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Abstract

In this thesis, electron collisions with molecules of biological interest are investi- gated. The main focus lies on the conduction of total scattering cross section and electron energy loss measurements at different apparatuses and energy ranges and includes the construction, testing and start of operation of a new experi- mental device using a strong magnetic field for confining the electron beam dur- ing the cross section measurements. Furthermore, theoretical electron-molecule cross sections are derived from the optical potentials of the atomic constituents taking into account intramolecular screening effects. The scattering targets thus studied in the general energy range of interest (1–10 000 eV) are argon, methane, ethylene, tetrahydrofuran, p-xylene, pyrimidine, and pyrazine.

Based on the original data obtained and aided by a critical analysis and compar- ison to other relevant results, carefully selected and self-consistent electron colli- sional data sets can be recommended for some of the molecules mentioned. They are compiled from the most representative and accurate sources for each type of interaction parameter in order to provide a complete reference describing elec- tron scattering from the respective molecules in the energy range 1–10 000 eV.

The tabulated data include integral partial cross sections for the different inter- action processes, differential cross sections for elastic scattering and also energy loss distribution functions for the same range of incident energies. In addition, an empirical approximation to inelastic differential cross sections is proposed.

Finally, a custom-programmed molecular-level Monte Carlo code, the Low- Energy Particle Track Simulation, directly uses the data base generated for the simulation of realistic macroscopic situations such as electron transport through gases or medical radiation applications, adding practical utility to the scientific results obtained.

Agradecimientos

Hay muchas personas que durante los trabajos que han llevado a la redacc´on de esta tesis me han prestado su ayuda y apoyo, y aqu´ı quiero mencionar especial- mente los esfuerzos de algunos de ellos.

Ante todo quiero dar las gracias a mi director de tesis Gustavo Garc´ıa, del que he tenido la suerte de aprender no s´olo mucho sobre f´ısica molecular y las t´ecnicas experimentales de nuestro ´ambito, sino adem´as muchas destrezas pr´acticas que han sirvido de enorme ayuda en el d´ıa a d´ıa de un laboratorio de f´ısica.

Tambi´en quisiera agradecer a mis compa˜neros de laboratorio Diogo Almeida, Ana Garc´ıa Sanz y Rafael Colmenares su ayuda en algunos momentos cr´ıticos, y sobre todo aquellas ideas y discusiones que a veces surgen de una duda inicial.

Entre nuestros colaboradores internacionales, quiero dar las gracias en especial a Michael Brunger y Paulo Lim˜ao-Vieira por su incansable asistencia a la hora de revisar los aspectos ling¨u´ısticos en nuestros art´ıculos cient´ıficos.

A Luis M´endez, mi tutor acad´emico, le quiero agradecer la ayuda y preocupaci´on con las que me ha guiado por los diversos procedimientos burocr´aticos de la universidad. Igualmente, doy las gracias a los responsables en la actualidad y el pasado del programa de doctorado en Biof´ısica del Instituto Nicol´as Cabrera, que siempre han estado dispuestos a facilitar las gestiones administrativas para los doctorandos ‘externos’ como yo.

Finalmente, agradezco a la Comunidad Aut´onoma de Madrid la concesi´on de un contrato de ‘Personal Investigador de Apoyo’ que ha hecho posible la realizaci´on de esta tesis por mi parte.

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Contents

Introduction 1

Introducci´on 5

1. Experimental Methods and Apparatuses 9

1.1. Magnetically Confined Electron Scattering System . . . 9

1.1.1. Design and Technical Characteristics . . . 9

1.1.2. Tests: Alignment, Focus, Resolution . . . 18

1.1.3. Measurement Protocol . . . 20

1.1.4. Experimental Uncertainties . . . 24

1.1.5. Benchmarking measurements . . . 28

1.2. Transmission Beam Spectrometer . . . 29

1.3. Differential Electron Energy Loss Spectrometer . . . 30

2. Measurements and Results 35 2.1. High-Energy Electron Energy Loss Spectra . . . 36

2.1.1. Argon . . . 36

2.1.2. Methane . . . 36

2.1.3. Ethylene . . . 39

2.1.4. Xylene . . . 42

2.1.5. Tetrahydrofuran . . . 44

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2.2.2. Ethylene . . . 47

2.3. Total Electron Scattering Cross Sections . . . 50

2.3.1. Pyrimidine . . . 52

2.3.2. Pyrazine . . . 56

3. Calculations 67 3.1. Theoretical Methods—IAM-SCAR . . . 67

3.1.1. Electron-Atom Scattering . . . 68

3.1.2. Molecular Scattering Cross Sections . . . 69

3.1.3. Rotational Excitation as Dipole Interaction . . . 70

3.2. Results . . . 70

3.2.1. Methane . . . 70

3.2.2. Ethylene . . . 71

3.2.3. Tetrahydrofuran . . . 78

3.2.4. Pyrimidine and Pyrazine . . . 81

4. Data Compilation and Recommendation 97 4.1. Data Selection Process . . . 97

4.1.1. Inelastic Differential Cross Sections . . . 99

4.2. Recommended Electron-Molecule Scattering Data . . . 101

4.2.1. Methane . . . 101

4.2.2. Ethylene . . . 107

4.2.3. Tetrahydrofuran . . . 112

5. Simulation 125 5.1. Monte Carlo Code Structure . . . 127

5.2. The Low Energy Particle Track Simulation (LEPTS) . . . 128

5.3. Application Examples . . . 132

viii

5.3.1. Electron Tracks and Stopping Power in Methane . . . 132 5.3.2. ¹⁰⁶Ru Applicator in Brachytherapy . . . 136

6. Conclusions 151

6. Conclusiones 155

A. Tabulated Results of IAM-SCAR Calculations 159

A.1. Integral Cross Sections . . . 159 A.2. Elastic Differential Cross Sections . . . 162

B. Recommended Data 223

B.1. Methane . . . 223 B.2. Ethylene . . . 226 B.3. Tetrahydrofuran . . . 227

List of Figures 259

List of Tables 265

List of Publications 267

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Introduction

It is well known [1] that high energy radiation produces abundant secondary electrons (∼ 4 ⋅ 10⁴ per MeV of energy primarily transferred), which are the main source of the energy deposition and radiation damage in biological tis- sues. These low-energy, possibly even sub-ionizing, electrons play an important role for inducing damage such as strand breaks or molecular dissociations in biomolecular systems, as has been extensively demonstrated [e.g. 2–4]. There- fore, when studying radiation effects in biological media, it is essential that the particular electron interaction parameters (integral and differential cross sections, energy loss spectra, partial scattering cross sections especially for dis- sociative interactions or radical generation) in the whole energy range are well known.

This need for accurate and complete electron interaction data applies in princi- ple for all different molecular constituents of biological tissues, including but not limited to water, DNA and RNA nucleobases or, ideally, even entire nucleotides or strands, aminoacids or entire peptides, fatty acid chains, carbohydrates, etc.

It is obvious that the obtention of electron interaction parameters for a simi- lar amount of molecular species is a huge enterprise that, most likely, cannot be accomplished in a timely fashion and could perhaps be best tackled in pro- gressive steps. On the one hand, such an approach is motivated by the sheer number of molecules of interest, and on the other hand, many potentially in- teresting biomolecules are especially demanding for experimentalists as well as for theorists due to their size or physicochemical properties. For those sub- stances/compounds which are not readily accessible for studies with current state-of-the-art methods, building blocks or model molecules may be first used as an approximation.

In view of this situation I aim at contributing to the available electron-molecule

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scattering data pool in various ways that can be viewed as different levels of the complex process of scientific reference data obtention and validation: Firstly, via the construction and benchmarking of a new experimental apparatus which can subsequently be utilized for conducting scattering cross section measure- ments; secondly, through the obtention of original data from experiments and calculations; thirdly, through the critical analysis and comparison to other, pre- viously available, results with regard to the compatibility and completeness of the resulting ensemble of data; furthermore, via the recommendation of carefully selected self-consistent collisional reference data sets for electrons with different molecules; and finally through the simulation of realistic applications using a custom-programmed Monte Carlo code that facilitates the direct use of the data base generated in the previous steps.

Specifically, these objectives are achieved by

1. designing, building and testing a new experimental system based on the strong axial magnetic confinement of the electron beam. This becomes operational for measuring total electron scattering cross sections and can eventually be used for obtaining partial and even absolute differential cross sections.

2. conducting experiments at three different apparatuses that yield electron energy loss distribution functions and total scattering cross sections and, additionally, performing theoretical calculations which conveniently com- plement the measured data.

3. examining my own results in the context of other published data in order to select the most representative and accurate sources for each type of interaction parameter. Those are checked for self-consistency and then recommended as a complete collisional interaction data set in the energy range 1–10 000 eV.

4. integrating the reference data compilations produced in 3. into a simu- lation code which is suitable for modelling radiation damage and energy deposition in a material at the molecular level.

Depending on the availability of experimental and/or theoretical results prior to the beginning of this work, not all of the steps 2.–4. mentioned above were com- pleted for all of the scattering targets studied here (argon, methane, ethylene, tetrahydrofuran, p-xylene, pyrimidine, and pyrazine). Rather, the necessary experiments and further analysis to be carried out were determined based on

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the previously existing ‘coverage’ of a given molecule in published literature.

(Note that for a rarely studied target, there is little sense in attempting to set up a complete scattering data base, but the scientific community should benefit from the measurement of its total cross section. On the other hand, an already heavily investigated molecule will probably only need complementary experi- ments such as electron energy loss spectra, followed by a critical revision of the existing data and its synthesis into a data base.) The aspects or individual studies belonging to the same step or level (according to the outline above), investigated for different targets, are grouped together as the chapters of this thesis in the following way.

The first chapter gives a detailed description of the experimental apparatuses used in the measurements conducted for this work. Special attention is paid to the newly designed, magnetically confined electron scattering system whose construction, testing and start of operation is among the main objectives of the present thesis. Afterwards, in chapter 2, the corresponding experimental results are presented and discussed. This includes high-energy electron energy loss spectra of argon, methane, ethylene, p-xylene, and tetrahydrofuran, low- energy electron energy loss spectra of methane and ethylene, and total electron scattering cross sections of pyrazine and pyrimidine. Chapter 3 then summa- rizes the theoretical methods followed for the calculation of scattering cross sections (CSs). Following, the integral and differential CS results obtained for methane, ethylene, tetrahydrofuran, pyrimidine, and pyrazine are presented and discussed. In the next chapter, the present original results, both experimental and theoretical, for methane, ethylene and tetrahydrofuran are examined in the wider context of the relevant CS data previously reported in the literature before recommending a comprehensive, self-consistent set of elastic and inelas- tic electron-molecule scattering data. Subsequently, chapter 5 deals with the Low-Energy Particle Track Simulation. After a summary of its characteristics and functionalities, two application examples are given. Finally, the conclusions drawn from the present work are presented together with some perspectives for the near future.

Bibliography

[1] I. Plante, F. A. Cucinotta, Cross sections for the interactions of 1eV–100MeV electrons in liquid water and application to Monte-Carlo simulation of HZE radiation tracks, New J. Phys. 11 (2009) 063047.

[2] B. Bouda¨ıffa, P. Cloutier, D. Hunting, M. A. Huels, L. Sanche, Resonant for- mation of DNA strand breaks by low-energy (3 to 20 eV) electrons, Science 287 (2000) 1658–1660.

[3] B. Bouda¨ıffa, P. Cloutier, D. Hunting, M. A. Huels, L. Sanche, Cross sections for low-energy (10-50 eV) electron damage to DNA, Radiat. Res. 157 (2002) 227.

[4] M. A. Huels, B. Bouda¨ıffa, P. Cloutier, D. Hunting, L. Sanche, Single, double, and multiple double strand breaks induced in DNA by 3–100 eV electrons, J. Am. Chem. Soc. 125 (2003) 4467–4477.

Introducci´ on

Es un hecho conocido [1] que las radiaciones de alta energ´ıa producen abundan- tes electrones secundarios (∼ 4 ⋅ 10⁴por MeV de energ´ıa transferida en procesos primarios), que son la principal fuente del dep´osito de energ´ıa y del da˜no por radiaci´on en los tejidos biol´ogicos. Estos electrones de baja energ´ıa, posiblemen- te incluso subionizantes, juegan un importante papel en la inducci´on de da˜nos en sistemas biomoleculares, como roturas de cadena o disociaciones moleculares, como ha sido ampliamente demostrado [p.ej. 2–4]. Por ello, a la hora de estudiar los efectos de la radiaci´on en medios biol´ogicos es esencial que los respectivos par´ametros de interacci´on de electrones (secciones eficaces integrales y diferen- ciales, espectros de p´erdida de energ´ıa, secciones eficaces de dispersi´on parciales especialmente para los casos de interacciones disociativas o la generaci´on de radicales) sean bien conocidos en el rango completo de energ´ıas.

Esta necesidad de datos de interacci´on de electrones exactos y completos se re- fiere en principio a todos los constituyentes moleculares de los tejidos biol´ogicos, incluyendo el agua, las bases del ADN y ARN o, en caso ideal, incluso nucle´otidos o cadenas enteras, amino´acidos o p´eptidos enteros, ´acidos grasos, carbohidra- tos, y muchos m´as. Es obvio que la obtenci´on de par´ametros de interacci´on de electrones para una semejante cantidad de especies moleculares es un enorme proyecto que, muy probablemente, no pueda ser abarcado de forma directa y pueda ser tratado mejor en m´ultiples pasos sucesivos. Por un lado, este enfoque est´a motivado por el mero n´umero de mol´eculas de inter´es, a´unque por otro lado, muchas biomol´eculas potencialmente interesantes tambi´en presentan exigencias especiales tanto para experimentales como te´oricos, debido a su tama˜no o sus propiedades fisico-qu´ımicas. Para aquellas sustancias/compuestos que no sean facilmente accesibles para estudios con los m´etodos del actual estado del arte, m´odulos o mol´eculas modelo pueden ser usados primero como aproximaci´on.

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En vista de esta situaci´on, pretendo contribuir al conjunto de datos de dis- persi´on electr´on-mol´ecula existentes de varias maneras que pueden verse como diferentes niveles del complejo proceso de obtenci´on y comprobaci´on de datos cient´ıficos de referencia: Primero, v´ıa la construcci´on y validaci´on de un nue- vo aparato experimental que ser´a posteriormente utilizado para llevar a cabo medidas de secciones eficaces de dispersi´on; segundo, con la obtenci´on de datos originales mediante experimentos y c´alculos, tercero, a trav´es del an´alisis cr´ıtico y la comparaci´on con otros resultados previamente disponibles con respecto a la compatibilidad y completitud del conjunto de datos resultante; adem´as, median- te la recomendaci´on de unas colecciones de datos de referencia para colisiones de electrones con distintas mol´eculas cuidadosamente seleccionadas y consistentes en s´ı mismas; y finalmente con la simulaci´on de aplicaciones realistas usando un c´odigo Monte Carlo previamente programado para este fin, que facilita el uso directo de las bases de datos generadas en los anteriores pasos.

Espec´ıficamente, estos objetivos se conseguir´an

1. dise˜nando, construyendo y probando un nuevo sistema experimental ba- sado en el fuerte confinamiento magn´etico en direcci´on axial del haz de electrones. Este sistema es puesto en marcha para medir secciones eficaces totales de dispersi´on de electrones y podr´a ulteriormente ser usado para obtener secciones eficaces parciales e incluso diferenciales absolutas.

2. realizando experimentos en tres aparatos diferentes que dar´an como re- sultado las funciones de distribuci´on de p´erdida de energ´ıa de electrones y secciones eficaces totales de dispersi´on; adicionalmente, llevando a ca- bo c´alculos te´oricos que, de forma conveniente, complementar´an los datos medidos.

3. examinando mis propios resultados en el contexto de otros datos publica- dos para seleccionar las fuentes m´as representativas y precisas para cada par´ametro de interacci´on. Los datos escogidos se comprueban en cuanto a la consistencia intr´ınseca y se recomiendan como conjuntos de datos de interacci´on colisional completos en el rango de energ´ıas 1–10 000 eV.

4. integrando las recopilaciones de datos de referencia producidos en 3. en un c´odigo de simulaci´on apropiado para modelizar el da˜no por radiaci´on y el dep´osito de energ´ıa en un material a nivel molecular.

Dependiendo de la disponibilidad de resultados experimentales y/o te´oricos an- tes del inicio de este trabajo, no todos los pasos 2.–4. arriba mencionados se

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completaron para todos los blancos de dispersi´on estudiados aqu´ı (arg´on, me- tano, etileno, tetrahidrofurano, p-xileno, pirimidina y pirazina). Por el contrario, los experimentos y dem´as an´alisis a realizar se determinaron en base a la “cober- tura” previa de una determinada mol´ecula en la bibliograf´ıa existente. (N´otese que para un blanco raramente estudiado, no tiene mucho sentido tratar de es- tablecer una completa base de datos de dispersi´on, pero la comunidad cient´ıfica se beneficiar´a de la medida de su secci´on eficaz total de dispersi´on. Por el otro lado, una mol´ecula ya fuertemente investigada probablemente ´unicamente ne- cesite experimentos complementarios tal como unos espectros de p´erdida de energ´ıa de electrones, seguidos por una revisi´on cr´ıtica de los datos existentes y su s´ıntesis en una base de datos.) Los aspectos o estudios individuales pertene- cientes al mismo paso o nivel (de acuerdo con lo esbozado arriba), investigados para diferentes blancos, son agrupados para formar los cap´ıtulos de esta tesis de la manera descrita a continuaci´on.

El primer cap´ıtulo muestra una descripci´on detallada de los aparatos experimen- tales usados en las mediciones obtenidas para este trabajo. Se presta especial atenci´on al sistema de dispersi´on de electrones, magneticamente confinado y de nuevo dise˜no, cuya construcci´on, prueba y puesta en marcha est´a entre los objetivos principales de la presente tesis. En el cap´ıtulo 2, son presentados y debatidos los correspondientes resultados experimentales. Incluye espectros de p´erdida de energ´ıa de electrones de alta energ´ıa en arg´on, metano, etileno, p- xileno y tetrahidrofurano, espectros de p´erdida de energ´ıa de electrones de baja energ´ıa en metano y etileno, y secciones eficaces totales de dispersi´on de electro- nes de pirazina y pirimidina. Luego, el cap´ıtulo 3 resume los m´etodos te´oricos empleados para el c´alculo de secciones eficaces de dispersi´on. Seguidamente, son presentados y discutidos los resultantes valores de secciones eficaces integrales y diferenciales para metano, etileno, tetrahidrofurano, pirimidina y pirazina.

En el siguiente cap´ıtulo, los presentes resultados originales, tanto experimen- tales como te´oricos, para metano, etileno y tetrahidrofurano se examinar´an en el amplio contexto de las secciones eficaces relevantes publicadas anteriormen- te en la bibliograf´ıa, antes de recomendar un conjunto de datos de dispersi´on el´astica e inel´astica electr´on-mol´ecula extenso y consistente en s´ı mismo. A con- tinuaci´on, el cap´ıtulo 5 trata sobre la simulaci´on de trayectorias de part´ıculas de baja energ´ıa (‘Low-Energy Particle Track Simulation’, LEPTS). Despu´es de un resumen de sus caracter´ısticas y funcionalidades, se dar´an dos ejemplos de aplicaciones. Finalmente, las conclusiones derivadas del presente trabajo son presentadas junto con algunas perspectivas para el futuro pr´oximo.

Bibliograf´ıa

[1] I. Plante, F. A. Cucinotta, Cross sections for the interactions of 1eV–100MeV electrons in liquid water and application to Monte-Carlo simulation of HZE radiation tracks, New J. Phys. 11 (2009) 063047.

[2] B. Bouda¨ıffa, P. Cloutier, D. Hunting, M. A. Huels, L. Sanche, Resonant for- mation of DNA strand breaks by low-energy (3 to 20 eV) electrons, Science 287 (2000) 1658–1660.

[3] B. Bouda¨ıffa, P. Cloutier, D. Hunting, M. A. Huels, L. Sanche, Cross sections for low-energy (10-50 eV) electron damage to DNA, Radiat. Res. 157 (2002) 227.

[4] M. A. Huels, B. Bouda¨ıffa, P. Cloutier, D. Hunting, L. Sanche, Single, double, and multiple double strand breaks induced in DNA by 3–100 eV electrons, J. Am. Chem. Soc. 125 (2003) 4467–4477.

Chapter 1

Experimental Methods and Apparatus

The experimental results presented in this thesis were obtained at three differ- ent apparatuses which are described in the following sections: a newly designed system for electron scattering cross section measurements within a strong mag- netic field (see section 1.1), a transmission beam spectrometer used for mea- suring electron energy loss distributions preferentially at high incident energies (up to keV, see section 1.2), and a differential electron energy loss spectrometer located at the University of Li`ege which is used for measuring differential energy loss spectra, preferentially at low incident energies (see section 1.3 for details).

1.1. Magnetically Confined Electron Scattering System

1.1.1. Design and Technical Characteristics

The design of this experimental apparatus recently constructed in the Radiation- Matter Interaction Laboratory at Instituto de F´ısica Fundamental (CSIC) in Madrid is based on the magnetic confinement of an electron beam from its en- trance into the collision chamber until its energy analysis. Owing to the axial

9

(RPA), 8 - electron detector (microchannel plate assembly), 9 - solenoids, 10 - cooling liquid inlet/outlet. The three regions (electron gun, gas chamber and detector) have separate mag- netic coils producing the fields Bg, B and BRPA, respectively. (b) and (c) Detailed view and electrical connections of the analyzer-detector region and electron gun, respectively. (b) R - retarding electrode, Vpol - polarization voltage of the detector anode. (c) Vacc- accelerating voltage, F⁺ and F⁻ - positive and negative pins of the emitting filament, ext - extraction electrode.

10

1.1 Magnetically Confined Electron Scattering System 11

magnetic field, scattered as well as unscattered electrons are guided in the for- ward direction while retaining all information about their energy and scattering angle and are detected together after the analysis of their energy. One can thus interpret the main magnetic field B simply as a means of transporting the electron, with its exact angle and energy after the collision but its local- ization confined to the central axis of the chamber—or in its initial state if no collision occurred—along the central axis to the end of the collision chamber (entrance collimator of the analyzer/detector region). In the retarding poten- tial analyzer (RPA) region, the independent magnetic field BRPA governs the particle trajectories and an altered beam confinement (gyroradius of the elec- trons’ perpendicular motion) can be used to select which electrons should be analyzed depending on the type of cross section to be measured. In principle, this experimental disposition makes it possible to undertake simultaneous ab- solute measurements of electrons scattered by (almost) all angles in a fashion similar to the one described in [1].

A schematic diagram of the whole apparatus is given in figure 1.1a, and a photo can be seen in figure 1.2. It consists of three separate regions (electron gun, collision chamber and analyzer-detector region) which are connected by 1 mm and 2.3 mm orifices and are differentially vacuum-pumped by two turbomolec- ular pumps of∼450 l/s (Turbovac 450, Leybold Heraeus, Germany) and ∼70 l/s (V-70, Varian, Italy) nominal pumping speed located below the electron gun and above the detector assembly, respectively. They reach a background pres- sure in the detector and electron gun compartments in the order of 10⁻⁷ mbar which can increase to 10⁻⁶mbar during measurements, as determined using two ionization gauges. All three compartments are surrounded by solenoids that are independently controlled and produce the magnetic fields Bg, B, and BRPA. The electron gun (fig. 1.1c) is formed by a tungsten filament (model A054 in- tended for electron microscopy, Agar scientific, United Kingdom) and three 5 mm thick electrodes of 1 mm central aperture (2.5 mm in case of the first one which is penetrated by the filament tip) that are separated from each other by 2 mm. A cloud of free electrons is obtained by thermionic emission from the filament held at negative bias −V^acc. The primary beam is generated by first extracting electrons using electrode ext at +9 V with respect to the filament, then accelerating them with an electrode grounded via the collision chamber.

Finally, the electron beam enters the collision chamber through a further colli- mator. Note that the magnetic field Bg of the electron gun region is oriented to oppose the main field B (collision chamber) in order to compensate the pres- ence of the peripheral components of the latter one inside the electron gun. This

12

1.1 Magnetically Confined Electron Scattering System 13

configuration ensures a low angular spread of the electron beam, since those elec- trons leaving the filament in directions other than the chamber central axis are not guided through the collimators magnetically (see section 1.1.2 for details).

Upon entering the collision chamber, all electrons are magnetically confined by B and, after a potential scattering event, are guided to the retarding potential analyzer while retaining all information about their energy and scattering an- gle. (Electrons scattered by > 90^°are reflected by the extracting electrode and traverse the collision chamber once again before being analyzed.)

The collision chamber itself has a geometrical length of 140 mm and an inner diameter of approximately 60 mm. Both are sufficiently large compared to the delimiting apertures to guarantee a well-defined region of constant pressure inside and steep pressure gradients at both ends. The surrounding magnetic coils, crafted from 3.1 mm thick copper wire insulated with heat-resistent (up to 200^°C) enamel, produce a maximum magnetic field of about 0.2 T when operated with a current of 35 A. A water jacket encases the vacuum chamber in order to facilitate heat dissipation of the solenoid. The target gas (or vapour of liquid or solid samples) is introduced into the system via a variable leak valve (model 951-5106, Agilent Technologies, California). The gas pressure in the chamber is determined by a Baratron capacitance manometer (type 627B, MKS, Germany). The temperature at the inner wall of the collision chamber (which is supposed to accurately reflect also the gas temperature) is monitored using a K-type thermocouple.

After passing into the detector region, the electrons are selected by a retarding potential analyzer (RPA) consisting of three 5 mm thick electrodes of 2.3 mm central aperture separated from each other by 2 mm, which are biased ground/

−V^R/ ground (see electrical scheme in fig. 1.1b). Only those electrons with par- allel (axial) components of the kinetic energy≥ eV^R can overcome the potential barrier and continue towards the detector, while other electrons are rejected by the analyzer and trapped in the chamber. At 9 mm distance from the ana- lyzer, the detector assembly is located. It is formed by two microchannel plates (Hamamatsu photonics, Japan) with a gain of 10^12.5sandwiched between three annular electrodes and followed by the anode as depicted in fig. 1.1b. The to- tal polarization voltage Vpolis divided between the anode and the microchannel plates (MCPs) in such a way that for the typical Vpolof∼2 keV, about 940 V are applied across each MCP. As insinuated in fig. 1.1b, the detector is mounted in a slightly asymmetric fashion with respect to the RPA. This enables a relatively straightforward 90^° rotation of the MCP assembly should localized material fatigue or damage occur in the beam axis.

Pulse Forming and Detection Electronics

The electron detector is operated in single-pulse counting mode throughout all tests and experiments. The cascade produced in the MCPs upon the arrival of an electron is first detected at the anode (polarized with Vpol around +2 keV) as a short negative signal. This electron current reaches a custom-built charge sensitive preamplifier (see figure 1.3) which outputs pulses of≥10 meV height and ∼5 µs duration (this pulse width is, in the configuration described, the principal source of dead time in the detection process and limits the electron count rate to about 10 000 pulses per second, equivalent to an electron current through the analyzer of 1.6⋅10⁻¹⁵A). These are amplified by an amplifier (model 2020, Canberra, Connecticut) set to bipolar output mode where the amplifica- tion is selected such that the maximum output amplitude of 5 V will not be saturated. Only the negative half of the resulting signal is taken into account by the discriminator (constant fraction discriminator 473a, Ortec, Tennessee) which eliminates any electronic and detector noise. The remaining pulses pro- duce standard rectangular signals of 5 V amplitude which are transferred to a data acquisition system (USB-6259, National Instruments, Texas) connected to a PC where a custom LabView (National Instruments) programme finally counts the pulses.

Figure 1.3: Electronic scheme of the preamplifier used in measurements with the magnetically confined electron scattering system.

1.1 Magnetically Confined Electron Scattering System 15

Figure 1.4: Photograph of the rack with most of the experiment’s electronics.

Liquid Cooling

The present experimental set-up depends on water cooling for the turbomolec- ular pump. Additionally, a flexible cooling solution for the coils of the main magnetic field B is of great usefulness with regard to the temperature control when working with solid or liquid samples (see section 1.1.1). For these reasons, a liquid cooling circuit as outlined in figure 1.5 was installed. It consists of a water reservoir (MCRES-Micro Rev2, Swiftech, California) that primes two parallel cooling loops each equipped with a variable speed (30–80 Hz, equivalent to max. 1200 l/h) water pump (Swiftech MCP655) leading to the solenoid and the vacuum pump. Both branches join again before reaching the air-cooled radi- ator (Airplex evo 1080, Aquacomputer, Germany) where the fluid is ventilated by nine 12×12 cm², 1850 rpm fans and then flows back into the reservoir. Dis- tilled water with approx. 5% of Swiftech HydrX anti-fungal heavy duty coolant is used as a cooling liquid. In addition to the water cooling, the solenoid can be air-cooled externally by different fans (10×10 cm² and 8×8 cm²) which are easily turned on and off. This configuration ensures that the turbomolecular pump is reliably cooled in a constant manner, while the temperature of the in- teraction chamber beneath the main solenoid can be controlled to some degree

in response to the electric current applied and/or the temperature required for an experiment with a given sample.

Figure 1.5: Scheme of the liquid cooling circuit. Note the parallel disposition of two branches for independently cooling the main solenoid and the turbomolecular pump.

Preparation for Solid Samples

In order to enable experiments with solid samples in the present apparatus, a total of 69.6 cm² of etched foil silicone heater mats supplied by RS-Amidata (United Kingdom) were attached to the inlet valve and the sample container (see photo in figure 1.6. For this purpose, a ConFlat 16-to-40 adapter closed at the wide end is used as a steel flask). Operated at 24 V, those heater mats attain a total nominal power of 28W and effectively transfer the generated heat to the metal surfaces. In these conditions, the flask and valve reach around 40^°C (some deviations occurred depending on the exact spot of measurement owing to the heater mat distribution/spacing). Higher temperatures could be easily obtained by raising the operating voltage up to∼30 V and/or increasing the number (total surface) of heater mats.

In addition to the heating provided locally around the gas inlet by the heater mats, the temperature of the gas inside the interaction chamber is influenced by the mechanism and intensity chosen for cooling the main magnetic coil. In order to avoid excessive condensation on the chamber wall, and thus obtain a uniform pressure inside the chamber and guarantee an adequate precision of its measurement, the adjustable cooling parameters (pump speed of the ‘magnetic

Figure 1.6: Gas inlet valve and sample containers. Some of the heater mats are visible on the valve and on the steel flask.

17

coil’ branch of the cooling circuit, use of the additional fans) are therefore flexibly adapted to the required chamber temperature.

Even though liquid samples can be usually introduced into the interaction cham- ber via the variable leak valve due to their equilibrium vapour pressure without difficulties, heating the valve even in that case helps to avoid condensation inside and facilitates a constant gas flow. For some oily (or ‘sticky’) liquids which have their melting point close to room temperature, such as pyrimidine, heating was found to be essential for preventing a film of condensed molecules to eventually obstruct the valve.

1.1.2. Tests: Alignment, Focus, Resolution

The first tests of the new experimental system were dedicated to geometrical aspects (focus and alignment) of the electron beam generated, followed by the inspection of the transmission curves obtained with regard to the cut-off be- haviour (shape in the region eVR≈ E) and energy resolution.

As explained above, the electron beam enters the collision chamber after col- limation to a diameter of 1 mm by the entrance orifice. Inside the chamber, the magnetic field B yields a maximum of ∼ 0.2 T capable of maintaining a similar beam diameter after scattering for electron energies up to 2 keV. (The maximum gyroradius of the electron’s perpendicular circular motion after scat- tering is calculated to be 0.5 mm for 1 keV electrons scattered by θ= 90^°.) The beam focus and alignment in vacuum and in the gas-filled (SF6) chamber have been verified (see figure 1.7) and do not exceed 1 mm diameter and 0.5 mm lateral displacement from the geometrical axis of the chamber (this is due to mechanical tolerances of the collimators as well as the filament and its base).

The effective localization of electrons after scattering, and before entering the analyzer, is thus expected to be within a radius of≤ 1 mm around the axis for all incident energies up to 1 keV.

The energy resolution δE of the beam in a given configuration (incident energy, magnetic fields applied, filament current/emission rate) is obtained from the transmission curve I(V^R) in vacuum, where I is the transmitted beam inten- sity (electron count rate) and VR is the retarding potential. It is acquired by ramping the retarding potential via our LabView electron counting programme, whereupon a sharp decrease in intensity appears near the incident beam energy E. Examples including the energy distribution density (gaussian function fitted to the derivative of the transmission curve) are depicted in figure 1.8. When a

1.1 Magnetically Confined Electron Scattering System 19

Figure 1.7: Cross section of the electron beam after traversing the collision chamber as visu- alized with a ZnS luminescence detector and photographed. The blue colour channel of the image files was inverted in order to obtain the present figure. (a) 2 keV electrons in vacuum.

(b) 2 keV beam in 20 mTorr of SF6. In both cases, the beam diameter is <1 mm.

target species is present in the collision chamber, transmission curves adopt a different shape without a sharp beam cut-off (see figure 1.8 for two examples), and exhibiting asymmetric derivatives. This occurs since E_∥^′, in vacuum nearly normally distributed, tends to decrease in response to changes both in electron energy and scattering angle (E_∥^′= E^′cos²θ, where E^′is the electron energy after collision). As a result, I(VR) presents undulations that originate from a super- position of the energy loss spectrum and the angular distribution of scattered electrons.

It should be noted that the angular spread of the primary beam, which depends on the balance of the magnetic fields B and Bg (namely the compensation of stray components of B in the electron gun region), among other factors, crucially influences the cut-off behaviour of the transmission curve (and hence energy resolution). This effect is illustrated in figure 1.9. It can be seen that a current igin the electron gun’s solenoid even slightly too large (a few %) leads to a poorer angular selection of the chamber’s entrance collimators and, as a consequence, to a shallower and visibly irregular slope of the beam intensity near the cut-off potential.

In this study, energy resolution is defined as δE= e(V^R,90−V^R,10)/2, with V^R,90 and VR,10 being the retarding potentials leading to 90% and 10% of transmitted electrons. For the total CS experiments reported, it ranged between 0.37 eV and 5.7 eV and was generally found to be similar to the FWHM (full width at half maximum) of the derivatives obtained. The best resolution observed was 0.25 eV at an incident electron energy of 12 eV.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.2 0.4 0.6 0.8 1

Transmittedbeamintensity ^vacuum_gas

Gaussian fit to derivative

0.85 0.9 0.95 1 1.05

0 0.2 0.4 0.6 0.8 1

Cut-off energy eVR/E vacuum

gas

Gaussian fit to derivative

Cut−off for measurements

Cut−off for measurements

a

b

Figure 1.8: Examples of transmission curves in vacuum and in (a) 1.5 mTorr of pyrimidine (‘gas’) at an incident energy E of 70 eV (b) 4 mTorr of pyrimidine (‘gas’) at E = 500 eV.

Also plotted are Gaussian functions fitted to the derivative of the vacuum transmission curves (corresponding to the electron energy distribution density), scaled to a maximum of 1. In all cases, the transmitted beam intensity is normalized to the maximum (V^R= 0). The cut-off energy of the retarding potential analyzer is given relative to the incident energy.

1.1.3. Measurement Protocol

After conducting some preliminary tests and validation experiments, certain aspects of the experimental work flow were found to be especially important or critical for carrying out reproducible and accurate total cross section mea- surements using the magnetically confined electron scattering system. They are summarized in the following measurement protocol and were taken into account during the preparation, measurement, and data analysis/interpretation of the experiments described in section 2.3.

11 12 13 14 15 16 0

0.2 0.4 0.6 0.8 1

Transmittedbeamintensity

a : ig= 0.65 A b : ig= 0.6 A c : ig= 0.55 A a^′

b^′ c^′

Gaussian fit a^′ Gaussian fit b^′ Gaussian fit c^′

45 46 47 48 49 50 51 52

0 0.2 0.4 0.6 0.8 1

Retarding potential VR

a : ig= 1.5 A b : ig= 1.55 A c : ig= 1.6 A a^′

b^′ c^′

Gaussian fit a^′ Gaussian fit b^′ Gaussian fit c^′

b a

Figure 1.9: Impact of the magnetic field Bg in the electron gun region on the transmission curve. (a) Transmission curves obtained at E = 15 eV in vacuum when applying slightly different magnetic fields Bg, indicated by the respective current ig through the solenoid (a current of 0.6 A produces a field Bg∼5.4 mT). For all three curves, the other fields remained constant at about B = 39 mT and BMCP= 21 mT (produced by the respective currents of 8 A and 10 A) The derivatives a^′, b^′ and c^′ (normalized to a maximum of 1) and Gaussian functions fitted to them are also shown. (b) Analogous situation at E = 50 eV when applying magnetic fields around 14 mT in the electron gun region. B and BMCPwere fixed at 60 and 23 mT (12.5 and 11 A, respectively).

21

Table 1.1: Currents applied to the three solenoids of the magnetically confined electron scat- tering system during total cross section measurements

Beam energy ig i iRPA

(eV) (electron gun) (main field) (analyzer-detector)

8 0.4–0.45 5.0–6.0 10.0

10 0.5 5.7 14.0

10 0.5 6.5 13.0

12 0.5 6.5 13.0

15 0.6 7.0 11.0

20 0.7 9.0 10.5

25 0.75 9.5 10.5

30 0.85 9.5 11.0–11.5

40 0.9 10.0–10.5 13.5

40 0.85 10.0 13.0

50 1.45 12.5 11.5

70 1.75 13.0 11.0

70 1.65 14.5 14.5

100 1.9 14.0 11.0

150 2.15 16.0 10.5

150 2.4 16.0 11.0

200 1.1 17.5 10.0

200 1.5–1.7 17.5–18.0 10.5

300 1.25 20.0 10.0

400 1.25 21.0 11.0–11.5

500 1.3–1.35 22.0 17.0

Before starting a series of measurements, the temperatures of the solenoids (and, thus, of the parts of the vacuum system covered by them) needs to have stabilized within± 1^°in order to avoid drifts in signal intensity. For the same reason, also the electron emitting filament must have reached a stable temperature (∼5 minutes should have elapsed after any variation of the operating current), ensuring a constant emission rate.

Care has to be taken not to exceed a maximum electron rate at the de- tector of about 10 000 pulses per second, otherwise signal losses due to an increased dead time could become non-negligible. (This is of particular importance within any given attenuation curve, as dead time would in

1.1 Magnetically Confined Electron Scattering System 23

this case depend on the count rate—and, indirectly, on the gas pressure—

and effectively skew the curve. Potential single measurement points with higher count rates are thus excluded from a curve.)

Before introducing the sample into the collision chamber, the adequate adjustment of the magnetic fields has to be ensured (and any artifacts avoided) by verifying the cut-off behaviour and resolution of the transmis- sion curve. Whereas the main role of Bgis to counteract B in the electron gun region and so reduce the angular spread, BRPAin the present experi- ments is used to help focus the electrons during their passage through the analyzer. A list of the currents applied to the three solenoids for the ex- periments performed at the different incident energies is given in table 1.1 to provide some orientation.

Beam attenuation curves are obtained with the retarding potential (en- ergy cut-off) value chosen at 85% of the maximum beam intensity in vac- uum, i.e. in such a way that the majority (the higher-energetic 85%) of all electrons are transmitted and will be included in the attenuation mea- surement. This criterion was found to ensure stable and reproducible measurements. Note that the resolution cannot be improved by attempt- ing to measure only a subset of the beam electrons (e.g., by selecting a higher cut-off potential VR).

Sometimes, even though the gas pressure does not exceed the 10⁻⁶ mbar range during measurements, an enhancement of the filament emission (or possibly, of the MCP response) in the presence of the sample gas can be observed. This takes generally place very slowly (at a different time scale than the pressure variation cycles during measurements), however the effect is minimized by delaying the measurements some time after in- troducing the gas into the interaction chamber (at the intended maximum pressure for the respective series), in order to permit the count rate to stabilize.

Due to the occasional observation of plasma focussing effects around the chamber apertures at very low (≤1 mTorr) sample pressures, the intensity value in vacuum (at background pressure) is not included in the mea- surements. Furthermore, due to the poorer precision of the capacitance manometer in the same pressure range, where only one digit can be dis- played, pressures<1 mTorr are avoided whenever this was feasible taking into account the approximate interaction probability (and hence the ex- pected attenuation) at a given energy. This measure leads to a lower

standard deviation amongst the ensemble of curves taken at a given inci- dent energy.

The beam attenuation curves obtained are thoroughly inspected and mea- surement cycles presenting apparent drifts or hysteresis between the curves of pressure increase/reduction are excluded from analysis. Similarly, curves that present undulations or do otherwise noticeably deviate from an expo- nential function—a rare problem being seemingly consequence of a nonuni- form pressure distribution and which can be solved by heating the collision chamber—are discarded.

Due to the strong focussing of the beam accomplished by the magnetic fields, the microchannel plates detect most of the electrons in very few channels. Since this circumstance could enhance material fatigue of the MCPs, leading to a poor electron multiplication or the need of a higher polarization voltage, the typical primary pulse height (as produced in the preamplifier) and the exact correlation of primary pulses and discriminator counts is checked on a regular basis.

A series of measurements yielding the total CS value at a given incident electron energy typically consisted of 7–10 attenuation curves acquired in alternating di- rections (increasing/decreasing pressure), each comprising normally 7–12 data pairs (pressure p and intensity I) and taking about 2–3 minutes to complete.

The intensity (count rate) was recorded continuously by a custom LabView pro- gramme connected to the data acquisition device and was afterwards analyzed manually in Matlab (The MathWorks, Massachusetts) to yield the averaged val- ues Ii for each pressure pi and, finally, an exponential attenuation curve I(p).

Representative examples at different incident energies can be seen in figure 1.10.

For details regarding the CS calculation from the fit function’s exponent, refer to section 2.3). For measurements that adhere to the conditions described above, the experimental uncertainty discussed in the following section applies.

1.1.4. Experimental Uncertainties

Statistical Uncertainties

General experimental uncertainties for the total CS measurements carried out at the magnetically confined electron scattering system are introduced by different variables. The effective collision chamber length l= lgeom+ 0.5d1+ 0.5d2(where

1.1 Magnetically Confined Electron Scattering System 25

1 2 3 4 5 6

0.1

Pressure [mTorr]

I/I0

10 eV 15 eV 30 eV 70 eV 100 eV 150 eV 200 eV 300 eV 500 eV

Figure 1.10: Example of representative attenuation curves, for incident electron energies from 10 eV to 500 eV (original data points (p, I) and exponential fit function), for scattering from pyrimidine.

lgeomis the geometrical length and d1and d2are the thicknesses of the delimiting boreholes where the pressure falls off) is afflicted with an uncertainty of±1.1%, obtained after quadratically summing the contributions arising from the length measurement (estimated 1 mm) and half of the difference in l whether or not taking into account d1+ d2 ≈ 2.5 mm) in l. Pressure measurements inside the chamber are accurate to<0.5% according to the manufacturer’s calibration. The collision chamber’s temperature is determined with an uncertainty of 2.5K by the thermocouple which converts to 1% in the range of temperatures observed and after admitting an additional 0.5% uncertainty for the multimeter readout.

The incident beam energy is affected by an uncertainty of approximately +1 eV, estimated through the comparison of the acceleration potential (at the filament) and the beam cut-off energy (at the analyzer). This corresponds to 0.2–10% of the incident energy in the range studied here and is equivalent to an uncertainty between 0.2% and 2–4.7% (at 500 eV and 10 eV, respectively) on the CS values measured for the two pyrazines (see section 2.3). The pulse processing circuitry efficiently discriminates against electronic noise, so no further uncertainty has to be assumed in this respect.

The standard deviation among the measurements of each series, calculated as a measure of the experiment’s reproducibility, was typically ≤3%. The exper- imental conditions influencing this amount are the filament emission stability,

temperature stability (particularly of the collision chamber temperature) during an experiment, and signal fluctuations caused by the electronic circuitry. Addi- tionally, the cited reproducibility comprises the uncertainty in the determination of the fit function (exponent of the attenuation curve) from the measured values.

Combining the aforementioned factors, one obtains a general precision of the present experimental total cross section determination of 3.5–4.4% at incident energies ≥20 eV, and of <5.1% for incident energies ≤15 eV (more details are given in section 2.3).

Angular acceptance

In addition to the general uncertainty of statistical nature discussed above, the angular acceptance δθ of the apparatus is a limiting aspect and presents an important source of systematic error. Due to the axial magnetic confinement, scattered electrons will pass the analyzer if the kinetic energy E_∥^′, corresponding to the parallel component of their velocity v_∥^′, can overcome the retarding poten- tial VR, i.e. mev^′_∥²/2 ≥ eVR (where me is the electron mass; the non-relativistic relationship between velocity and kinetic energy can be assumed for the present experimental electron energies not exceeding 500 eV). Those electrons are hence identified as ‘unscattered’ and do not contribute to the measured beam atten- uation. The angular resolution in forward direction (which is at the same time the angular acceptance of elastically scattered electrons that applies during total cross section measurements) of an experiment can thus be easily calculated from the energy resolution δE as obtained from the corresponding transmission curve.

An elastic collision, as sketched in figure 1.11, is supposed since it represents the case where scattered electrons have to be distinguished from unscattered ones based only on the scattering angle θ and the smallest distinguishable scattering angle is directly affected by the energy resolution. In this case,

E^′_∥= E cos²(δθ) = E − δE (1.1)

δθ= arccos

√ 1−δE

E = arcsin

√δE

E . (1.2)

In any comparison of the present experimental results to other total CS data it thus needs to be taken into account that the elastic scattering angles 0≤ θ ≤ δθ and 180−δθ ≤ θ ≤ 180 (for the case of backscattered and reflected electrons) are not distinguished from unscattered electrons.

1.1 Magnetically Confined Electron Scattering System 27

Figure 1.11: Parallel and perpendicular components of an elastically scattered electron’s ve- locity and kinetic energy.

For inelastically scattered electrons, E_∥^′ depends on energy loss as well as on the scattering angle. For the experiments conducted (see section 2.3) it can be generalized that electronically inelastic energy losses are readily resolved, while rotational excitation energies remain energetically unresolved. In order to be detected as ‘scattered’ after collisions leading to rotational excitations, electrons therefore need to exhibit scattering angles similar to δθ.

In consequence, the experimental values σexprepresent in fact an apparent value ignoring the contributions of electrons scattered elastically or rotationally in- elastically into extremely small and large angles (≤ δθ and ≥ 180 − δθ):

σexp(E) ≈ σ(E) − σ^forw(E) with (1.3) σforw= 2π(∫₀^δθd(σ^el+ σ^rot)

dΩ sin θdθ+ ∫_180−δθ¹⁸⁰ d(σ^el+ σ^rot)

dΩ sin θdθ), (1.4) where σel and σrot denote the integral elastic and rotational CS, respectively.

Although it should be also considered that, depending on the energy resolu- tion attained, vibrational excitations of the ground state may in principle also contribute to σforw, these vibrations are estimated to represent≤ 1% (reaching 2.5% for merely one experimental point, at 8 eV) of the elastic scattering in terms of the absolute integral cross sections [2, 3]. We have therefore neglected the respective contribution to the systematic error (of the order of ^‡ of the experimental values) in comparison to that derived for the elastic scattering and rotational excitations.

The error introduced by the angular acceptance (1.2) consists always in an un- derestimation of the total CS, as some of the scattered electrons are detected as if they had not undergone any collision and thereby cause a smaller beam attenuation with increasing pressure as would correspond to the ‘true’ total CS (σ). Since the angular resolution depends on the incident electron energy and the exact circumstances (transmission curve) of each series of measurements, no

global value can be given. For the measurements carried out, the angular ac- ceptance δθ lies in the range 3.3^°–18.2^°and is explicitly stated for each total CS measurement in section 2.3. Based on this value, a reasonably accurate estima- tion of the corresponding systematic error can be derived using the theoretical IAM-SCAR results presented in chapter 3. This error estimation will be also presented and discussed in the Results section 2.3 and should be understood as additional to the statistical uncertainty discussed in the previous section.

1.1.5. Benchmarking measurements

In order to validate our apparatus and our measurement procedures, some pre- liminary total electron scattering cross section measurements were conducted with argon according to the measurement protocol described in section 1.1.3.

The total CS obtained for a few incident energies in the range 20–500 eV are plotted in figure 1.12 together with some results reported in the literature [4–7].

As can be seen, there is excellent accord (≤ 2.5% difference) between these pre- liminary results and the data published by Nickel et al. [4], Szmytkowski et al.

[5] and Zecca et al. [6].

Figure 1.12: Total electron scattering cross sections for argon as measured in preliminary tests and comparison to existing data [4–7].

1.2 Transmission Beam Spectrometer 29

1.2. Transmission Beam Spectrometer

Figure 1.13: Sketch of the transmission beam spectrometer located in Madrid and used in the high energy range. 1 - electron emitting filament, 2 - extraction and accelerating electrodes, 3 - quadrupole electrostatic plates for beam deflection, 4 - decelerating and accelerating lenses for beam focussing, 5 - collision chamber; 6 - retarding potential analyzer, 7 - hemispherical electrostatic energy analyzer, 8 - channel electron multiplier, 9 - turbomolecular vacuum pumps

The transmission beam system used for acquiring high-energy electron energy loss (EEL) spectra has been described earlier by Garc´ıa and Manero [8] and Williart et al. [9]. Here, only a brief description of the present configuration is therefore given. A schematic diagram of the entire apparatus is provided in figure 1.13. The three regions (electron gun, collision chamber, analyzer) are differentially pumped by two turbomolecular pumps of 70 l/s and 250 l/s speed (Varian, Italy) reaching a background pressure lower than 10⁻⁶mbar.

The primary beam is emitted from a home-made, negatively biased tungsten filament and collimated and accelerated by extraction and acceleration elec- trodes, the last of which is grounded and presents an inner diameter of 1 mm.

Subsequently, the electrons pass an electrostatic quadrupole lens system which controls the beam’s direction and reduces its energy spread. The electron beam is again focussed by 2 mm-aperture diaphragms and passes the entrance orifice of the gas-filled (typically ∼0.01 mbar) collision region. It has a total geo- metrical length of 33 mm and is delimited by two diaphragms of 1 (entrance) and 1.5 mm (exit) aperture. The sample gas is introduced via a variable leak valve (Varian, Italy) and its pressure is determined by an absolute capacitance manometer (type 627B, MKS, Germany). The entire interaction chamber can be biased at a negative potential if necessary, implying that the electron in-

teractions do effectively take place at a lower potential energy than the initial acceleration potential. This method enables experiments with electron energies as low as 5 eV or less without requiring any additional shielding against stray electric and/or magnetic fields. (On various occasions, the energy loss spectra obtained at identical interaction energy but using different chamber potentials have been compared and no deviations exceeding normal statistical uncertain- ties have been observed.) Typical electron currents in the interaction region were of 10⁻¹³ A. At the chamber exit, a further quadrupole lens system is used to deflect the transmitted beam before entering the analyzer region. There, it is retarded with a three-element lens and analyzed by means of a hemispheri- cal electrostatic spectrometer at a constant pass energy of∼100 eV. Finally, the electrons are detected using a channel electron multiplier working in single-pulse counting mode. The energy resolution achieved by this experimental system is

≤2 eV (FWHM) over the whole energy range. Usually, spectra were recorded up to an energy loss of about 95 eV (max. ∆E= E) for all incident energies.

This high-energy system is designed for directly measuring an average EEL spec- trum for mixed small angles—accounting for the majority of scattering events in the energy range 100–10 000 eV—due to the transmission beam technique used.

By deflecting the beam before and after the collision chamber in a way that only the intensity above∼10% of the maximum (primary beam) was considered while avoiding the primary beam itself, the angular range was selected such that the measurements represent the scattered electrons contributing most to the integral inelastic CS (approx. 0-15^°). The uncertainty introduced by electrons scattered beyond the angular acceptance is ≤5% in terms of the average energy loss of a distribution for the molecules here included and in the corresponding energy range studied. This includes particularly the possibly distorting effect of elec- trons having suffered high energy losses and being thus preferentially scattered by higher angles, according to the conclusions of section 4.1.1. Note that this uncertainty lies around or below the statistical variation that has been observed between single energy loss spectra (5–14% difference in the average energy loss values).

1.3. Differential Electron Energy Loss Spectrometer

The high-resolution, differential electron energy loss spectrometer (modified Vacuum Generator SEELS 400) used for acquiring low-energy (≤ 100 eV) dis-

1.3 Differential Electron Energy Loss Spectrometer 31

tributions has been described earlier by Furlan et al. [10] and Motte-Tollet et al. [11]. Only a brief description of the apparatus is therefore given here. A schematic diagram of the instrument is provided in figure 1.14. The outer vessel is built of mumetal which reduces any residual (stray) magnetic fiels to≤2 mG in the interaction region. Background pressure is maintained at 2⋅10⁻⁸Torr by a turbomolecular and a cryogenic pump. A 150^°hemispherical-sector electrostatic electron monochromator followed by focussing and accelerating electrodes pro- duces an energy-selected electron beam (∼ 5−10⋅10⁻¹⁰A) of the desired impact energy. This is crossed at 90^°with an effusive molecular beam which enters the vacuum via a hypodermic needle of 1 mm diameter, enclosed in a molybdenum cylinder in order to minimize the presence of stray electric fields in the colli- sion region. In experimental conditions (when sample gas is introduced into the apparatus), pressure increases to 1⋅ 10⁻⁵ Torr. After scattering, electrons are focused into the entrance of a second 150^°hemispherical electrostatic monochro- mator used as an energy analyzer. It can be rotated by an angle θ from -35^° to 120^°with respect to the incident electron direction in a plane perpendicu- lar to the molecular beam for performing angularly differential measurements.

The analyzer is operated in combination with a retarding potential at constant pass energy. Finally, electrons are detected by a channel electron multiplier (channeltron).

During the experiments presented in section 2.2, the apparatus was operated in energy loss mode, i.e. at fixed electron impact energy and angle, but variable retarding potential so that the electron energy loss distribution of the elastic peak and the complete inelastic region (until energy losses ∆E of approximately the incident energy E) was directly recorded. The energy loss distributions presented (see section 2.2) result from the accumulation of numerous groups of individual spectra. These groups were calibrated separately before addition in order to take into account possible potential drifts. The energy resolution of the elastic peak was found to be in the range of 40–80 meV (FWHM), while a step size of 20–40 meV was used for controlling the retarding potential.

6 - needle used for introducing sample gas, 7 - Faraday cup, 8 - focussing lenses, 9 - retarding potential, 10 - energy analyzer, 11 - channeltron.

32

BIBLIOGRAPHY 33

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