1 Deuteride preparation . . . 192

10.2 Structure solution of La(Ni_4.5Sn_0.5)D_3.85 . . . 193

10.3 PDF analysis . . . 193

11 Discussion and Conclusions 199

References 215

Part I

Introduction

What is this thesis about?

1.1 Motivation

The subject of this thesis follows the global world politics of looking for new source of pure energy, especially concentrating on the hydrogen as a new energy carrier. The hydrogen studies have been already developed for decades in ad- vanced countries but the importance of this work has increased during last 10 years.

There are three main reasons for searching for new energy sources. First of all, the energy system based on hydrogen instead of oil allows maintaing ener- getic independence from eastern countries which are rich in oil but politically unstable. As it is known, the energetic stabilization is a crucial factor for mil- itary stabilization so rich countries (as USA, Japan or UE) are ready to invest a lot of resources into developing new energy technologies. Secondly, the global amount of oil is limited and, sooner or later, mankind will be forced to find other source of energy. Additionally, the currently very fast developing countries as China or India are increasing significantly the demand for electricity and trans- portation, what in consequences leads to much faster consumption of existing oil pools and increasing the petroleum price. Finally, energy system based on oil is harmful for global habitat and hydrogen technology allows decreasing the amount of unwanted dangerous compounds emitted to the atmosphere.

The biggest advance of new technologies is visible on car market, where the global politics of governments is supported by private funds of car companies and new engineering ideas are currently tested and applied. Nowadays almost all

1.1 Motivation

Figure 1.1: The electric car designed by Ital Design Giugiaro presented at ”Motor Show Geneva 2010”

companies have designed electric cars (Fig. 1.1) and a few biggest ones (BMW, GM, Honda, Toyota) have presented hydrogen fuel cells driven cars (Fig. 1.2, 1.3).

Of course, both types of ecological cars are still not perfect. In case of electric cars, the main problems are the price and lifetime of batteries, the maximal range and batteries recharging time. With hydrogen car technology the biggest problem is the hydrogen storage. Under normal conditions the hydrogen volume is around 3000 times larger than energeticaly equaled amount of petrol so it is obvoius that the most important thing is finding the best way of keeping hydrogen as somehow ”compact” phases. The ideal way of hydrogen storage seems to be as hydrides of certain compounds in shape of solid (powder) materials. However, it is important that such hydride should be cheap, easy to be synthesized (at neither too high a temperatures, nor pressure), rechargeable and safe (hydrogen desorbtion should be obtained only under precisely defined conditions applicable in cars). Therefore, the scientific world’s attention is focused on this very field of investigations. Additionally, the cheap and safe way of hydrogen storage can be applied in fuel cells, which could be used as energy sources in private houses.

Figure 1.2: The hydrogen car designed by Honda presented at ”Motor Show Geneva 2010”.

The Honda FCX-Clarity is a first electric car serial produced which works by hydrogen fuel cell. It is available in California (US) and Japan. It emits only water. The maximal range is 460 km. The hydrogen tank refilling takes 4 minutes. In 2009 this car won the ”World Green Car Award”.

Figure 1.3: The hydrogen fuel cell designed by Honda presented at ”Motor Show Geneva 2010”.

The maximal power is 100 kW.

1.2 Hydrogen as energy carrier

1.2 Hydrogen as energy carrier

The idea is to use hydrogen for energy production, especially to fulfill the needs of transport market. Why hydrogen? This gas seems to be the best because of its utility properties (Tab. 1.1, 1.2). It is relatively cheap, safe (not more dangerous than other types of fuel), nontoxic and abundant - there are almost endless sources of hydrogen on Earth. It is the main constituent part of Sun and cosmic matter, and apart from almost unlimited amount of it in water, it additionally makes up organic compounds and biomass.

Hydrogen has the biggest combustion energy per kilogram (Tab. 1.2); it is 2.5 times more efficient than petrol what means that a small car can drive 100 km on 1.6 kg of hydrogen emitting only water (in a fuel-cell mode hydrogen consumption is twice less than in a combusting mode [Schlapbach 2002]). Hydrogen has the smallest initiation energy and is flammable at a very wide range of concentrations 4-75% in mixture with air. Its transportation is cheaper than that of electricity.

Hydrogen is lighter than air, so in case of leak it flies up.

Of course, this gas is not a perfect fuel and there are also numerous disad- vantages. Despite huge hydrogen resources, the production of it remains quite expensive. Additionally, hydrogen storage problem has still not been solved. Hy- drogen has the lowest energy density (4.7 MJ/kg for gas pressed under 700 bars) which means that 1 l of petrol corresponds to 6.4 l of hydrogen (under 700 bars).

A large (110 l) bi-layered and highly insulated tank for liquid hydrogen has been installed in BMW Hydrogen 7 car [Wiesenfelder 2010]. Another dangerous fea- ture seems to be its invisible flame. A hydrogen molecule is the smallest one what consequently determines that it has the highest velocity at a given temperature and very high diffusion coefficient. In result, hydrogen is extremely ephemeral, and even when closed in a very tide container about 1.5 % of its volume is lost per day. Despite high vacuum between two layers of doubled wall (which corresponds to 17 m thick wall of polystyrene) the tank will be empty within 10-12 days [Gain 2011].

Besides specific physical features, hydrogen has interesting chemical proper- ties. Being the simplest of all elements (1 proton and 1 electron) but the atomic

Table 1.1: Hydrogen properties

general properties

atomic number 1

element category nonmetal atomic weight 1.00794 gmol⁻¹ electron configuration 1s¹ atomic properties

oxidation states -1, 1 electronegativity 2.20 atomic radius 0.79 ˚A covalent radius 0.32 physical properties

abundancy by mas 75 %

thermal conductivity 0.1805 W m⁻¹ K⁻¹ boiling point 20.3 K melting point 14.0 K heat of fusion 0.117 kJ mol⁻¹ heat of vaporization 0.904 kJ mol⁻¹ specific heat capacity 28.836 J mol⁻¹ · K⁻¹

hydrogen H⁰ is highly unstable as it ’wants’ to have completely empty or com- pletely filled 1s shell. In nature pure hydrogen exist as a molecule H₂ where the enthalpy of the H-H bond is huge, 4.52 eV, comparing to other light elements.

What is interesting, accepting or giving off one electron hydrogen changes 100%

of its total number of electrons. In result, it behaves generally as a hard cation toward nonmetal and as a soft anion towards metals [Grochala & Edwards 2004].

As it has +1 or -1 oxidation state, the question arises what is more likely to occur. Comparing the values of the first ionization energy (+13.60 eV) with the electron affinity (-0.75 eV) it leads to the conclusion that a hydride anion H⁻¹ seems to be a better source of hydrogen than a proton (less energy is necessary to take hydrogen out from a material). On the other side, hydrogen absorbed by

1.2 Hydrogen as energy carrier

Table 1.2: Hydrogen as a fuel (compares with other energy sources)

higher/lower heating value [kJ/g]

hydrogen 141.86/119.93 methane 55.53/50.02

gasoline 47.5/44.5 propan 50.36/45.6

diesel 44.8/42.5

energy density [kJ/m³]

hydrogen 10050 (gas 1 atm and 15 ^oC) 8491·10³ (liquid)

methane 32560 (gas 1 atm and 15 ^oC) 20920·10³ (liquid)

gasoline 31150 ·10³

propan 86670 (gas 1 atm and 15 ^oC) 23488·10³ (liquid)

diesel 31435 ·10³ octan number hydrogen 130+

methane 125 gasoline 87

propan 105 diesel 30

certain compounds doesn’t have to make any bond (see chapt. 1.3).

Therefore, a daunting task is to find the best method of hydrogen storage - in the form of a solid compound.

Pioneer work in the field of hydrogen-metal system was done by T. Graham in 1866. He discovered that Pd metal exposed to H₂ gas can absorb a big amount of hydrogen near ambient conditions [Grochala & Edwards 2004]. Since that time the science of H-M systems has been developed and a lot of different systems (binary, ternary, etc.) have already been investigated.

Everybody searches for compounds which would fulfill all conditions of perfect

Table 1.3: Ideal solid hydrogen storage material [DOE 2011]

high storage capacity: minimum 6.5 wt % desorption temp. Tdec = 60-120 ^oC

reversibility of an absorption/desorption cycle low cost

low toxicity of all substrates and products

storage material (see Tab. 1.3). Ideally, the compound should have high hydrogen storage capacity of order of 6.5 wt %. This is related to economic ratio between fuel efficiency and tank mass. Despite intensive investigation in this field, such material still has not been designed yet. Optimal assumed desorption temperature ranges between 60-120 ^oC. The higher temperatures desire more energy supplied by a car but too low would be dangerous due to unfavourable external conditions - it cannot be allowed that all hydrogen is released during a sunny day. Reversibility is an obvious condition. Ideally desorption should take place at normal pressure and T_dec, should absorption happen at a lower pressure of a few bars and not too high a temperature - it would result significantly in the cost of fuel. The total cost of a car running on ’ecological’ fuel should not be higher than 20 % of that run on a conventional one. The same condition is related to fuel [Schlapbach 2002]. Therefore, hydrogen storage material cannot be too expensive. As people are looking for more and more pure energy sources, an ideal compound should have low toxicity during the whole absorption-desorption process. Finally, a new fuel should be a nonexplosive material which behaves safely even during a car accident.

Clearly, finding the ideal hydrogen storage material is a huge challenge for whole scientific world and any good result in this field of investigation will signif- icantly influence our future.

1.3 Hydrogen storage materials for chemical storage

1.3 Hydrogen storage materials for chemical stor- age

In general, it has been discovered that hydrogen can be ”trapped” within hydrides in three ways,and so it can be named as hydrides withsaline, metallic orcovalent bonding, accordingly.

The saline metal hydrides are based mainly on alkali and alkaline earth ele- ments (groups IA and IIA). They are usually highly exothermic, the metal be- comes a cation M⁺ and hydrogen exists as H⁻ anions. The hydrogen storage efficiencies can reach 5.7 wt % (for Ca₄Mg₃H₁₄) but this type of compounds are usually too stable to be interesting for reversible hydrogen storage application.

These compounds are insulators and show non-directional bonding. The con- dition of existing of such hydrides is rather related to atomic size and packing effect than to electronic factors. The pure ionic hydrides generally show the lattice contraction [Yvon 2003].

In the covalent metal hydrides the covalently bonded transition metal-hydride complex is present, so this category of compounds is often called ’complex hy- drides’. What is exciting the complex is mostly built around metals which form none or very unstable binary hydrides (e.g. [FeH₆]⁴⁻ in Mg₂FeH₆). The complex hydrides are usually non-metallic, ordered at room temperature and they reveal a wide range of thermal stability. The hydrogen can appear in metal complexes which show directional bonding but also as an anion surrounded by metal cation matrix where non-directional bonding is presented. The condition for the com- plex hydrides occurence is clearly based on simple electron counting rules (f. ex.

the 18-electron rule).

Contrary to complex hydrides, formation of the metallic ones cannot be ex- plained by any rules based on electron counting. They are usually obtained by solid-gas reaction of binary or ternary intermetallic compounds (see chapter 4).

The H atoms occupy the interstitial sites in metal lattice - that is why this type of compounds is often called interstitial hydrides. They are usually disordered at room temperature and hydrogen ordering takes place below certain temperature which is characteristic for any particular hydride. The hydrogenation process

does not influence too much the crystal structure (except a lattice distortion and cell expansion) so usually the metallic properties are conserved. Generally, there is no directional bonding between hydrogen and metals though it can sometimes be observed [e.g. Ropka et al. 2009]. What is interesting, at least one element of binary (or ternary) intermetallic compound is a binary hydride former (e.g.

YH_x, x = 2−3 in YFe₂H_x) and usually hydrogen coordinates this atom. How- ever, it has been observed that even in case of interstitial hydrides, hydrogen can make directional bond with metal with weakest affinity to hydrogen (as in case of complex hydrides) [Ropka et al. 2009]. Comparing to saline or covalent hydrides, the properties of interstitial ones are less well understood, so they are still a very exciting subject of research.

All hydrides investigated within this thesis are interstitial ones.

1.4 Why local order?

In the material science there are a lot of compounds with properties determined thanks to very small changes in crystal structure. One of the best known exam- ples of a remarkable change in properties caused by small admixture is a ruby - very well known mineral used for jewelery. Only 0.05% of chromium (Cr⁺³) homogenously distributed in Al₂O₃ determine the deep red color of Al₂O₃:Cr⁺³, whereby it is transparent in case of pure Al₂O₃ [Maiman 1960]. Another ex- ample is steel which is much harder than pure iron because of introduction of small amount of carbon (less than 6 %) and creating crystal structure defects by quenching. One can find many more similar examples. In the hydride field, one of them can be the La(Ni,Sn)₅ compound (described in chapter 10): only 5 % of Sn instead of Ni in La(Ni,Sn)₅H_x makes this hydride very stable comparing to pure LaNi₅H_x.

Thanks to recent technology development scientists and engineers are able to design materials which better meet technology market needs. Development of new tools and methods allows studying much more complex materials. From crystallographic point of view, most of them cannot be conventionally classified to one of the two categories: neither pure crystals with long-range order nor as pure amorphous (or liquid) materials with short-range order - they are localized

1.5 The goal of this project

somewhere in between. What is significant, the new materials revel properties which are presumably determined by short range atomic interaction.

With hydrides, the attention is turned to the amount and arrangement of hy- drogen atoms within investigated compound. Therefore - related to hydrides - the local microscopic order of hydrogen atoms determines their physical properties, such as, for example, sorption ability and thermostability, what is particularly important for scientist and engineers dealing with hydrogen storage materials.

It can be generally said that a lot of properties of a given material are not determined by average (long range order) crystal structure but rather by little distortion in the structure. Therefore, the investigations of local order of certain elements fill up the image of an average structure and can help understand better the studied compounds.

1.5 The goal of this project

Looking at the periodic table, the hydrides formed by elements ”on the left” (I, II groups) by alkali metals are generally too stable for practical applications. Those which are present ”on the right” of periodic table are usually not stable enough.

Therefore, the middle part (transition metals, lanthanides) become very interest- ing for material scientists. A number of scientific teams concentrate on ”tuning”

of existing compounds by substituting of one element with another in order to receive expected properties. Unfortunately, the compounds containing the tran- sition metals form the interstitial hydrides which are still not well understood.

In particular, sometimes the interstitial hydrides show a directional bonding that can be discovered by investigation of a local order of H atoms within the metal lattice. But then, the development of powder diffraction method based on new sources of intense radiation (synchrotron, neutron source) combined with Pair Distribution Function analysis allows very precise structural characterization of studied materials.

The goal of this thesis is to investigate whether hydrogen in apparently dis- ordered hydrides reveals any local order.

Investigated metal hydrides

2.1 Structure and stability of Laves phases

Laves phases (LP) are special cases of AB₂ compounds, which are known as tetra- hedrally coordinated close packed structures. It is expected that formation and stability of such structures are determined by ratio of atomic radii, electronega- tivities and valence electron concentration (VEC) of the atoms which build the structures.

The classification performed on the crystal structure geometry basis requires that the ratio of the radii of A and B atoms should follow the formula:

r_A rB

= r3

2 ≈1.225 (2.1)

Owing to this geometrical condition Laves phase can be found in quite narrow range of elements concentrations. In reality, the Laves phase structures form for wider range of atom radii: r_A/r_B = 1.05−1.68 what leads to more than 1400 representatives [Villars & Calvert 1991].

Laves phase can crystallize in one of three crystal structures: MgCu₂-type cubic C15 (Fig. 2.1), MgZn₂-type hexagonal C14 (Fig. 2.2) and MgNi₂-type hexagonal C36 (Fig. 2.3).

The Laves phases do not reveal any clear correlation between the value of the radii ratio and the structure type formed (Fig. 2.4). Remarkably, the radii of A and B atoms in Laves phases always differ from the radii of these atoms as pure elements. In result, the distances between B atoms in Laves phases structures

2.1 Structure and stability of Laves phases

Figure 2.1: The unit cell of cubic C15 structure

Figure 2.2: The unit cell of hexagonal C14 structure

Figure 2.3: The unit cell of hexagonal C36 structure

Figure 2.4: Frequency of Laves phase structure type versus the ratio of A and B atomic radii [Stein et al.2004]

2.1 Structure and stability of Laves phases

are usually smaller than in pure B crystals [Stein et al. 2004]. However, this rule does not refer to A atoms.

Depending on the structure type there are 1 (for C15), 2 (C14) and 3 (C36) independent crystallographic sites for the B atoms (see Table 2.1).

Table 2.1: Three types of Laves phases structures

phase type MgCu2 MgZn2 MgNi2

crystallographic lattice cubic hexagonal hexagonal

type C15 C14 C36

space group F d−3m P6₃/mmc P6₃/mmc

VEC 1.3-1.8 1.8-2.3 1.8-2.3

more than 2.3

examples MgCu₂, AgBe₂ MgZn₂, CaCd₂ MgNi₂,ZrFe₂ BiAu₂, CaAl₂ CaLi₂, CaMg₂ UPt₂,U(Fe,Ni)₂

YFe₂, YMn₂ NbMn₂, SrMg₂ TiCo₂- α ZrV₂, ZrFe₂ WFe₂, ZrCr₂

In AB₂ compounds structures the atom A is always bigger than B. The A atoms are localized in interstitial sites between tetrahedra made of B atoms. In consequence, A atom is surrounded by Z16 Frank-Kasper polyhedron [Frank &

Kasper 1958, Frank & Kasper 1959], where 12 vertices are the B atoms and 4 are A atoms. Neighborhood of each B atom is found as an icosahedron formed by 6 A and 6 B atoms. The average coordination number of that structure is 13.33 what is more than for pure elements A and B. It is due to the fact that in Laves phase compounds atoms are cloasely packed. The B atoms form the tetrahedra which are stacked in layers in various ways what is characteristic for different types of Laves phases: C15 -abc,abc,. . .; C14 -ab,ab,. . .; C36 -abac,abac,. . . [Steinet al.

2004].

There exist compounds which are not so stable as the Laves phases ones even if they reveal the proper ratio of A and B atoms radii [e.g. Skripov et al.

2000]. Therefore, scientists assume some other condition which will determine the possibility of LP forming. An investigation of valence electron concentration as

a potential LP stabilizing condition has been made [Stein et al. 2004] and it has been found out that certain group of compounds shows correlation between VEC and type of formed Laves phases (Fig. 2.5). However, these relations cannot be straightforward extrapolated for all other compounds. In general, it is assumed that the cubic Laves phase is formed for VEC value in the range of 1.3-1.8 and above 2.3, whereas the hexagonal one exists for 1.8-2.3 (Table 2.1), but many exceptions are known a lot of exception.

Figure 2.5: The ranges of different LP structures appearance depending on number of valence electrons per atom (VEC) [Steinet al.2004]

The Laves phases are mostly formed for stoichiometric AB₂ compounds but they also exist with A or B in excess (for example the YFe₂ form pure Laves phase C15 only if Y exceeds around 4% what in reality leads to Y_1.04Fe₂ stechiometric formula).

The most of LP compounds are binary ones. However, they can form also ternary compounds, even - or maybe especially - for the systems which do not exist in a binary form [e.g. Skripov et al. 2000].

2.2 Hydrides and deuterides of Lave’s phase compounds

2.2 Hydrides and deuterides of Lave’s phase com- pounds

Many Laves phases easily absorb hydrogen, even up to high concentration level.

These types of hydrides are studied very intensively because of their properties.

From one point, they reveal very interesting structural, but also electronic and magnetic properties. From the other, the simple geometry of cubic and hexagonal phases allows understanding and explaining a lot of experimental observations.

Following the main subject of this thesis, only structural properties of Laves phase hydrides have been taken into account, but very detailed description of electric and magnetic properties can be found for example in [Schlapbach 1992].

Very often the crystal structures of Laves phase hydrides are the same as initial intermetallic compounds (hydrogen absorbing leads to solid solution - see chapter 2.2.1), or the new crystal structure is a results of 2^nd order phase transition, what allows finding the relation between ”parent” compound lattice, and the lattice of formed hydride [Sikora et al. 2007].

Generally, the Laves phase compounds can absorb up to around 4 H/f.u. under normal conditions. However, there are known the investigations (performed for example by Filipek - [Filipek et al. 2010]) where the high pressure of H₂ gas (order of 1.2 GPa) applied during hydrogenation process leads to 6 H/f.u., but it is almost always connected with 1^st order phase transition, so final hydride crystal structures can completely differ from the structure of initial compounds.

In the studies performed within this thesis normal conditions have been assumed, so the results have not been related to high pressure hydride phases.

The hydrogenation process increases the volume of a unit cell, in certain cases, even up to 30% in comparision with the initial compound [Paul-Boncour et al. 2005a]. It leads often to destroying crystalline materials and significantly decreases the size of crystallites. Therefore, the hydrides obtained by exposing the intermetallic compounds to H₂ gas can also be obtained as powder samples (derivation of single crystals of hydrides are very rare [Filinchuk & Yvon 2005a]).

As it has been mentioned, the hydrides of intermetallic compounds are the examples of interstitial hydrides (chap. 1.2). In case of Laves phases, there are

3 types of tetragonal sites: A₂B₂, AB₃ and B₄. The Fig. 2.6 shows these sites located in C15 structure.

Figure 2.6: Three types of interstitial sites (in the C15 crystal structure) which can be occupied by H atoms: 96g (red), 32e (blue) and 8b (grey)

The probability of finding a H atom in a certain type of interstitial site is not the same. First of all, it is dependent on the size of a given tetragonal site (A₂B₂ is the biggest one) but, it can also be related to the type of A and B atoms, and their affinity to hydrogen. For example in case of YFe2 compounds, the H atoms are localized mostly in A₂B₂ sites, much less in AB₃ and almost barely in B₄ (see chapt. 7.2).

2.2.1 Hydrogen absorption

A metal or alloy exposed to hydrogen gas can start to react with H₂ molecules what finally leads to obtaining the expected hydride of a given compound. How to briefly describe the whole process? In general, the potential of a system is chang- ing when H₂ approaches the surface of an alloy. In the beginning the potential of H₂ molecules is lower hence energetically better comparing to two separated H atoms (the difference is determined by the dissociation energy of 220 kJ/molH - Fig. 2.7). Therefore, the Van der Waals interaction plays the main role during

2.2 Hydrides and deuterides of Lave’s phase compounds

Figure 2.7: H2+M system potential [Zuttel 2003]

attracting the H2 molecules to the surface of the alloy what leads to the phys- iosorbed state. If H2 molecules have been already attracted, it means they have enough energy to overcome an activation barrier for dissociation and separated H atoms appear. Free hydrogen can react with not-bound metal atoms at the surface what results in chemisorbed state (Fig. 2.7).

Next, the H atoms what are already trapped inside an alloy can jump deeper to the next sublayers (diffusion process), and swap (jump) between the interstitial sites in the metal lattice. Finally, depending on hydrogen concentration the so- called solid solution (α-phase) transforms into hydride phase (β-phase) - Fig. 2.8 [Zuttel 2003]. The heat of AB₂H_x hydride formation results from energy changes summation: the lowering of occupied metal states (an exothermic term) and the upwards shift of EF (an endothermic term) [Gupta & Schlapbach 1992].

Experimentally measured pressure of external hydrogen gas versus hydro- gen absorbed by metal lattice for given temperature leads to drawing the p-c-t (pressure-concentration-temperature) curves (Fig. 2.8).

As one can see, initially the pressure increases with hydrogen concentration, then the flat plateau is observed and next again the pressure strongly rises with larger amount of absorbed hydrogen. The first slope indicates the alpha-phase

Figure 2.8: The pct isotherme and α-phase to β-phase transformation [Schlapbach & Zuttel 2001]

(solid solution) what is observed for small ratio between H and M (metal) atoms:

H/M<0.1 [Schlapbach & Zuttel (2001)]. Significant expansion of metal lattice is proportional to the amount of absorbed hydrogen as 2-3 ˚A³ per H atom. Gener- ally, the behavior of this state can be described by Sievert’s law [Fukai 2005]:

c∝√

p (2.2)

where cis the hydrogen concentration and p is the external hydrogen pressure.

Relation between concentrationcand pressure pdepends on the temperature as well, so overall solubility formula takes the form:

c= rp

p₀e^{∆SS/ke−∆HS/kT} (2.3) where ∆SS is the entropy (reffered to H2 gas of pressurep0 and temperatureT),

∆H_S is the enthalpy (heat) of reaction.

What is important, Sievert’s law is held for such a small concentration of hydrogen which can still be assumed as an ’ideal gas’. For higher pressure the solubility is larger than Sievert’s law predicts [Fukai 2005].

2.2 Hydrides and deuterides of Lave’s phase compounds

Figure 2.9: pct isotherm and Van’t Hoff plot [Schlapbach & Zuttel 2001]

Following the pct curve, there is a significant range of hydrogen concentration shown as a flat plateau, whereα-phase coexists withβ-phase which starts to grow .

Finally, putting more and more hydrogen let a hydride phase with typical concentration as H/M=1 forme (Fig. 2.8). β-phase appears when enough amount of hydrogen absorbed by alloy causes that H-H repulsive interactions become important. In most M-H systems Switendick rule [Switendick 1979] holds that two H atoms cannot come closer than 2.1 ˚A apart.

The example of the pct isotherms measured for different temperatures is shown in the Fig.2.9. A few important features can be seen in this picture. First of all, the critical temperature Tc appears where two-phase region ends. Secondly, the value of the pressure observed for the plateau gives information about stability of β-phase: if this plateau lays below 1 bar then β-phase is stable under normal pressure for a given temperature. Thirdly, the length of it lets the amount of hydrogen stored in given material approximate. Finally, it’s possible to draw the Van’t Hoff plot (Fig. 2.9), what lets briefly approximate the entropy and enthalpy for the hydrogenation process under given conditions [Schlapbach 1992]

Of course, the temperature and H₂ gas pressure necessary to invent the whole hydrogenation process depends strongly on the kind of initial metal or alloy. All details related to hydrides synthesized within this project are given in experimen- tal part III.

2.2.2 Maximal hydrogen capacity

The straightforward counting of all available interstitial sites leads to a conclusion that the maximal capacity of Laves phase compounds should be 17 H/f.u. In fact, it is never more than around 4-5 H/f.u. (under normal conditions). There are two important rules which limit the amount of absorbed hydrogen: Westlake’s [Westlake 1983] and Switendick’s rules [Switendick 1979].

Westlake’s studies of hydrogen storage materials allow him to draw a conclu- sion that hydrogen can be absorbed and localized in that interstitial site which is large enough to contain the sphere with the radius of 0.4 ˚A. Instantly, the B₄ sites are usually too small to hold this condition so the probability of finding the hydrogen on B₄ sites is generally close to zero.

Switendick’s rule states that two H atoms cannot be placed closer than 2.1

˚Aapart because of their repulsive interaction [Switendick 1979]. Therefore, when one site is taken by H atom all neighboring sites have to stay empty. It signif- icantly decreases the number of available interstitial sites, and in consequence, the hydrogen concentration. However, a few examples are known which break Switendick’s rule [i.e. Yartys et al. 2002].

2.2.3 Hydrogen diffusion

The hydrogen diffusion studies in a number of C15 Laves phase hydrides led to discovering an interesting phenomenon - coexistence of two types of hydrogen mo- tions with different characteristic jump rates [Skripov 2005]. For small hydrogen concentration the H atoms occupy only 96g sites. The sublattice of these g sites is created by hexagons lying in the planes perpendicular to < 111 > direction (Fig. 2.10. Each site (vertex of hexagon) has two nearest neighbors at a distance r₁ (belonging to the same hexagon) and one neighbor at a distance r₂ (on the

2.2 Hydrides and deuterides of Lave’s phase compounds

adjacent hexagon). The ratior₂/r₁ depends on type of compounds (size of A and B atoms) and on the positional parameters of H atoms. For example, for TaV₂D_x this ratio r2/r1 = 1.45. That means, hexagons are very well separated, while for YMn2Dx: r2/r1 = 0.78.

It has been found [Skripov 2005] that for these types of compounds where r₂/r₁ > 1, there are two types of motion: fast - between sites belonging to one hexagon and slow - between neighboring hexagons. It is worth pointing out that the motion on the hexagon circumference can be even 3 orders of magnitude faster comparing to jumps between two hexagons. The slower jump process is responsi- ble for the long-range diffusion, while the fast motion determines the distribution of H atoms on g sites within certain hexagon. In that case, where r₂/r₁ <1, the fast motion occurs between the pair ofg sites belonging to neighboring hexagons.

Figure 2.10: Example of YFe₂D_xC15 Laves phase: coordination of yttrium and iron by tetrahe- dral Wyckoff sites (96g - red, 32e - blue and 8b - gray) partly occupied by deuterium. Distance r1

within the deuterium hexagons in the Y coordination sphere, distance r₂between the hexagons

For bigger hydrogen concentration the AB₃ (32e) sites are occupied as well.

The problem is that for such mixed occupancies the behavior of hydrogen diffusion is less tractable. However, the investigation of ZrTi₂H₄ and HfTi₂H₄ (where 32e sites are occupied) shows that jumps from one e position to another via g can be

described as a long-range (slow) diffusion while H atoms jumps on the hexagon circumference represents the fast motion type.

2.2.4 Hydrogen ordering

Interstitial hydrides can exist as a one of two phases: ordered and disordered.

At high temperature a hydrogen diffusion coefficient is big and hydrogen atoms move between all available positions (chapt. 2.2.3). Interactions are mainly long- range attractive forces and short-range repulsion (chapt. 2.2.2) as in the pair of gas particles - that’s why, sometimes, hydrogen in such phase can be described as a ’lattice gas’ model [Kohlmann 2002]. In result it leads to a structure with hydrogen distributed statistically on all possible interstitial sites. From crys- tallographic point of view, disordered (high temperature HT) phase has certain average structure in which hydrogen sites occupancies are less than 1.

With temperature decreasing, it is expected that the hydrogen diffusion de- creases leading to ”freezing” the H atoms on given positions. What is interesting, the hydrogen can prefer certain positions what finally creates the ordered (low temperature - LT) structure. The ordered structure has always lower symmetry than the disordered one and the hydrogen sites are fully occupied [Ropka et al.

2009].

A temperature for which the order-disorder transition takes place is called the ordering temperature T_OD, and it is a characteristic feature regarding given compounds (chapt. 2.3).

’Ordered’ and ’disordered’ terminology is rather used instead of ’lattice gas’

model since with developing of better experimental techniques it proves that even in interstitial hydrides hydrogen can form bonds with metals [Filinchuk

& Yvon 2005b, Filinchuk & Yvon 2006a, Filinchuk & Yvon 2006b]. They are still called ’interstitial’ hydrides as no rule (like 18-electron rule) which leads to treating them as complex hydrides can be found. It’s almost impossible that conventional crystallography methods can distinguish between ’pure’ interstitial hydrides and those having directional bonds - it is a field of total scattering experiment completed by PDF analysis.

2.2 Hydrides and deuterides of Lave’s phase compounds

Additionally, the nature of order-disorder transformation is not liquid-gas like. Apart from the 1^st order transition (characteristic for gas systems) it is very common that the 2^nd order transition and structural relationship between high and low temperature phases can be represented as their group-subgroup relationship. All possibilities of hydrogen ordering in C15 Laves phases have been analyzed in [Sikora et al. 2007].

2.2.5 Hydrogen influence on properties of formed hydrides

The hydrogen presence in a given structure significantly influences its properties.

The crystallographers are generally interested in structural changes determined by hydrogen. However, usually these properties are related to others, especially magnetic, and it seems impossible or very difficult to distinguish how hydrogen affects them. Therefore, the description of structural properties infused with hydrogen has been supplemented with roughly mentioned magnetic aspects.

It is visible at first sight that a material which absorbs hydrogen breaks down into smaller pieces. From microscopic point of view, it occurs so because of crystal structure expansion due to hydrogen absorption. The increasing of a unit cell volume can be very significant (even up to 30% [Figiel et al. 1998]) and it is not a simple linear function of hydrogen concentration. More advanced studies of this correlation [Somenkov & Shil’stein 1998] which takes into account a type of investigated compound (alloy, intermetallic compound) have not resulted in a general formula. However, for particular group of hydrides it was possible to find the function of cell volume expansion versus the amount of absorbed hydrogen.

In case of RMn₂-H , the hydrogen was taken as a negative chemical pressure, and the unit cell volume increasing relation was found by [Hirata et al. 2004]:

V V₀ =

B₀+bx B₀

1/b

(2.4) where B₀ - the bulk modulus at ambient pressure for pure material (x= 0),

b is the first pressure derivative of B.

It seems that given relation works quite well for known groups of hydrides (YMn H , TbMnH , DyMnH , GdMnH )

Next to cell expansion, the hydrogen absorption strongly influences the sym- metry of crystal structure by introducing different distortions. The hydrides have generally lower symmetry than a ’parent’ compound. Thanks to neutron diffrac- tion experiment it is usually possible to describe the positions of hydrogen atoms within given structures and following the occupancies of its Wycoff sites, hydrides fall into two categories: ordered and disordered (see chapt. 2.2.4).

The characteristic of hydrogen absorption is that it does not so obviously reach a single hydride phase. For very small or large amount of hydrogen it is usually only one phase. However, for ’middle’ range, there quite often coexist two phases: hydrogen ’poor’ and ’rich’ one. Only special heat and/or pressure treatment leads to obtaining a single phase for such concentration, and usually it is not a stable phase.

Finally, the hydrogen changes magnetic properties as well. It happens in two ways. Changing the unit cell volume and structure symmetry, the distance between given atoms is changed, and so, it can induct the magnetic moments.

Additionally, the hydrogen presence in the given structure means that there are more electrons potentially influencing on _3d shell of transition metal atoms.

2.2.6 Hydrogen or Deuterium

It is quite common to exchange hydrogen for deuterium in investigated samples.

Obviously, only hydrogen and hydrides have good prospects for commercial use because of huge deuterium price. From the other side, one of the main crystal- lographic tools - neutron diffraction experiment, shows much better results for deuterium than hydrogen, because of a difference in neutron scattering length (see Tab. 2.2). There even one ”trick” exists which leads to a zero neutron scattering power thanks to using hydrogen and deuterium in certain proportion H_0.64D_0.36.

Table 2.2: The coherent and incoherent scattering length of hydrogen and deuterium

H D

coherent [10⁻¹⁵m] -3.7406 6.671 incoherent [10⁻¹⁵m] 25.274 4.04