Photoelectron Spectroscopy on Atoms, Molecules and Clusters

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 375

The Geometric and Electronic Structure Studied by Synchrotron Radiation and Lasers

TORBJÖRN RANDER

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– Olof Rudbäck d. ä.

ListofPapers

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

I Experimental evidence for molecular ultrafast dissociation in O2 clusters T. Rander, M. Lundwall, A. Lindblad, G. Öhrwall, M. Tchaplyguine, S. Svensson, O. Björneholm Eur. Phys. J. D 42, 253-257 (2007)

II Suppression of the ultrafast dissociation of bromomethane molecules in clusters T. Rander, A. Lindblad, A. Rosso, H. Bergersen, G. Öhrwall, S. Svensson, O. Björneholm In manuscript

III Core-level electron spectroscopy on the sodium dimer Na 2p level T. Rander, J. Schulz, M. Huttula, A. Mäkinen, M. Tchaplyguine, S. Svensson, G. Öhrwall, O. Björneholm, S. Aksela, H. Aksela Phys. Rev. A 75, 032510 (2007)

IV The diffusion behavior of O2 doped on large Ar clusters T. Rander, A. Lindblad, M. Lundwall, M. Tchaplyguine, G. Öhrwall, S. Svensson, O. Björneholm Submitted to J. Chem. Phys.

V The far from equilibrium structure of argon clusters doped with krypton or xenon A. Lindblad, H. Bergersen, T. Rander, M. Lundwall, G. Öhrwall, M. Tchaplyguine, S. Svensson, O. Björneholm Phys. Chem. Chem. Phys. 8, 1899-1905 (2006)

5 VI The role of molecular polarity in cluster local structure studied by photoelectron spectroscopy A. Rosso, T. Rander, H. Bergersen, A. Lindblad, M. Lundwall, S. Svensson, M. Tchaplyguine, G. Öhrwall, L. J. Sæthre, O. Björneholm Chem. Phys. Lett 435, 79-83 (2007)

VII Shakedown in core photoelectron spectra from aligned laser-excited Na atoms J. Schulz, M. Tchaplyguine, T. Rander, O. Björneholm, S. Svensson, R. Sankari, S. Heinäsmäki, H. Aksela, S. Aksela, E. Kukk Phys. Rev. A 72, 10702-1-4 (2005)

VIII Characterization of weakly excited ﬁnal states by shakedown spectroscopy of laser-excited potassium J. Schulz, S. Heinäsmäki, R. Sankari, T. Rander, A. Lindblad, H. Bergersen, G. Öhrwall, S. Svensson, E. Kukk, S. Aksela, H. Aksela Phys. Rev. A 74, 12705-1-6 (2006)

Reprints were made with permission from the publishers.

6 The following is a list of papers to which I have contributed, but which are not included in this thesis.

Observation of elastic scattering effects on photoelectron angular distributions in free Xe clusters G. Öhrwall, M. Tchaplyguine, M. Gisselbrecht, M. Lundwall, R. Feifel, T. Rander, J. Schulz, R. R. T. Marinho, A. Lindgren, S. L. Sörensen, S. Svensson, O. Björneholm J. Phys. B 36, 3937-49 (2003)

Femtosecond Interatomic Coulombic Decay in Free Neon Clusters: Large Lifetime Differences between Surface and Bulk G. Öhrwall, M. Tchaplyguine, M. Lundwall, R. Feifel, H. Bergersen, T. Rander, A. Lindblad, J. Schulz, S. Peredkov, S. Barth, S. Marburger, U. Hergenhahn, S. Svensson, and O. Björneholm Phys. Rev. Lett. 93, 173401 (2004)

Final state selection in the 4p photoemission of Rb by combining laser spectroscopy with soft-x-ray photoionization J. Schulz, M. Tchaplyguine, T. Rander, H. Bergersen, A. Lindblad, G. Öhrwall, S. Svensson. S. Heinäsmäki, R. Sankari, S. Osmekhin, S. Aksela, H. Aksela Phys. Rev. A 72, 32718-1-4 (2005)

The electronic structure of free water clusters probed by Auger electron spectroscopy G. Öhrwall, R. F. Fink, M. Tchaplyguine, L. Ojamae, M. Lundwall, R. R. T. Marinho, A. N. de Brito, S. L. Sörensen, M. Gisselbrecht, R. Feifel, T. Rander, A. Lindblad, J. Schulz, L. J. Sæthre, N. Mårtensson, S. Svensson, O. Björneholm J. Chem. Phys 123, 54310-1-10 (2005)

Ioniclike energy structure of neutral core-excited states in free Kr clusters S. Peredkov, A. Kivimäki, S. L. Sörensen, J. Schulz, N. Mårtensson, G. Öhrwall, M. Lundwall, T. Rander, A. Lindblad, H. Bergersen, S. Svensson, O. Björneholm, M. Tchaplyguine Phys. Rev. A 72, 21201-1-4 (2005)

7 Postcollision interaction in noble gas clusters: observation of differences in surface and bulk line shapes A. Lindblad, R. F. Fink, H. Bergersen, M. Lundwall, T. Rander, R. Feifel, G. Öhrwall, M. Tchaplyguine, U. Hergenhahn, S. Svensson, O. Björneholm J. Chem. Phys. 123, 211101-1-4 (2005)

Enhanced surface sensitivity in AES relative to XPS observed in free Ar clusters M. Lundwall, M. Tchaplyguine, G. Öhrwall, A. Lindblad, S. Peredkov, T. Rander, S. Svensson, O. Björneholm Surf. Sci. 594, 12-19 (2005)

Photon energy dependent intensity variations observed in Auger spectra of free argon clusters M. Lundwall, A. Lindblad, H. Bergersen, T. Rander, G. Öhrwall, M. Tchaplyguine, S. Peredkov, S. Svensson, O. Björneholm J. Phys. B 39, 3321-33 (2006)

Shell-dependent core-level chemical shifts observed in free xenon clusters M. Lundwall, R. F. Fink, M. Tchaplyguine, A. Lindblad, G. Öhrwall, H. Bergersen, S. Peredkov, T. Rander, S. Svensson, O. Björneholm J. Phys. B 39, 5225-35 (2006)

Lineshapes in carbon 1s photoelectron spectra of methanol clusters M. Abu-samha, K. K. Børve, L. J. Sæthre, G. Öhrwall, H. Bergersen, T. Rander, O. Björneholm, M. Tchaplyguine Phys. Chem. Chem. Phys 8, 2473-82 (2006)

Preferential site occupancy of krypton atoms on free argon-cluster surfaces M. Lundwall, A. Lindblad, H. Bergersen, T. Rander, G. Öhrwall, M. Tchaplyguine, S. Svensson, O. Björneholm J. Chem. Phys 125, 14305-1-7 (2006)

Laser excitation combined with 2p photoionization and Auger decay of potassium K. Jänkälä, R. Sankari, J. Schulz, M. Huttula, A. Calo, S. Heinäsmäki, S. Fritsche, T. Rander, S. Svensson, S. Aksela, H. Aksela Phys. Rev. A 73, 22720-1-8 (2006)

8 Magnetron-based source of neutral metal vapors for photoelectron spectroscopy M. Tchaplyguine, S. Peredkov, H. Svensson, J. Schulz, G. Öhrwall, M. Lundwall, T. Rander, A. Lindblad, H. Bergersen, S. Svensson, M. Gisselbrecht, S. L. Sorensen, L. Gridneva, N. Mårtensson, O. Björneholm Rev. Sci. Instrum. 77, 033106 (2006)

5p photoemission from laser-excited cesium atoms J. Schulz, M. Määtä, S. Heinäsmäki, M. Huttula, R. Sankari, E. Kukk, T. Rander, S. Svensson, S. Aksela, H. Aksela Phys. Rev. A 73, 062721 (2006)

Self-assembled heterogeneous argon/neon core-shell clusters studied by photoelectron spectroscopy M. Lundwall, W. Pokapanich, H. Bergersen, A. Lindblad, T. Rander, G. Öhrwall, M. Tchaplyguine, S. Barth, U. Hergenhahn, S. Svensson, O. Björneholm J. Chem. Phys. 126, 214706 (2007)

Synchrotron radiation study of chloromethane clusters: Effects of polarizability and dipole moment on core level chemical shifts A. Rosso, A. Lindblad, M. Lundwall, T. Rander, S. Svensson, M. Tchaplyguine, G. Öhrwall, O. Björneholm J. Chem. Phys. 127, 024302 (2007)

Free nanoscale sodium clusters studied by core-level photoelectron spectroscopy S. Peredkov, G. Öhrwall, J. Schulz, M. Lundwall, T. Rander, A. Lindblad, H. Bergersen, A. Rosso, W. Pokapanich, N. Mårtensson, S. Svensson, S. L. Sorensen, O. Björneholm Phys. Rev. B 75, 235407 (2007)

Direct observation of the non-supported metal nanoparticle electron density of states by X-ray photoelectron spectroscopy M. Tchaplyguine, S. Peredkov, A. Rosso, J. Schulz, G. Öhrwall, M. Lundwall, T. Rander, A. Lindblad, H. Bergersen, W. Pokapanich, S. Svensson, S. L. Sorensen, N. Mårtensson, O. Björneholm Eur. Phys. J. D 45, 295 (2007)

9 Localized versus delocalized excitations just above the 3d threshold in krypton clusters studied by Auger electron spectroscopy M. Tchaplyguine, A. Kivimäki, S. Peredkov, S. L. Sorensen, G. Öhrwall, J. Schulz, M. Lundwall, T. Rander, A. Lindblad, A. Rosso, S. Svensson, N. Mårtensson, O. Björneholm J. Chem. Phys. 127, 124314 (2007)

10 Contents

List of Papers ...... 3 Comments on my own participation ...... 12 1 Populärvetenskaplig sammanfattning ...... 15 1.1 De olika experimenten ...... 15 1.2 Experimentella metoder ...... 17 1.2.1 Elektromagnetisk strålning ...... 17 1.2.2 Elektronspektroskopi ...... 17 1.3 Beräkningar ...... 19 1.4 Resultat ...... 19 2 Introduction ...... 21 3 Fundamental concepts ...... 23 3.1 The electronic structure of matter ...... 23 3.1.1 Atoms ...... 23 3.1.2 Molecules ...... 25 3.1.3 Clusters and solids ...... 27 3.2 The geometric structure of matter ...... 28 3.3 The photoelectric effect ...... 30 4 Experimental equipment ...... 33 4.1 Vacuum ...... 33 4.2 Synchrotron radiation ...... 34 4.3 Laser Light ...... 36 4.4 The MAX laboratory and beam-line I411 ...... 37 4.5 Sample production ...... 39 4.5.1 Cluster production ...... 39 4.5.2 Doped cluster production ...... 40 4.5.3 Metal vapor production ...... 41 5 Probing techniques ...... 43 5.1 Ultra-violet Photoelectron Spectroscopy (UPS) ...... 43 5.2 X-ray Photoelectron Spectroscopy (XPS) ...... 44 5.3 Auger Electron Spectroscopy (AES) ...... 45 5.4 Near-edge Absorption Fine Structure (NEXAFS) ...... 46 5.5 Resonant Auger Spectroscopy (RAS) ...... 47 5.6 Interpretation of X-ray spectra ...... 48 5.6.1 Koopmans theorem and the chemical shift ...... 48 5.6.2 Atomic photoelectron spectra ...... 49 5.6.3 Molecular photoelectron spectra ...... 49 5.6.4 Cluster photoelectron spectra ...... 50 6 Summary of papers ...... 53 6.1 Dissociation of molecules ...... 53 6.1.1 Oxygen clusters ...... 54 6.1.2 Bromomethane clusters ...... 55 6.1.3 Sodium dimers ...... 59 6.1.4 Conclusions ...... 60 6.2 The structure of doped and molecular clusters ...... 61 6.2.1 Conclusions ...... 65 6.3 Laser excited metal vapors ...... 66 6.3.1 Conclusions ...... 69 7 Future outlook ...... 71 8 Acknowledgments ...... 73 Bibliography ...... 75

12 Commentsonmyownparticipation

Working in the field of experimental physics takes a lot of team-work, and all of the papers in this thesis reflect this fact. Without the fruitful exchange of ideas and without a helping hand running the experiments, not much of the work presented here could have been performed. Common to all of the included articles is that I have been actively involved in the experiments, and in discussions regarding them. For the papers where I am the first author, I was the main responsible for data analysis and manuscript preparation.

1. Populärvetenskaplig sammanfattning

Världen vi lever i, och allt som ﬁnns däri, består av atomer. En atom består av en atomkärna, som är positivt laddad, och negativt laddade elektroner. Atom- kärnan består i sin tur av ännu mindre enheter, så kallade neutroner och pro- toner. De består i sin tur av ännu mindre byggstenar, men detta behöver vi inte tänka så mycket på i vårt fall eftersom atomkärnan är väldigt liten (c:a 10000 gånger mindre än hela atoms storlek). I våra experiment kan vi där- för behandla atomkärnan som en laddad punkt. Atomer hittar man ibland tillsammans med andra atomer, i molekyler, kluster eller fasta material. Ett kluster är en “liten” klump av atomer eller molekyler (3-50000 st), som sitter ihop med varandra. Man brukar säga att ett kluster är ett system som länkar samman förståelsen för egenskaperna hos en enskild atom eller molekyl, och förståelsen för egenskaperna hos ett fast material. Denna avhandling handlar om atomer, molekyler och kluster, och vad som kan hända när man blandar dessa, eller utsätter dem för laserljus eller röntgenstrålning. Egenskaperna hos en atom, en molekyl eller ett kluster bestäms av dess geometriska struktur (hur atomer eller molekyler sitter ihop i en större en- het) och av dess elektroniska struktur (hur elektronerna är fördelade kring en atom, en molekyl eller i ett kluster). Vi har undersökt (med direkta metoder) denna elektroniska struktur, och kan genom denna dra ganska långtgående (indirekta) slutsatser också om den geometriska strukturen hos de studerade systemen i vissa fall.

1.1 De olika experimenten Grovt sett kan vi dela in denna avhandling i tre delar. De första tre inkluderade arbetena behandlar processer i molekyler, som sker när en molekyl be- strålas med röntgenstrålning av varierande energi. I de två första arbetena har vi undersökt hur molekylers beteende förändras då de sitter ihop med andra molekyler av samma sort i ett kluster. Systemen vi har studerat är kluster av tusentals syremolekyler och kluster av hundratals metylbromidmolekyler. Vi har även studerat vad som händer när man bestrålar en mer exotisk molekyl, nämligen natriumdimeren, Na2, utan att den befinner sig i ett kluster. Vi ville ta reda på om molekylerna går sönder när de bestrålas, och i så fall om de går sönder “lika mycket” och lika ofta när de befinner sig i kluster som när de är i en gas. Att studera sådana system är intressant, eftersom det finns många ställen där kluster och exotiska molekyler förekommer, men där man inte kan

15 komma åt att göra mätningar. Man tror till exempel att mycket av den absorption av den elektromagnetiska strålning som kommer från rymden görs av små vattenkluster, och att mycket av den kemi som sker i atmosfären (till exempel den s.k. Ozon-cykeln) katalyseras på olika sätt genom förekomsten av kluster. Vi har också studerat den geometriska strukturen hos kluster av metylbro- mid. Metylbromidmolekylen är vad man kallar en permanent dipol, vilket be- tyder att många av elektronerna i molekylen finns vid en av dess ändar. Detta gör att den får en elektriskt negativ laddning i änden där de flesta elektronerna finns, och en positiv laddning där det finns färre elektroner. Detta fenomen kallas för polarisation. Strukturen hos kluster som skapats genom att vi låtit kluster krocka med med atomer och molekyler som då fastnat på eller i klustret (så kallad “dopning”) har även den undersökts. Man kan tänka sig att detta sker på ungefär samma sätt som om man skulle hälla russin på en stor klump smör. Som figur 1.1 visar, så finns det två varianter av hur detta kan ske. Vilken som inträffar beror på smörklumpens temperatur.

Figur 1.1: Den vänstra bilden visar vad som händer med russinen som hälls på smör som man precis tagit ur kylskåpet. Den högra bilden visar vad som händer med russinen om de hälls på smör som man värmt upp i en kastrull.

Om man precis har tagit ut smörklumpen ur kylskåpet så fastnar som vi alla vet russinen på smörets yta, men om vi smält smöret innan vi häller russinen på det så hamnar de inuti det som tidigare var smörklumpen. Ungefär samma sak händer med klustren när de dopas, eftersom varje krock som klustret ut- sätts för tillför det lite värme. Vi har mätt hur mängden kollisioner påverkar strukturen hos dessa kluster. Sist, men inte minst, har vi också mätt vad som händer med den elektroniska strukturen hos två olika atomslag (natrium och kalium) som först belyses med laserljus, och sedan bestrålas med röntgenstrålning. Sådana mätningar kan ge värdefull information om hur den elektroniska strukturen i en atom eller molekyl ser ut innan den belyses med laserljus, eftersom det inte alltid är helt

16 icke-joniserande strålning joniserande strålning

ökande våglängd ökande energi

Lågfrekvens Mikrovågor UV Gamma

Radio IR Röntgen

Synligt Figur 1.2: Figuren visar olika våglängder av elektromagnetisk strålning, samt vad dessa brukar kallas.

enkelt att studera detta på grund av diverse effekter som gör att elektronstrukturen blir “diffus”; somliga elektroniska tillstånd kan till exempel blanda sig med varandra i atomens grundtillstånd, så kallad konﬁgurationsväxelverkan.

1.2 Experimentella metoder En mängd kompletterande experimentella tekniker har använts för att genom- föra de studier som presenteras i denna avhandling. De flesta av dessa kan klassificeras som s.k. elektronspektroskopier, men även andra tekniker, så som mass-spektroskopi och fluorescensmätningar har varit till hjälp under det experimentella arbetet.

1.2.1 Elektromagnetisk strålning Egentligen är ljus och röntgenstrålning samma sak, och kallas tillsammans med många andra former av strålning (ex. vis. radiovågor, gammastrålning och mikrovågor) för elektromagnetisk strålning. Det som skiljer de två först- nämnda åt är våglängden, alltså energi-innehållet hos var och en av dem. Rönt- genstrålning innehåller mycket mer energi än vanligt ljus gör. Figur 1.2 visar en bild av de olika våglängdsområdena för elektromagnetisk strålning. I våra experiment används dels laserljus och dels röntgenstrålning för olika ändamål. Laserljuset främsta användningsområde var att preparera exciterade tillstånd i metallatomerna, medans röntgenstrålningens främsta uppgift var att jonisera våra prov.

1.2.2 Elektronspektroskopi Efter det att vi joniserat vårt prov med röntgenstrålning kan vi mäta en mängd olika saker. En möjlighet är att mäta massan hos den kvarvarande jonen, för att på så sätt få reda på om systemet vi joniserat har gått sönder i processen eller

17 ej. En annan möjlig mätning är att mäta energin hos den elektron som frigörs från molekylen genom jonisationen. Det är detta, som kallas för fotoelektron- spektroskopi, som vi oftast utför i våra experiment. Figur 1.3 visar en schematisk bild över den elektroniska strukturen hos en atom. De energinivåer där det ﬁnns, eller potentiellt kan ﬁnnas elektroner kallas för orbitaler. Jonisationsgräns EE

Tom valensorbital Laserljus Fyllda } valensorbitaler

Core-orbital

Grundtillstånd Exciterat tillstånd

Figur 1.3: En schematisk bild över elektronstrukturen hos en atom i sitt grundtillstånd, och i ett exciterat tillstånd.

Man kan även mäta så kallade Augerelektroner. Vid en röntgenjonisation bildas en vakans i elektronstrukturen. Detta gör att elektroner i den yttre elektronstrukturen känner en positiv laddning. Elektronerna kommer, eftersom de själva har negativ laddning, attraheras mot denna vakans, och rusar dit för att fylla den. Den energi som frigörs i en sådan process ges till en annan elektron – Augerelektronen – som frigörs från systemet. Sluttillståndet i detta fall är ett dubbelladdat tillstånd. Det ﬁnns även en variation på samma tema, så kallad resonant Augerspek- troskopi. Här föregås det s.k. Augersönderfallet inte av en jonisation, utan av en excitation av en elektron till en tidigare tom elektronplats, som beﬁnner sig mycket långt ut i elektronstrukturen. Detta har ungefär samma effekt som en jonisation, med skillnaden att den exciterade elektronen kan deltaga i det påföljande Augersönderfallet. Man får alltså en jon med ett enkelladdat slut- tillstånd. Resonant excitation försätter många molekyler i dissociativa till- stånd, vilket innebär att molekylen går sönder. Detta kan ske mycket snabbt, ofta inom ett fåtal femtosekunder. Om en molekyl går sönder så fort så hinner inte Augerjonisationen hända innan molekylen har blivit till två fragment. Ef- fekten av detta blir att man kan mäta Augersönderfallet från en av de två bitar av molekylen som skapats, och på så sätt studera vilka fragment som bildas och hur fort fragmenten fjärmar sig från varandra.

18 Vi använder även en teknik som kallas för röntgenabsorption, med vilken vi studerar de tomma elektroniska orbitalerna hos atomer, molekyler och kluster.

1.3 Beräkningar För att bättre förstå de saker vi ser när vi gör våra experiment använder vi oss av datorberäkningar, med hjälp av vilka vi kan förutsäga både hur den elektroniska och geometriska strukturen hos en molekyl eller i ett kluster ser ut. Vi har använt oss av diverse beräkningsmodeller, dels av så kallade ab initio-beräkningar, som förutsäger elektronisk och geometrisk struktur genom kvantmekaniska beräkningar utan att några parametrar anpassas till experiment. Ett kluster är ofta för stort för att kunna behandlas med kvantmekaniska metoder. Vi använder därför även så kallade molekyldynamiksimuleringar. I dessa beräkningar använder man en kombination av klassisk- och kvant- mekanik för att förutsäga, till exempel, strukturen hos ett kluster.

1.4 Resultat För de första tre arbetena som är inkluderade i denna avhandling har våra experiment visat följande. Syremolekyler i kluster går fortfarande sönder i samma omfattning som fria molekyler om de bestrålas med röntgenstrålning av rätt energi. Metylbromidmolekyler i kluster, å andra sidan, verkar gå sönder i mindre utsträckning när de bestrålas. Vi kan förklara detta genom att det i metylbromidklustren verkar finnas vad som brukar kallas för “bandbildning”, som är ett välkänt fenomen som förekommer i fasta material. För natrium- molekylen har vi studerat hur avvikelsen från den atomära, sfäriska, geometrin påverkar de energinivåer som uppkommer. Vi har också karaktäriserat den re- pulsiva potential som uppstår då ett Augersönderfall sker i en sådan molekyl som en Coulombpotential. För de tre följande artiklarna har vi utfört experiment med syftet att studera geometrin hos kluster av diverse atomer och molekyler. För kluster av argon, dopade med syremolekyler, finner vi att syremolekylerna ligger kvar på ytan fram tills dess att dopningsgraden (d.v.s. antalet kollisioner mellan argonklustret och syremolekyler) är tillräckligt hög; då blir argonklustret fly- tande och syremolekyler kan åka in i det (jfr. figur 1.1). En liknande situation uppkommer när vi studerar vad som händer då vi dopar argonkluster med krypton eller xenon. I dessa två senare fall visar jämförelser med vad som händer när man skapar blandade system genom så kallad “co-expansion” (när man blandar de två gaserna och sen gör kluster av gasblandningen) att dopningsproceduren tillåter skapandet av geometrier som är långt ifrån den termodynamiska jämviktspunkten. Även detta är en indikation på att klustren, vid låga dopningsgrader, inte har smält. Strukturen hos metylbromidkluster

19 studerades också. Vi kom fram till att strukturen hos dessa molekylära kluster stämmer väl överens med den man hittar i den fasta fasen. I de sista två artiklarna undersökte vi vad som sker när man joniserar atomer som i initialtillståndet är exciterade. Vi använde ett lasersystem för att skapa dessa exciterade tillstånd. En schematisk bild över hur detta går till kan ses i ﬁgur 1.3. I den första av artiklarna kunde vi i natriumatomer konstatera att ex- citeringen har som konsekvens att en magnetisk likriktning introduceras i systemet. Vi kunde även observera en effekt som kallas för “shake-down”, nedskakning. I en sådan nedskakningsprocess inducerar jonisationen av atomen en “skakning” i elektronstrukturen, som leder till att den i förväg exciterade elektronen ger sin energi till den elektron som är på väg ut ur systemet. I och med detta så ramlar den exciterade elektronen ner till det ställe den kom ifrån från när den exciterades. Således får man i en nedskakningsprocess från en i förväg exciterad atom samma elektroniska sluttillstånd som man får vid jonisation av en atom i sitt grundtillstånd, men med en elektron som kommer ut från systemet med högre energi. Den extra energin motsvarar den energi som tillförts atomen av laserljuset. I den andra artikeln studerades kaliumatomer som också var exciterade med hjälp av laserljus. Även här observerades nedskakning. Fenomenet utnyttjades i detta fall till att karaktärisera de toppar som sågs i våra experimentella spektra. Detta är möjligt, då nedskakningen, trots att sluttillståndet är detsamma för den som för jonisation av en atom i sitt grundtillstånd, följer en annan sönder- fallsväg. Symmetrin mellan de olika elektroniska tillstånden påverkar sanno- likheten för vilka tillstånd som kommer populeras av elektroner. Eftersom den exciterade elektronen kommer från en elektronorbital med annan symmetri än den elektron vi senare mäter energin hos, kan vi direkt i våra experimentella spektra se vilka toppar som är av en sådan karaktär att de blir tillåtna i och med att vägen till sluttillståndet förändras.

20 2. Introduction

This thesis is based on investigations of the electronic and geometric structure of gas-phase clusters and metal vapors. Our method of choice is, primarily, photoelectron spectroscopy. Used together with supplementary techniques such as mass spectroscopy, and with the support of first principles calculations, this family of experimental methods allow for this and more. Common to most of the techniques used in this work is that they rely on photons to create electrons, which can then be measured. Over the years, new light sources, like synchrotrons, lasers and free electron lasers (FEL), together with extensive development in instrumentation for electron detection have made a large array of experiments possible, like studies of magnetism, ultra-fast processes and charge- and nuclear dynamics. In this thesis, synchrotron radiation has been used to study ultrafast phenomena, composition of artificially created cluster structures, and fundamental properties of certain exotic molecules. Lasers were used together with synchrotron radiation in some of the experiments to, for example, prepare and probe aligned samples and to probe processes occuring in the decay of excited states. There are many motivations for performing this kind of research, both within the area of fundamental research and within more practically applied fields; like miniaturization and improvement of hard-drives, solar cells, computer chips, exhaust catalysis, hydrogen fuel cells and so on. Gas phase clusters, which has been the main focus of the work in this thesis are important model systems, which are said to “bridge the gap” between the single atom or molecule and the infinite solid [1]. They do so by presenting an opportunity to study the size-regime where miniaturization of transistors, magnetic storage etc. becomes influenced by quantum effects. Figure 2.1 shows a schematic figure of a generic physical property as a function of cluster size. As depicted in the figure, for small clusters, there are discontinuous jumps of the property depicted when varying the size. For larger clusters, the property as a function of size converges towards the bulk value, and follows a more continuous trend. Exactly where the transition between the “quantum” and the “bulk” regimes is varies for different properties, and for different compounds. This research topic is highly active, and attracts a lot of interest. Likewise, metal vapors, which have been the second subject of study in the thesis, present a way of studying the individual properties of the kind of atoms that form many of the most common solids that are used in everyday

21 life. This leads to a better understanding of how to model solids from existing knowledge about atomic and molecular properties.

Quantum regime Bulk value

Bulk regime Property P(N)

1 ∞ Size N Figure 2.1: Schematic overview of a generic property versus cluster size. In the bulk region, the value P(N) follows a continuous trend towards an asymptote, while in the quantum region there are signiﬁcant variations between the various sizes.

Another very appealing property of clusters is that their surface area is very large, i.e. that almost all atoms or molecules are situated on their surfaces. In a solid, an inﬁnitesimal percentage of the atoms are situated on the surface, while in a cluster of 13 atoms 92% are found in the surface layer. Even in a cluster of a size of several thousands of atoms, 25% of the constituent particles are found in the surface layer. This means that, in contrast to the case of the solid, surface effects considerably affect physical properties such as the melting point, conductivity, ionization potential and absorption frequencies in clusters [2, 3]. The cluster part of this thesis deals with rare-gas clusters, molecular clusters of O2 and CH3Br, and mixed rare-gas/molecular clusters. All of these systems form clusters mainly by van der Waals interaction. The metal vapor part focuses on alkali-metals, namely sodium and rubidium, and dimers of sodium. The information provided by studies of this kind of systems can provide in- sight into matters not accessible to solid-state experiments. The approach of this thesis is to begin with a brief overview of some fundamental concepts, such as electronic and geometric structure of molecular and cluster objects, to describe the experimental techniques used to create and probe such systems, and then to give a more detailed description and discussion of the experiments performed in the papers included in the thesis.

22 3. Fundamental concepts

To facilitate comprehension of the works that are presented in this thesis, the following overview of various fundamental aspects of related subjects such as the electronic structure of atoms, molecules and clusters, the geometrical structure of molecules and clusters and the photoelectric principle will be discussed brieﬂy in the following chapter.

3.1 The electronic structure of matter What we commonly think of as ’matter’ consists of large collections of atoms or molecules. An atom is composed of a nucleus and of electrons. The nucleus consists of protons and neutrons. In neutral ground state cases, the number of electrons in an atom is equal to the number of protons in the nucleus. The number of neutrons can vary, and gives rise to various isotopes of the same atom. Molecules consist of several atoms bound together by intra-molecular forces. How the electrons are arranged in the atoms or molecules determine how these particles interact with each other within the lump of matter, like if they form a solid iron ingot, or if they form a puddle of water. The arrangement of electrons also determines how the matter interacts with other nearby pieces of matter through, for example, magnetism. To understand such macro- scopic properties of large collections of matter, a good understanding of the electronic structure on the atomic and molecular level is needed.

3.1.1 Atoms An atom is the most basic system that has an electronic structure. It is from the understanding of atomic electron structure that molecular electron structure is inferred. The electrons are arranged in a somewhat peculiar manner, following what is known as the Aufbau principle, as a consequence of the quantization of energy [4]. The most basic structure in the electron arrangement is the shell. This is usually denoted either by a capital letter; K,L,M,...or by a corresponding principal quantum number n = 1,2,... In this thesis, the number notation will be used throughout. Electrons in a shell with a lower quantum number are, typically, more tightly bound to the nucleus, and generally contribute less to the chemical properties of a compound than electrons in a shell with higher quantum number.

23 A shell can also be divided into subshells. In this case, what differentiates the electronic states from each other are their orbial angular momentum. Con- ventionally, the subshells are denoted by lower case letters, s, p,d, f ,..., corresponding to angular momentum quantum numbers l = 0,1,2,...,(n − 1).As in the case of the shells, electrons with a lower l quantum number are generally more tightly bound to the nucleus than those with higher ones. The shell and subshell can be combined into an orbital, which is designated by nl, for example 2s. In this example, the orbital describes the electrons in shell n = 2 and subshell l = 0. In many cases, this is enough information to specify the complete electronic structure of an atom, due to the fact that various constraints such as the Pauli exclusion principle [5] implicitly determine the remaining quantum numbers. Such a description is done by utilizing an atomic configuration.A configuration is composed of one or more orbitals, and might look like (1s); corresponding to the H atom in its ground state, where there is only one electron, which is located in the first shell, and in the first subshell of that shell, (1s)2; corresponding to the He atom, also in its ground state, which has two electrons in the first shell, and in the first subshell. A sodium atom, which has 11 electrons, has the configuration (1s)2(2s)2(2p)6(3s) in the ground state.

yˆ

xˆ

zˆ

s-orbital

yˆ yˆ yˆ

xˆ xˆ xˆ

zˆ zˆ zˆ

pz-orbital px-orbital py-orbital

Figure 3.1: Schematic picture of contour surfaces for s and p orbitals.

One designates the projection of the electron orbital angular momentum l onto the z-axis of the reference system as ml, the magnetic quantum number. The deﬁnition is such that lz = ml · h¯. This number is restricted to the values

24 ml = 0,±1,±2,...,±l. As a consequence, there is only one energy level for electrons in s-subshells (ml = 0), while there are three for p-subshells (ml = 0,ml = ±1). In the case of the p-subshell, ml = 0 corresponds to the orbital along the z-axis, pz, and ml = ±1 corresponds to the orbitals along the x- and y-axes, px and py. When visualizing orbitals, contour surfaces are normally used, where the surface is taken to be at a distance from the nucleus within which there is a 90% chance of finding the electron at any given moment. An example of s and p contour surfaces is shown in figure 3.1. Each electron also carries what is known as spin. The spin quantum number for an electron is s = 1/2. Analogue to the case of the angular momentum vector of the electron, the projection of the spin vector s along the z-axis is known as ms, and can take values ms = ±1/2. Typically, one also defines a total angular momentum j = l +s, and its projection along the z-axis is designated m j = ml + ms. In many-electron systems, one uses the vector sum of the individual electron angularmomentum vectors; L = ∑i li. This angular momentum is quan- tized by an integer quantum number L such that |L| = h¯ · L(L + 1). A similar approach is taken when describing the spin of such systems. The quantum numbers ML = 0,±1,±2,...,±L and MS = 0,±1,±2,...,±S are the projections of L and S along the z-axis of the reference systems also in this case. In addition, ML = ∑ml and MS = ∑ms. The orbital angular momentum and spin are connected also in this case by the total angular momentum vector J. The total angular quantum number J is calculated according to J = L + S,L + S − 1,...,|L − S| and the projection value MJ = 0,±1,±2,...,±J. In the cases where additional information is needed, such as about the spin of the electrons, the configuration is usually accompanied by a term symbol. The term symbol is constructed by using the quantum numbers L, S and J, and 2S+1 is taken to be LJ. Similar to the simple case of the subshells, the quantum number L = 0,1,2,... is designated S,P,D,.... The term symbol notation is very useful when describing, for example, excited or ionic states. A distinction is usually made between the more tightly bound electrons in an atom, and those electrons that are easier to remove. The electrons that are tightly bound to the nucleus are called core electrons. The remaining electrons, which are not as strongly bound, are known as valence electrons, and are the electrons primarily responsible for forming bonds with other atoms. More specifics can be found in a regular text-book, such as [6].

3.1.2 Molecules A molecule is commonly deﬁned as being a stable, electrically neutral group of atoms, held together by chemical bonds [7]. In this thesis, molecules consisting of atoms bound by the sharing of electron pairs have been studied. Such bonding is known as covalent bonding. Examples of such covalently bound systems are the O2,H2O and Na2 molecules. Many of the terms used to describe the electron structure of molecules are conceptually similar to

25 those used in the atomic case, and most understanding of molecular electron structure stems from using various schemes of combining atomic orbitals into molecular orbitals. A way to describe the electron structure of a molecule is by using an approach known as molecular orbital linear combination of atomic orbitals (MO-LCAO). As is implied by the name, this approach makes use of the sums of atomic orbitals to combine them into molecular orbitals. In, for example, a diatomic molecule, the spherical symmetry of the electrostatic field of the individual atom is broken, and replaced by a cylindrically symmetric field. For electrons in the molecule, the angular quantum momentum vector l precesses around the symmetry axis of this field, with a constant value ml = l,l − 1,l − 2,...,−l. In molecules, the orbital angular quantum number l is designated by λ, and analogous to the atomic case subshells λ = 0,1,2,... is designated as σ,π,δ,.... Molecular orbitals are designated by their principal quantum number and their angular momentum quantum number. Orbitals that are rotationally symmetric around the z-axis are σ-orbitals. Thus the atomic s- and pz-orbitals both become σ-orbitals in a diatomic molecule. The px- and py-orbitals become π orbitals, and so on. If we take the example of O2, we can construct the molecular electronic configuration of the molecule by using the electronic configuration for individual O atoms. Each such atom has 8 electrons, in a (1s)2(2s)2(2p)4 configuration. A schematic picture of how the combination can be done is shown in figure 3.2. The configuration of the O2 molecule becomes

(1σ)2(1σ ∗)2(2σ)2(2σ ∗)2(3π)4(3σ)2(3π∗)2 where the ∗ denotes antibonding orbitals. Term symbols are used also in the case of molecular electron structure, to describe spin and geometry. One then uses quantum numbers corresponding to the sum of the individual electron spins and orbital angular momenta. The individual electron spin projection quantum number, which in the atomic case is denoted ms is denoted σ. This should not be confused with the λ = 0 quantum number designation σ. The total angular momentum is denoted by ω and is deﬁned as ω = λ + σ. The sums are designated by Λ, Σ and Ω. Note that a simple arithmetic sum is sufﬁ- cient in the case of molecules, since both λ and σ are, inherently, projections Σ+ on the molecular axis. The term is given by 2 1ΛΩ. Sometimes, the mirror symmetry of the spatial part of the electron wavefunction is given by adding eithera+ora-totheterm symbol, and sometimes the property of inversion symmetry for the entire wavefunction is also denoted by a g or u (gerade or 3Σ− ungerade) added to the term. The oxygen molecule, for example, is a g in its ground state. For an in depth discussion, see for example [4].

26 E

3σ∗

3π∗ 2p 2p

3σ

3π

2σ∗ 2s 2s 2σ

1σ∗ 1s 1s 1σ

O O O2

Figure 3.2: Schematic picture of the electron structure of O2 The atomic levels that contribute to certain molecular levels have a dashed line connection to these levels. The ∗ denotes antibonding orbitals.

3.1.3 Clusters and solids The step towards bulk solids from atoms or molecules is rather large. In between the two exists a category of objects known as clusters [1]. A cluster can be loosely deﬁned as a collection of atoms or molecules held together by intra-molecular forces, such as van der Waals forces, polar forces, metal bonds etc. Some objects in this category can be classiﬁed as both molecules and clusters, and the nomenclature is not always entirely unambiguous. Com- mon to all clusters are that they consist of 3 to some 107 atoms or molecules. The electronic structure of clusters evolve very differently depending on the type of bonding mechanism(s) present in the cluster. This thesis focuses on van der Waals clusters, and in these, the electronic structure of the consituent atoms or molecules is, in most cases, largely unperturbed from the gas phase case. There are some differences, where atomic and molecular orbitals are compressed by neighbours in the cluster [8], and there might be breaking of molecular symmetries in the cluster lattice to some extent [9], but in the ex-

27 periments performed within the framework of this thesis, these differences cannot be made out due to limitations in the resolution. When a cluster becomes large enough, it becomes a bulk solid. It has then acquired all solid state properties, like conductivity, magnetism and heat ca- pacity. The electron structure of solids is characterized by electron bands, which are, in principle, overlapping orbitals in which electrons can move freely in the entire solid. As this is beyond the scope of this thesis, a further description will not be given here. For a detailed discussion, see for example [10]

3.2 The geometric structure of matter In addition to the electronic structure, matter also possesses geometric structure. For atoms, one can define certain radii, beyond which interaction with other atoms is neglible, such as the covalent radius and the van der Waals radius [11]. These determine at which distances the atoms bind to other atoms with the respective kind of bonding mechanism. These, together with the electronic structure determine how the atoms form molecules, clusters and solids. Molecules are, as previously mentioned, composed of several atoms. This means that they can be classified within certain geometrical point groups [12]. Knowing what point group a molecule belongs to gives information about the geometry of the electronic orbitals, about the vibrational modes of the molecule and about which transitions between the different orbitals that are possible. In this work, molecules of three kinds have been studied. These kinds are homo-nuclear, diatomic molecules belonging to the point group D∞h, such as O2 and Na2, and the more complex CH3Br molecule, belonging to the point group C3v. As a part of the description of the different electronic and geometric states of a molecule, potential surfaces are often used. These surfaces map the energy of the molecule as a function of the internuclear distances, and are often used to to predict molecular dissociation limits, equilibrium distances in molecules and to interpret vibrationally resolved spectra. The use of potential surfaces is motivated by the Born-Oppenheimer approximation, which states that electron and nuclear movements can be decoupled [13]. This is not entirely true, but in most cases it gives a good agreement to experiments. Figure 3.3 shows an example of a 1-D potential surface (i.e. a potential curve) for the oxygen molecule in its ground- and first ionized state. The horizontal solid lines in the potential wells in figure 3.3 mark the vibrational levels of the oxygen molecules in its different states. Vibrations come into play for molecules, since they consist of more than one nuclei, which can move with respect to each other. These intramolecular vibrations can, for example, be induced by absorption of, or ionization by radiation. A change in the vibrational state of the molecule is governed by the transition moment

28 FC region

2 X Πg

3 + Potential energy (arb. units) X Σg

01 2 345

Internuclear distance (A)˚

Figure 3.3: The potential surfaces of the oxygen molecule in its ground state (bottom) and in its ﬁrst ionized state (top). The Franck-Condon region is marked with a shaded rectangle, the horizontal solid lines are some of the vibrational levels. .

Rv. The intensity of a given vibrational transition is proportional to the square 2 of the transition moment, i.e. Rv . In a notation where μ is the dipole opera- tor, the ﬁrst vibrational level is denoted by Ψi and the second one by Ψ f , the transition moment is given by the integral Rv = ΨiμΨ f dR (3.1)

The transition moment depends somewhat on the internuclear distance in the molecule. If this dependence is disregarded, one arrives at the Franck- Condon (FC) approximation. The approximation states that the transitions between two vibrational levels can be treated as vertical in a potential diagram like the one in ﬁgure 3.3. The square of the overlap integral between the initial and ﬁnal vibrational state 2 F = ΨiΨ f dR (3.2)

if known as the Franck-Condon factor. Vibrational transitions can be said to be proportional to this factor, since the equilibrium distance in the molecule,

29 Re, is constant within the FC approximation. The shaded area in figure 3.3 is the so-called Franck-Condon region. Most of the vibrational transitions upon excitation or ionization takes place within this region. Knowing the FC- region, and by measuring the relative intensities of the different vibrational levels, it becomes possible to experimentally determine potential surfaces of molecules. This is highly desirable, as they can provide information about equilibrium distances, vibrational frequencies, dissociation limits and a variety of other molecular properties. Clusters can be formed in a large variety of geometries, depending on the thermodynamical conditions during the formation process, on the method of production and on the type of bonding mechanisms present in the clusters. Typically, the geometrical structure of clusters resemble the geometrical structure of the infinite solid more and more as the cluster grows in size. In this thesis, the radial segregation of oxygen molecules in large Ar clusters have been investigated. The infinite solid is characterized by its crystal structure or lack thereof. As in the case of molecules, one can classify various kind of geometries within mathematical groups, which determine various properties. This is a subject discussed in for example [10].

3.3 The photoelectric effect When light shines onto matter, be it a single atom or a sheet of metal, electrons can be ejected. This is provided that the light is of sufﬁcient energy to overcome the so-called work function, Φ of the material, or ionization threshold in an atom or molecule. This effect was discovered by H. R. Herz in 1887 [14], and explained by A. Einstein in the famous paper from 1905 [15]. A schematic picture of the effect is shown in ﬁgure 3.4.

What Hertz found experimentally, and Einstein explained using the quantization of energy, is that electrons are emitted from a material with a kinetic energy related to the energy of the incident radiation. In principle

Ekin = hν − Φ −|EB| (3.3)

describes the relation. Ekin is the kinetic energy of the emitted photoelectron and EB is the binding energy of the electron. The work function Φ is well known for many materials. All energies and calibration of spectra in this work are given with respect to the vacuum level, as is commonly done when working with atoms, molecules and clusters [16]. The photoelectric principle is the corner-stone of photoelectron spectroscopy (PES), the family of experimental techniques employed in this work, since it allows for the determination of the binding energy of electrons

30 Solid Single atom

Figure 3.4: A schematic picture of photoelectrons being emitted from a material under irradiation. The leftmost image shows a solid piece of material ﬁlled with an electron gas, and the rightmost shows an atom with well deﬁned energy levels for the electrons.

by measuring their kinetic energy. These various techniques are further described in a following chapter.

4. Experimental equipment

The experimental work in this thesis was performed mostly at the MAX laboratory in Lund, Sweden, and at the department of physical sciences at Oulu university, Oulu, Finland. The following chapter gives an introduction to the experimental equipment used in the experiments. The concepts of synchrotron radiation and laser light are introduced, along with a description of the experimental systems and the way they are prepared and handled. The MAX laboratory and the beam-line I411 will be presented more thoroughly, since this is were most of the research was done.

4.1 Vacuum The different kinds of experiments, such as photoelectron spectroscopy, performed in this thesis have high demands for vacuum around the sample. This is due to the fact that the spectroscopic information in such an experiment is mediated by electrons, which interact strongly with air. In a vacuum, the electrons are free to ﬂy a long distance without interacting with any other particles and thus to preserve the spectroscopic information about the probed sample. Similarly, a synchrotron storage ring requires even higher vacuum, since the electron beam that is stored in the ring would be quickly depleted and scattered at atmospheric pressure, and since the soft x-rays emitted from it would be absorbed quickly in an atmosphere. Typically, the pressure at the experimental station should be at most in the 10−5 mbar range for electron spectroscopy to be feasible. In the synchrotron ring, pressures in the 10−10 mbar range are common. To maintain this kind of vacuum is quite hard, and requires continuous pumping of the experimental chamber and surrounding equipment [17]. In our experiment, we use standard oil roughing pumps, and turbomolecular pumps of different sizes to maintain vacuum even under very demanding experimental conditions (i.e. very high gas loads). An additional beneﬁt of performing experiments in vacuum is that the sample contamination is inherently low, since there are fewer particles in the surroundings that can interact with the sample before it is probed. This also has the consequence that there will be less residual contributions to the experimental spectra acquired under vacuum conditions.

33 4.2 Synchrotron radiation In 1947, Elder, Gurewitsch, Langmuir and Pollock, at the General Electric synchrotron accelerator, observed light emitted from their machine [18]. First thought to be Cherenkov radiation, it soon became apparent that what was seen was something else. This radiation turned out to be produced by the accelerated electrons that were travelling at relativistic speeds in the synchrotron accelerator, and thus it was termed synchrotron radiation. The explanation was given by Schwinger in 1949 [19]. Some years later, in 1956, synchrotron radiation was also observed in astronomical processes by Burbridge [20]. In the case of astronomical processes, high-energy electrons are accelerated in the magnetic fields of cosmic objects, producing jets of synchrotron radiation. The development of synchrotron light sources have gone on from the hum- ble beginnings in the General Electric lab, to the large 3rd generation synchrotron facilities in operation at a multitude of places today. Development of 4th generation facilities and the so-called x-ray free-electron lasers (FEL) is ongoing, with the first such facilities just recently becoming operational. Ina3rd generation synchrotron facility, the most important part is the electron storage ring, where electrons, as the name implies, are stored in a cir- cular orbit at relativistic speeds. The storage ring consists of long, evacuated tubes, magnetic structures and conditioning devices to control the electron speed, beam-path and divergence. The velocity of the electrons determines the amount of beaming, i.e. the brightness of the light, in such a way that the closer to light speed the electrons travel, the more light is emitted into the for- ward tangential direction of the electron velocity [21]. This is schematically shown in figure 4.1.

a) b)

v v

a a

Figure 4.1: The emitted power at two different electron velocities. In a), β = 0 and in b), β = 0.9. The emission is beamed in the tangential direction of the electron path when at relativistic speeds. a andv denotes acceleration and velocity, respectively.

34 At certain points in the magnetic structure, synchrotron radiation can be ex- tracted in a number of ways [22]. Either, by using one of the ring bending magnets, which produces a rather broadband and comparatively low-intensity radiation, or by introducing a so-called insertion device into the ring. An insertion device can, for example, be an undulator or a wiggler. In these, periodic magnetic structures are used to extract synchrotron radiation. The characteristics of wiggler- and undulator radiation differ from bending magnet radiation, and from each other, in the intensity and the wave-length distribution of the generated radiation. Figure 4.2 shows a schematic picture of the three afore- mentioned magnetic structures.

e− e− hν

hν

Bending magnet Undulator/Wiggler

Figure 4.2: Schematic picture of a bending magnet, and an insertion device of the undulator/wiggler type.

Common to all of these kinds of artiﬁcially generated synchrotron radiation is that they all have some very peculiar characteristics, namely:

• High brigthness, intensity and brilliance. • Tunability over a large energy range, from eV to MeV. • Well deﬁned polarization. • Time structure.

35 For the end-users, this opens up possibilities to perform a wide range of experiments that have hitherto been impossible, with regards to different techniques and also for very dilute samples. For example, core level photoelectron spectroscopy, x-ray absorption spectroscopy and x-ray crystallography are techniques that can be routinely applied to systems such as gas phase samples, surface ﬁlms, and protein crystals by utilizing synchrotron radiation.

4.3 Laser Light Building on the fundaments laid down by Einstein [23] and other important theoretical works by many prominent researchers, C. H. Townes demonstrated the first working maser (Microwave Amplification by Stimulated Emission) in 1953 [24], This device had a non-continuous output of microwaves. The term “Laser” was coined by R. G. Gould in 1959, in a conference paper titled The LASER, Light Amplification by Stimulated Emission of Radiation [25]. As the name suggests, a laser is a device that emits amplified light, rather than microwaves. Typically, a laser consists of two main parts; a gain medium and a oscillator cavity. The gain medium can be, for example, a crystal, a liquid, or a gas mixture which is selected to provide optimal characteristics for some experimental parameter, such as light wavelength or intensity. The oscillator cavity is, in most cases, limited by two mirrors, one of which is semi-transparent, thus letting a part of the amplified light through. Other designs might include only one, or no mirrors, but they are limited by large beam divergence. Fig- ure 4.3 shows a schematic picture of the difference in divergence between zero, one and two mirror lasers.

Figure 4.3: Three different laser designs. a) has no mirrors, and a large divergence, b) has one mirror and medium divergence, c) has two mirrors and small divergence.

36 Like synchrotron radiation, laser light has some very special properties that makes it useful to perform a wide range of experiments [26, 27]. Among these are the facts that lasers are • Highly collimated. • Spatially coherent. • Quasimonochromatic, i. e. has a very narrow wavelength range. • Very bright, or have a very large radiant power. • Time structure. This makes them highly usable in various kinds of applications, in research (spectroscopies, quantum optics etc.), in industry (drilling, cutting and so forth) and in every day life (cd-players, bar code readers and many other common apparatus).

4.4 The MAX laboratory and beam-line I411 The MAX laboratory in Lund, Sweden, is one of two national research lab- oratories, the other being the radio telescope facility in Onsala. At the MAX laboratory, research in a wide range of topics is performed, utilizing the three synchrotron storage rings and the linear accelerator at the facility. The three storage rings are the MAX I, a second generation storage ring, the MAX II, a third generation ring and the MAX III, also a third generation ring. Most of the work in this thesis was performed at the I411 soft x-ray beamline at MAX-II, where photon energies of roughly 60-600 eV are accessible. Figure 4.5 shows an overview of the MAX laboratory.

Figure 4.4: The different elements of the beam-line I411 at the MAX laboratory in Lund. The leftmost part is connected to the undulator insertion device, experiments are performed at one of the experimental stations at the right end of the beamline.

This beamline and its experimental station is specially designed to accomo- date high pressure experiments, like gas phase samples. This is achieved by using many vacuum pumps and so-called differential pumping stages, which provide a steep gradient in the local pressure in the beamline. In the experimental station, pressures can be in the 10−5 mbar range without affecting the vacuum in the synchrotron storage ring measurably. The permanent experi-

37 Figure 4.5: The layout of the MAX laboratory facility in Lund, Sweden.

mental station of the beamline is equipped with a Scienta R4000 photoelectron spectrometer. Just before the permanent experimental station is a part of the beamline which can be interchanged with user experiments. It is in this part of the beamline all of the laser experiments have been performed, using a set-up built in Oulu, Finland [28]. The spectrometer in this case was a Sci- enta SES-100 hemispherical analyzer. A drawing of the beam-line is shown in ﬁgure 4.4 Beside the beamline is a sealed hutch, where a state-of-the-art laser system is installed. This system consists of a 10W CW (continuous wave) Coherent Verdi laser, operating at 532 nm wavelength, most often used to pump one of the other lasers that are available. These other lasers are a Coherent 899-21 ring laser, which can use either a Ti:Sa crystal or a dye jet as gain medium, providing an effective output power of up to 2 W CW in a wavelength range of 550-1000 nm. There is also a pulsed Ti:Sa fs laser, giving optimal output at around 600 nm wavelength. In addition to this, the equipment includes com- puterized control of the cavity optics for the Coherent 899-21 laser, which allows for wavelength scans, and a doubler ring allowing users to reach UV wavelengths. A schematic picture of the CW laser system which has been used in the present work is shown in ﬁgure 4.6.

38 Verdi pump Frequency Beam doubler diagnostics

Ti:Sa ring laser Reference chamber

I411 synchrotron radiation Experiment λ/4 Fresnel romb Polarizer

Figure 4.6: A schematic overview of the different components in the CW laser system employed in this work.

4.5 Sample production In this thesis, beams of clusters of atoms and molecules as well as free metal atoms were used as samples. There is no way to commercially obtain a bottle of clusters or vaporized metal, so the samples have to be produced in situ. The sections below will detail how this is done with our different set-ups.

4.5.1 Cluster production Clusters can be produced in many ways, each with advantages and drawbacks for certain types of experiments. In our experiments we are limited by the photon ﬂux at the undulator beam-line we use, which means that we have to have a relatively high target density to be able to use electron spectroscopy as an efﬁcient experimental probe. Our method of choice is to produce clusters from gases through adiabatic expansion, which produces fairly large clusters in a large abundance. We have built our source in-house, and the set-up is similar to that of [29]. The source works by feeding gas under high pressure (usually 1-5 bar) into a stagnation volume, from which the gas is fed through a small, conical nozzle to an expansion volume. The pressure in the expansion volume may vary between 10−5 and 10−3 mbar. The small conical nozzle has an opening of 150 μm, and an opening angle of 20◦. Gas coming from the stagnation volume to the expansion volume through the nozzle is adiabatically expanded, and forms a supersonic jet [30] in the expansion volume. The clusters are mostly formed on the axis of the jet, which means that it is possible to suppress the atomic or molecular residue by introducing a skimmer in front of the nozzle. This skimmer also works as a separating stage in the differential pumping of the set-up. The clusters and the residual atomic or molecular gas that pass through the skimmer then enters the interaction region, where the synchrotron beam in- tersects the cluster beam. Clusters formed in the jet-expansion are distributed around a mean size N, which is governed by the expansion parameters; nozzle temperature, nozzle geometry and stagnation pressure [29, 31, 32]. Higher pressure and lower temperatures generally give larger clusters.

39 Figure 4.7: Schematic picture of the cluster source (to the left) attached to the experimental station (to the right).

Our set-up is designed to allow for high stagnation pressures, liquid nitrogen cooling of the nozzle and relatively large nozzle diameters. Two large turbo-pumps are used to maintain the pressure in the expansion volume. All these considerations allow for a source that produces a dense enough beam to perform even very demanding types of electron spectroscopies [33]. We use calibrated pressure regulators and gauges to control the pressure in the experiment, and a LN2 cooling system together with an electrical heater to maintain stable nozzle temperatures down to around -170◦C. To give some idea of the characteristics of the source, it allows us to perform electron spectroscopy experiments on Ar clusters in the size range from 100 to 50000 atoms. A schematic picture of the cluster source is shown in ﬁgure 4.7.

4.5.2 Doped cluster production To create structures of mixed clusters, we have used the post-expansion doping technique, pioneered by Scoles et al. [34, 35]. In our case, the doping stage consisted of four needles of 150 μm inner diameter, mounted perpendicularly with respect to the cluster beam and at a variable distance from the expansion nozzle. The doping stage in this set-up is mounted before the cluster beam is skimmed. This design minimizes the deﬂection of the cluster beam, which passes through the centre point of the needle “cross”. A schematic picture of the set-up is shown in ﬁgure 4.8. The doping stage is capable of delivering most kinds of gaseous substances to the cluster beam, thereby allowing cre- ation of, for example, a chemically reactive sample system.

40 Figure 4.8: Schematic picture of the doping stage. The four needles are mounted perpendicularly with respect to each other, and with respect to the sample beam that passes between them.

4.5.3 Metal vapor production Metal vapors can, just like clusters, be produced in many ways. These differ in the vapor density they provide and are suited to different applications. In our experiment, we have chosen to use resistively heated ovens, which give a large amount of metal vapour. Our experimental set-up with an oven was situated in a user-endstation built in Oulu [28], which included a Scienta SES-100 electron energy analyzer. Another similar oven was situated inside the laser hutch beside the beamline, to provide a sample for the reference chamber. Such a reference chamber allows for finding laser flourescence lines and thus tuning the laser system independently of what is going on in the main experimental chamber. Figure 4.9 shows the flourescence from 3s → 3p excited sodium atoms, produced with this set-up.

41 Figure 4.9: Photograph of ﬂourescense from laser excited sodium atoms.

42 5. Probing techniques

There are several different techniques within the broad deﬁnition of electron spectroscopy. Those that have been used in this work will be given a thorough introduction in the following chapter, together with a brief explanation of how such spectra can be interpreted with the help of, for example, calculations and curve ﬁtting.

5.1 Ultra-violet Photoelectron Spectroscopy (UPS) UPS, also known as valence photoelectron spectroscopy [36], is used to probe the shallower part of the electron cloud, the valence electrons. The way the photoelectrons are produced is by valence photoionization, a straightforward photon in–valence electron out process. Figure 5.1a shows a schematic picture of UPS. For the studies in this thesis, UPS has mainly been used as a tool for roughly determining the sizes of clusters, but also, in the case of (Ar)m(O2)n clusters, to determine the structure of mixed cluster systems. Due to several factors contributing to an efficient production of photoelectrons in this energy region (such as the maximum photon flux of the beam-line I411 and the high ionization cross-sections of most valence orbitals around 60 eV) it is also an excellent tool for aligning the cluster beam with the synchrotron radiation beam, and a good way to see contaminations in the spectra. Two examples of UPS spectra can be seen in figure 5.2 where the leftmost spectrum is the UPS spectrum of Argon clusters and the rightmost spectrum is the UPS spectrum of O2 clusters. One can note that the cluster feature in the Argon spectrum is very broad compared to the atomic feature in the same spectrum. This is commonly attributed to band formation of the valence states in rare-gas clusters [37]. In the case of O2, on the other hand, the width of the cluster feature envelope is not that much different from that of the molecular ditto. This effect is, so far, not well studied, but might be due to the fact that the oxygen-oxygen symmetry inside a cluster lattice prevents band formation or that the oxygen valence orbitals are smaller than those of rare-gas atoms. UPS energies can be found easily in the literature, for example in [38].

43 E a)γ E b)

Figure 5.1: a): Schematic picture of UPS. b): Schematic picture of XPS. Note the difference in origin of the photoelectrons.

hν=61 eV hν=61 eV Intensity (arb. units)

0 -1 0 -1 Relative binding energy (eV)

Figure 5.2: Spectra of the 3p level of Ar clusters and of the X-state in O2 clusters. The dashed lines represent the total envelope in the cluster spectrum, the solid lines represent the molecular envelope and the shaded areas represent, roughly, the cluster features in the spectra.

5.2 X-ray Photoelectron Spectroscopy (XPS) XPS, or core electron spectroscopy, is used to probe the electronic structure deeper in the electron cloud than UPS. Just like UPS, it is a straightforward photon in–electron out process, but where in UPS a valence electron is emitted, the XPS electron is emitted from one of the core orbitals of the atom or molecule. As mentioned in section 3, core electrons does not participate in chemical bonding, and remain atomic-like even in a solid. Although this is the case, there is a feature in XPS which makes is an extremely powerful technique for identifying various compounds. This feature is the chemical shift of core level binding energies. This concept of chemical shift means that the

44 energy of a core level will be affected by its surroundings, which makes it possible to identify and study even individual atoms of a certain type in, for example, an alkane chain, since the atoms at different places in the molecule will have different surroundings. The principle of XPS is shown in ﬁgure 5.1b, and the XPS spectrum of O2 is shown in ﬁgure 5.3. In the case of O2, there are two peaks in the XPS spectrum. These two components are due to the paramagnetic splitting in the O2 molecule, which comes about because the oxygen molecule has only two electrons in its highest occupied molecular orbital (HOMO), and because this HOMO has space for two more electrons. Thus, O2 is said to be an open shell molecule, leading to this kind of splitting. XPS energies for a wide variety of species can easily be found in tables such as for example [39].

Molecular Cluster features features Intensity (arb. units)

548 547 546 545 544 543 542 Binding Energy (eV)

Figure 5.3: The O1s XPS spectrum of O2 clusters. Note that for clarity, the spectrum displays only the adiabatic vibrational components as shaded areas, while the solid black line takes into account all of the vibrational components used in the ﬁt. The ionizing photon energy was 570 eV.

5.3 Auger Electron Spectroscopy (AES) Auger electron spectroscopy is different from UPS and XPS in that it isn’t merely a photon in–electron out process. Instead, AES studies the electrons that are emitted when a core-hole decays. A schematic picture of this is shown in ﬁgure 5.4. To observe Auger electrons, a core hole is ﬁrst created by, for instance, photoionization. The core-ionized state is unstable, and after a short period of time (typically in the fs range) it will decay to a lower, more sta-

45 ble energy state. This may for instance happen by a valence electron “falling down” into the core-hole, while another valence electron is emitted with a certain energy. This latter electron is called an Auger electron and its kinetic energy can be measured by an electron spectrometer. The bandwidth of the ionizing radiation is of no consequence for the resolution in the Auger spectra, since the kinetic energy of the Auger electrons is given by the energy difference between the energy levels involved in the Auger decay and the second ionization threshold energy. Rather, the width of Auger lines will be determined by the lifetimes of the intermediate and ﬁnal states. Therefore, features in atomic Auger spectra may often be quite sharp. Auger electron energies can give valuable information of the relative positions of energy levels in an atom or molecule.

Photoelectron Auger electron

Figure 5.4: Schematic picture of AES. In the ﬁrst step, the sample is photoionized, and in the second step the Auger process takes place.

5.4 Near-edge Absorption Fine Structure (NEXAFS) The fourth type of spectroscopy used in this thesis is Near-edge Absorption Fine Structure spectroscopy, or NEXAFS. This kind of spectroscopy measures the x-ray absorption near an ionization threshold. In our case, this method was used to map out unoccupied electron orbitals, that is, eigenstates of the system wavefunction that are not populated in the electronic ground state. Com- monly, NEXAFS is used in surface science to determine molecular orientation and symmetry in adsorbed molecules, since the technique is sensitive to bond angles. With the equipment at our disposal, we measure what is known as par- tial electron yield (PEY). This works in a way that the exciting photon energy is swept over a certain energy region, and for each step in the sweep, most

46 of the electrons that are emitted, regardless of their source channel, will be collected and summed by the electron spectrometer. When this sum is plotted against the photon energy, one obtains the a spectrum that is approximately proportional to the “real” absorption intensity.

5.5 Resonant Auger Spectroscopy (RAS) Resonant Auger spectroscopy works much like AES, with the notable excep- tion that there is no core ionization preceding the Auger decay, but rather a core excitation. In such an event, a core electron is excited by a photon with just the right energy to move it out of the core, and into one of the unoccupied orbitals that was mentioned earlier in the description of NEXAFS. When in such an orbital, the atom or molecule will be in a similarly unstable state as when core-ionized, but the ways to a more stable situation are somewhat different. There are two main cases, both of which have the common denomi- nator that a valence electron falls down to fill the core hole. The first of these is where the excited electron takes part in the core hole decay, leaving the atom or molecule in a one-hole state. This is called a participator decay. The second case is one where a valence electron is emitted as the Auger electron, leaving the atom or molecule in a one-particle, two-hole state. This is called a spectator decay. A schematic picture of RAS is shown in figure 5.5. In this thesis, RAS has been used as a probe of molecular dissociation, and it will be further described in this context in the results section.

Spectator decay Participator decay E

Decay types

Figure 5.5: Schematic picture of RAS. The shaded box shows the two different decay channels, participator and spectator decay, that succeeds the core-excitation.

47 5.6 Interpretation of X-ray spectra The interpretation of photoelectron spectra is not always a straightforward task. There may be overlapping or unresolved features, making an unambiguous interpretation of the spectra hard, but with modern tools many of these difficulties may be resolved. Two common approaches when it comes to interpretation is to either use curve fitting, based upon previous empirical knowledge and known formulas for a given system, or to use ab initio calculations to predict what should be seen in the spectra (binding energies, lineshapes and linewidths, differential and total cross-section) and then assign features from this calculation. There are several ways and methods to perform such calculations, and if such a method was used it will be described in greater detail in context of the experiment it was applied to. If nothing else is mentioned, the spectral analysis was done by curve-fitting. For the sake of simplicity, only UPS and XPS will be shown in the following discussion. Interpretation of RAS, AES and NEXAFS spectra will be discussed together with the results.

5.6.1 Koopmans theorem and the chemical shift A theorem that is commonly used when interpreting photoelectron spectra is Koopmans theorem [40]. According to this theorem, the ionization energy of a molecule is equal to the energy of the highest occupied molecular orbital (HOMO);

EB,k −εk (5.1)

This allows for ab initio calculation of ionization energies of molecules, since orbital energies can be calculated using methods such for example density functional theory (DFT) or Hartree-Fock (HF) theory. This theorem does not take electron correlation or relaxation of the orbitals upon ionization into account when determining ionization energies, which is a problem in many systems. However, the relaxation of orbitals upon ionization gives a contribu- tion to the binding energy that, in many cases, is of opposite sign from that of electron correlation. Relaxation effects come in many forms; but primarily from two sources. These are relaxation of orbitals in the same atom or molecule, and charge transfer to or from the surrounding atoms or molecules. Because of the cancelling character of the relaxation and electron correlation effects, Koopmans theorem often gives sufﬁciently good results for spectral interpretation where there are clearly observable features in the spectra. One of the most prominent features of photoelectron spectroscopy is its inherent element and geometric sensitivity. This sensitivity is due to the so-called chemical shift, which was mentioned earlier. The chemical shift is mainly due to what is known as screening, i.e. differences in the Coloumb interaction of the vacancy in the ion with the rest of the atom or molecule. A conceptually simple example is the sodium azide molecule, NaN3. The ionic character of the various parts of this molecule (two N−, one N+ and one Na+

48 part) give rise to three distinct spectral features. One from the N+ ion, one from both of the N− ions and one from the Na+ ion. The negative charges screen the charge from the nitrogen nucleus, reducing the binding energy on the negatively charged ions; this makes it possible to assign features even from atoms of the same element, which differ only in position in a molecule. In a covalently bound system, the chemical shift is mostly related to the electronegativity difference of various parts of a molecule.

5.6.2 Atomic photoelectron spectra The simplest case to begin with when discussing the interpretation of photoelectron spectra is the atomic photoelectron spectra. As mentioned earlier, molecular spectra can be said to be derived from the atomic spectra, and cluster spectra in turn can be understood from the spectra of its constituents. An ordinary atomic UPS spectrum is shown in ﬁgure 5.6a. Here, one clearly sees two sharp peaks. These can be assigned to an atomic orbital which is spin- orbit split, and the difference in energy between the two peaks is the difference in energy that the photoemitted electron has depending on its spin state. In atomic XPS spectra, the situation is much the same. There is, however one more thing that one needs to consider in XPS, namely the phenomenon known as Post-Collision Interaction, or PCI [41, 42]. This is a mechanism that introduces a kinetic energy dependent asymmetry in many XPS spectra. In a classical picture, this can be viewed as a consequence of the outgoing photoelectron being overtaken by the Auger electron after some time. The asymmetry becomes larger if the photoelectron has a low kinetic energy, meaning that the photoelectron is overtaken at an earlier stage. Usually, one tries to avoid this by choosing the photoelectron kinetic energy to be large enough to avoid the photoelectron being overtaken at all.

5.6.3 Molecular photoelectron spectra Molecules differ from atoms in that they have at least two nuclei. These nuclei move with respect to each other depending on how the electron cloud is cur- rently conﬁgured, by vibrations and rotations along and around the bonds in the molecule. This gives rise to vibrational features in the molecular spectra, as is shown in 5.6b, as was discussed earlier. From such spectra it is possible to deduce for example the bond-lengths in a molecule. The relative probability of a vibrational transition is given by the Franck-Condon factor (see eq. 3.2). From these it is possible to deduce various things about the molecule, such as the shape of its potential surfaces. In XPS, the main difference between the atom and the molecule is that the molecule may have many different core- levels, each situated in an individual atom in the molecule. These may differ much in energy, such as the levels C1s and O1s levels in CO, or have levels that are close to each other like the two N1s levels in N2O. One of the

49 hν=61 eV a hν=61 eV b Relative intensity (arb. units)

16 15 13 12 Binding energy (eV) Binding energy (eV)

Figure 5.6: UPS spectra of the atomic Ar 3p state (panel a) and of the O2 X-state (panel b). The two peaks in the Ar spectrum are due to the spin-orbit splitting of the 2 2 atomic 3p level. The corresponding term symbols are P1/2 and P3/2 from left to right. The peaks in the O2 spectrum are due to the intramolecular vibrations.

strongest points with XPS is that it can separate the core levels for each individual inequivalent atom in the sample, by the chemical shift induced by the neighboring atoms. XPS is, for example, sensitive enough to differentiate between the core level of the far-end N and the central N in N2O. This fact can be, and is commonly, used to ﬁngerprint molecules, as mentioned earlier in section 5.2.

5.6.4 Cluster photoelectron spectra In addition to all the mechanisms mentioned above, clusters have some more things that complicates the spectral interpretation. In the systems presented in this thesis, the main difference between the previous cases is that the neighbors in a cluster induce additional polarization screening of the core hole when photoionization occurs [43]. Disregarding initial and minor ﬁnal state effects, this means that the effective binding energy of the electrons is lower in a cluster of a given atom or molecule than in the free ditto. The screening is, to a large extent, determined by the nearest neighbor atoms or molecules. This leads to that vacancies in bulk atoms are screened to a higher degree than in surface atoms, since bulk atoms have more nearest neighbors. Figure 5.7 shows a schematic picture of the polarization screening mechanism. In core- level photoelectron spectra of rare gas clusters, this is seen as two distinct features of different binding energy, the surface feature being closest to the atomic feature. This is mainly used to study the difference between surface and bulk properties, but can also be used to determine approximate cluster size [44].

50 hν e−

+ - + - +

Figure 5.7: A schematic picture of the screening of an electron (core) hole in an in- sulating van der Waals cluster. The positive charge is screened by electrons of neighboring particles being polarized towards it.

Clusters are also, though very small, extended systems. That means that there is an effective electron attenuation length, which is the distance an electron statistically travels inside the cluster before being absorbed or scattered by another atom. This attenuation length is strongly dependent on the electron kinetic energy [45, 46]. This dependence is often used to vary the contrast between the cluster surface and the cluster bulk contributions to the spectrum. Last, cluster features are broader than atomic or molecular features. This is due to various mechanisms [47], but mainly to variations of polarization screening depending on the position of the ionized atom. This is due to the fact that the sample beam that we probe consists of clusters of a lot of different sizes, as has been discussed earlier. Furthermore, the clusters do not always form as perfect crystals, but rather as a mix between locally well ordered chunks and other more randomly ordered parts. The ﬁnal spectral shape of clusters will be an average with contributions from all of the possible cluster sizes and geometries. There are other, minor effects which also broaden the cluster spectra; for example vibrations in the clusters. All this considered, one has a fairly good idea of how to decompose a cluster spectrum. There are also recent advances in the theoretical lineshape modeling of clusters that can potentially ease the burden of cluster scientists by predicting the cluster size theoretically from experimental spectra [48, 47].

6. Summary of papers

In this section, a summary of the results of all the papers will be presented, together with a more detailed discussion of the different experiments and the theory employed to interpret the results.

6.1 Dissociation of molecules

In papers I-III, the dissociation behavior of different molecules (O2,CH3Br and Na2) in different media (O2 clusters and Ar clusters) and in vacuo respectively is investigated. In section 3.2, potential curves of molecules were discussed. These all showed bound states, i.e. states in which, without vibrational excitation, the intra-molecular bonds are not broken. Keeping this discussion in mind, there are also electronic states in molecules which are purely repulsive. Figure 6.1(a) shows a schematic comparison between a bound state potential and a repulsive potential. The steepness of the dissociative potential in the FC-region will, in principle, determine the time duration of the dissociation. By experimentally measuring the kinetic energy release (KER) of the dissociation, such potential curves can be characterized [49, 50].

FC region 3π∗ =10000

3σ∗

1s−1σ∗

Cluster PEY 123

3 + Potential energy (arb. units) X Σg Intensity/arb. units

Molecular TIY

0 123 45 530 535 540 545

Internuclear distance (A)˚ Photon Energy/eV

(a) A schematic picture of the ground (b) The x-ray absorption spectrum of state potential and the 1s−1σ ∗ excited free oxygen molecules (bottom) and clus- state potential tered oxygen molecules (top). Figure 6.1: A dissociative potential curve and the oxygen cluster NEXAFS spectrum

A way of preparing such a dissociative state is to perform a core-to-valence excitation. This means that one excites an electron from a core-orbital to an unoccupied valence level, by absorption of an x-ray photon as in for exam-

53 ple RAS spectroscopy (see section 5.5). A molecule in such an excited state will, in some cases, dissociate on a fs time-scale. This means that the dissociation takes place on the same time-scale as an Auger decay. Breaking of the molecular bond on this time-scale is often termed ultra-fast dissociation (UFD) [51, 52, 53, 54]. The consequence of this is that one can observe spectral features from Auger decays both in the intact molecule and from decays taking place in fragments of the molecule. This type of spectroscopy has been performed in papers I and II. Both of these papers address the question of what effect the surrounding medium has on the dissociative character of the core-excited state.

6.1.1 Oxygen clusters In paper I, clusters of oxygen have been studied in an attempt to quantify the effect of clustering on dissociation after core excitation. Oxygen was chosen as an experimental system, since it is fairly easy to handle and since here are an abundance of data already published for the molecule in vacuum and in solid phase [54, 55]. NEXAFS spectroscopy was employed to locate the 1s−1σ ∗ resonance in the clustered molecules, the spectrum is shown in ﬁgure 6.1(b).

ΔEv =0.8 eV ΔEv

ΔE=1.0 eV ΔE

2 ΔE D 2P ΔE 13 c 11 3

Δ =0.7 Ec eV ΔE

Intensity/arb. units c 2 Intensity/arb. units

546 544 542 470 475 480 485 490 495 Binding Energy/eV Kinetic Energy/eV

(a) UPS and XPS spectra of oxygen clus- (b) RAS spectra of oxygen clusters. Ex- ters. The polarization screening shift was citation energies are marked by the num- found to be 0.7-0.8 eV. In the UPS spec- bers 1 through 3, and match the ver- trum (top) the molecular progression is tical bars in ﬁgure 6.1(b). The bottom the spectral feature with the highest bind- spectrum is the RAS spectrum of the ing energy, and the broad feature at lower free molecule. The other spectra are from binding energy is the cluster feature. The the clustered molecules; for each energy XPS spectrum is ﬁt by a molecular com- point there two spectra are displayed. The ponent and a cluster component. topmost of these two is the total spectrum while the lower one shows the cluster spectrum only (where molecule has been subtracted). Figure 6.2: UPS, XPS and RAS spectra of oxygen clusters.

54 In the NEXAFS spectrum it can be seen that the shape and position of the 1s−1π∗ resonance is virtually unaffected by clustering. This is not the case for the 1s−1σ ∗ resonance, which is somewhat blue-shifted and broadened in the clusters. Figure 6.2(a) shows UPS and XPS spectra of oxygen clusters, which were used to extract the shift due polarization screening for a singly charged molecule in the cluster matrix. The shift turned out to be around 0.7-0.8 eV in these spectra. A detuning study was performed to characterize to 1s−1σ ∗ resonance in the clusters. In the resulting RAS spectra, which are shown in figure 6.2(b), one can see that there are spectral features that are shifted towards a higher kinetic energy (i.e. a lower binding energy) relative to those corresponding to decay in an atomic oxygen fragment in the case of the free molecule. The shift towards higher kinetic energy is approximately 1 eV. This is slightly larger than the polarization screening shift for a singly charged molecule seen in XPS and UPS. An explanation for this difference is that the excited molecule breaks into fragments which have time to move inside the cluster matrix; a typical path-length of 1 Å before the Auger decay takes place can be calculated for the excited fragment. Since this, on average, moves the fragment closer to its neighbors, the screening increases. These facts, when taken together, are very strong indications of the UFD process taking place inside the clusters. In this case it was not possible to distinguish contributions from the surface/bulk components, due to the very demanding experimental conditions. What one can observe, though, is that there seems to be no radical differences between the molecular and the cluster RAS spectra, save that of the shifted features that can be attributed to polarization screened fragments. These findings indicate that the valence electronic structure of oxygen molecules is not affected by clustering to any significant amount.

6.1.2 Bromomethane clusters Paper II presents a similar study as that of paper I, with the principle difference that bromomethane (CH3Br) clusters have been used in the sample beam. The extent of the CH3Br valence orbitals is larger than that of O2, and the interaction between the molecules is governed not only by van der Waals forces, but also by dipole-dipole interactions. This gives the CH3Br clusters a local ordering of Pnma packing [56], in contrast to the rather amorphous packing of oxygen molecules under the experimental conditions employed in paper I [57]. To characterize the band formation in bromomethane clusters, we have performed ab initio model calculations on the bromomethane dimer. We have utilized the geometries found in [58], and performed an MP2 calculation, using the LANL2 effective core potentials [59] together with a cc-PVDZ basis set. All of the calculations were performed using Gaussian 03c [60]. The splitting of the outermost molecular 2e valence level due to dimerization can be viewed as a lower limit to the band-width in the larger cluster system. It

55 is found that the splitting in the dimer becomes 0.2 eV. The calculations show also that the valence state in the dimer is formed by orbitals that are delocalized over neighboring molecules. This makes it rather probable that even more overlap will occur in a cluster matrix, where there are more nearest neighbor to each molecule. A picture of a resulting electronic orbital in the bromomethane dimer is shown in ﬁgure 6.3.

Figure 6.3: A resulting molecular orbital (HOMO-3) in the dimer.

The onset of band formation means that the valence electronic structure is very much affected by clustering. Thus, there might be signiﬁcant differences between the cases of bromomethane and oxygen. In the case of bro- → momethane, the core-to-valence excitations of interest are 3d5/2 4a1 or → 3d3/2 4a1. Figure 6.4(a) shows the NEXAFS spectra of molecular and clustered bromomethane. In spite of the apparent similarity of the 3d → 4a1 absorption spectrum in the molecular and cluster cases, we observe signiﬁcant differences in the character between the two, when analyzing the RAS spectra at different points on the resonance. In the molecule, both of the spin-orbit states are dissociative. There have been previous studies on the bromomethane molecule to map this shape resonance [52, 53]. Figure 6.4(b) shows molecular RAS spectra, at different excitation energies. The spectral shape has been assigned in the previous studies as being due to a mixture of molecular Auger features and atomic Auger features. The shift between the two spectral features at the higher and the lower excitation energies can be attributed to the difference in energy between the two excited states. The spin-orbit splitting between the 3d5/2 and 3d3/2 levels has been found to be approximately 1 eV, which is consistent with what has

56 1 3 → σ∗ D P 3d3/2

hν=71.8 eV ΔE

hν=71.4 eV

hν=71.0 eV

Intensity (arb. units) hν=70.6 eV ∗ → σ∗ 3d5/2 → σ 3d3/2 Intensity (arb. units)

hν=70.2 eV

→ σ∗ 1 3 3d5/2 D P

69.5 70.0 70.5 71.0 71.5 72.0 72.5 50 52 54 Photon energy (eV) Kinetic energy (eV)

(a) NEXAFS of bromomethane (b) CH3Br molecular RAS spectra. molecules and clusters. Within the Atomic features are shown as solid lines, measured statistics, no change in the as is the total fit lineshape. The shaded ar- peak shape can be observed. eas represent molecular Auger features. Figure 6.4: The NEXAFS spectrum of molecules and cluster, and the RAS spectra of the molecule, detuned over a range of energies as indicated in the figure. been observed in earlier works [52, 61]. This splitting corresponds very well to the Auger feature shift when exciting the two spin-orbits components. Figure 6.5(a) shows the XPS spectrum of bromomethane clusters of two different sizes. These have been used to extract the shift due to polarization screening for a singly ionized state. In clusters, if the electronic final state is localized to an individual molecule, the vacancy will be affected by polarization screening. If this is the case, and if UFD takes place in the bromomethane clusters, one should be able to observe spectral features from atomic fragments that are shifted up in kinetic energy. Figure 6.5(b) shows cluster RAS spectra at the same excitation energies as for the molecule. These have been treated within the framework proposed above, i.e. by modeling the cluster lineshape as a shifted and broadened copy of the features stemming from the free molecule. As can be seen from the figure, this kind of model works rather well to describe the experimental spectrum for both of the spin-orbit components. However, upon analysis of the ratios between decays in the molecule and the cluster, and between the resonant Auger decays and photoionization, one comes to several conclusions. There is a clear effect on the dissociative character of the 3d → 4a1 excitation in clusters when compared to the same excitation in the free molecule. The number or decays in screened fragments, i.e. atomic fragments that are within the cluster matrix is suppressed compared to the number of decays in fragments from free molecules. Also, the total number of decays observed in the RAS spectra is suppressed as compared to the

57 Large clusters ΔEL=0.81 eV

hν=110 eV

1 3 → a D P 3d3/2 4 1

hν=71.8 eV Small clusters ΔEL=0.72 eV

hν=110 eV hν=71.4 eV

Intensity (arb. units) hν=71.0 eV

Intensity (arb. units) hν Molecule =70.6 eV

hν=110 eV

hν=70.2 eV

→ a 1 3 3d5/2 4 1 D P

78 77 76 75 50 52 54 Binding energy (eV) Kinetic energy (eV)

(a) XPS spectra of the CH3Br molecule, (b) The RAS spectra of large clusters, small clusters and large clusters. The po- at the same excitation energies as those larization screening shift was found to be used in 6.4(b). 0.72 eV for the small clusters and 0.81 eV for the larger size. Figure 6.5: The XPS spectra from the molecule and two sizes of clusters and the RAS spectra from large size clusters.

RAS spectra of the free molecule. The latter fact is somewhat surprising, since the NEXAFS spectra are very similar. Several possible explanations exist for these observations. However one can rule out some explanations, like electron recapture, fragment cage exit, neighbor closing and secondary ionization due to various reasons. Remaining explanations include band formation in the initial and final states (charge transfer) or physical differences between the two spin-orbit components induced by geometry, for example variations in the molecular field splitting components. As can be seen, all of the valence states in the dimer are delocalized to some extent, so it is not unreasonable to believe that this might be the case also for the RAS intermediate states. Such delocalization would explain the effects seen above, since it would imply that many of the excited electrons are delocalized, thereby forming an, in principle, core ionized final state which would then undergo normal Auger decay. Normal Auger features are not visible in our RAS spectra because of the narrow energy region we examine. However, they will be counted when performing NEXAFS spectroscopy, which makes this a plausible explanation for what is seen in the spectra.

58 6.1.3 Sodium dimers Another way of inducing dissociation of a molecule is by performing core photoionization. A core-ionized, bound state can relax by an Auger process. The ﬁnal state can then be dissociative. In a spectrum where Auger electrons are measured, a dissociative state will give rise to a broad, featureless bump. The width of this bump can be related to the slope of the potential surface of the ﬁnal state. Figure 6.6(a) shows a schematic picture of this relationship. Such an analysis was performed in paper III. A beam of sodium dimers (or, really, Na2 molecules; the dimers are covalently bound with the outermost 3s electrons forming a binding molecular σ orbital) was chosen as a proto- type system, since its electron structure is very simple, with only two valence electrons, and since it is a case where, in the atom, Auger decay from the core-ionized 2p−1 state is not allowed while it becomes possible in the dimer.

Excited state

1 FC-region (excited state)

Eﬀective FC-region Auger 1 1,3S Dimer feature 3P width

Final state Energy (arb. units)

FC-region (ground state) Auger width Intensity (arb. units) 0 Ground state 0

1234 5 16 18 20 22 24 Interatomic distance (A)˚ Kinetic energy (eV)

(a) A schematic picture of how the (b) The Auger spectrum from the 2p- width of an Auger feature can be esti- ionized Na2 molecule. The width of the mated from knowledge about the poten- Auger feature is well estimated using the tial curves of a molecule. In this case, an model with an effective FC-region. “effective” FC-region was deﬁned, to ac- commodate the fact that the transition to the dissociative state takes place from an excited state.

Figure 6.6: Potential curves and Auger spectrum for the 2p-ionized Na2 molecule.

In this work, we have modeled the Auger ﬁnal state by a pure Coulomb potential on the form q · q V = 1 2 (6.1) col r where the charges q1 and q2 were each set to one. This is based on the as- sumption that, in the ﬁnal state, the two positive charges in in the valence orbitals repel each other and end up on different Na atoms in the molecule. Using the effective-FC-region approximation, we come to the conclusion that

59 a pure Coulomb potential represents the Auger final state very well in this case. Another point in favor of this conclusion is the fact that the Na+ ions in the final state have smaller radii than the the neutral atoms that constitute the molecule; thus the overlap between the outermost Na orbitals will be much smaller in the final state than in the initial state (2.32 Å [12] as compared to 3.08 Å [62]). The main point of this paper, however, is to assign the molecular field splitting and life-time of the Na2 molecule Na 2p core hole. This was done using XPS, in combination with ab initio calculations. Density functional theory (DFT) [63] was employed to calculate the inter-nuclear distance in ground state, and in the core-ionized state (using the Z+1 approximation [64]). The experimental spectrum was subsequently fitted using the calculated vibrational progressions. Figure 6.7(a) shows 2p binding energy region from both the atom and the molecule, while figure 6.7(b) shows only the molecular spectrum with the fit components. The molecular field splitting was determined to be 42±10 meV and the core-hole lifetime was found to be 15±8 fs from the Lorentzian width of the fitted peaks. The spin-orbit splitting corresponds well to previous studies of solid sodium [65], with a value of roughly 160 meV. However, the lifetime of the core-hole is much shorter than what has previously been reported [66]. Even though many competing processes take place in the solid state that can affect the lifetime, this might indicate that the lifetime in the solid state might have been overestimated.

hν =61eV hν =61eV 2p3/2 3 P2 1 1

p 2 3/2 2p1/2 1 3 P1 P1 E 2p1/2 m

3 P0 Intensity (arb. units)

x15 Intensity (arb. units)

0 0 39 38.5 38 37.5 37 36.5 36 36.4 36.3 36.2 36.1 36 35.9 35.8 Binding Energy (eV) Binding Energy (eV)

(a) An overview spectrum of the 2p bind- (b) The XPS spectrum of the molecule. ing energy region for the Na atom and for The solid line represents the ﬁtted line- the Na2 molecule. shape, the dotted lines represent the individual ﬁt components and the vertical bars represent the vibrational bar spectrum. Figure 6.7: XPS spectra from the sodium atom and the sodium dimer molecule.

6.1.4 Conclusions Synchrotron radiation based techniques were used to probe dissociation dynamics in various systems. It was shown that dissociative states of

60 molecules in the free phase is not necessarily dissociative when the same kind of molecule is in a cluster. The reason for this is, as of yet, not entirely clear, but with more theoretical effort and better experimental set-ups, the future of this kind of experiments is very promising. It was also shown that it is possible to determine the core-hole lifetime and molecular ﬁeld splitting in alkali-metal dimers with a good accuracy. This is highly interesting, since there are no solid-state limitations and effects to take into account when performing the analysis of effects such as molecular ﬁeld splitting and lifetime.

6.2 The structure of doped and molecular clusters Paper IV-VI deals with the geometric structure of doped and pure free molecular clusters. Not much is known about these structures a priori, since it is relatively recently that experimental and computational tools have become available that allow for reasonably accurate structure determination of clusters [47, 57, 67, 68, 69]. Performing calculations on large clusters (several thousands of atoms or molecules) is still prohibitively computationally ex- pensive, but the feasible size limit has been pushed upwards to at least a few thousands of atoms or molecules. In such calculations, a classical or semi- classical approach is most often taken, using molecular dynamics (MD) or Monte-Carlo methods to predict the geometric structures of clusters. Limita- tions to these models are mainly that electronic effects, such as magnetism, are not properly taken into account. This is not always a problem, but, for example, in the case of oxygen clusters, the paramagnetic nature of the constituent molecules dramatically influences the phase diagram [57]. In paper IV, the diffusion behavior of oxygen molecules adsorbed on large (N 8000) Ar host clusters has been investigated. There are many comprehensive theoretical studies of the diffusion behavior of atoms and molecules doped on inert host clusters [68, 69], and also a range of measurements performed by fluorescence spectroscopy [34, 35]. Recently, XPS spectra of polar molecules adsorbed on Kr clusters were also published [70]. Figure 6.8(a) shows the X-state UPS spectrum of oxygen molecules which are doped on Ar. An important point here is that intra-molecular vibrations can still be resolved even in the cluster feature. This indicates that there is no significant band formation between the different oxygen molecules in this case. That it is the case does not come as a surprise, since the oxygen valence levels are fairly confined to the molecule, and since the oxygen molecules probably are fairly sparse in the Ar matrix. This allows us to use UPS as our structural probe, instead of using XPS, which is the most commonly used technique for this purpose [47, 48, 71, 72, 73, 74, 75, 75, 76]. Using UPS has several advantages, especially in the case of oxygen. First, the photon flux at the beamline where the experiment was

61 hν Edge

=60 eV Face Bulk Vertex Interface Pd=9 mbar

hν=60 eV Pd=18 mbar

A Pd=14 mbar

Pd=18 mbar Intensity (arb. units)

* Intensity (arb. units) Pd=29 mbar

13 12.5 12 11.5 11 10.5 13 12.5 12 11.5 11 Binding energy (eV) Binding energy (eV)

(a) The O2 X-state in O2/Ar clusters. The (b) Spectra of the O2 X-state in the vertical solid bars mark the molecular FC O2/Ar clusters at different doping con- proﬁle. The dashed vertical bars mark the ditions. The shaded areas represent ion- same FC proﬁle shifted to a lower bind- ization at different sites in the cluster. As ing energy to try to match the cluster the doping pressure increases, the black feature. The * marks the region of the (bulk) feature grows dramatically. spectrum which cannot be described using just one vibrational progression.

Figure 6.8: UPS spectra of the O2 X-state in O2/Ar clusters. performed is optimal at energies that access the valence region. Second, the resolution is not limited by the lifetime of the vacancy, since the typical decay pathway of a valence ionized state is radiative decay. In the case of oxygen, it is very hard to probe the core-levels with an acceptable resolution and still have a sufficient photon flux at the beamline utilized in this experiment. A complicating fact is that the valence states are quite rich in vibrational structure; however, this is not such a big problem as one might first think, since the valence spectra of molecules are often well known and extensively studied. From figure 6.8(a) it can be seen that the simple shift-and-broadening approach that is usually applied in the case of XPS does not work very well to describe the oxygen cluster spectral feature. Instead, we have employed a modified version of this approach. To be able to quantify where the oxygen molecules are sited in the Ar matrix, we have used electrostatic calculations (Tinker package, using the AMOEBA polarizable forcefield [77]) to get the polarization screening shift values for different sites in and on the Ar cluster. With the help of depth-profiling, (pure) surface/bulk splitting has been ruled out as the source of the discrepancy between the simplest shift- and-broadening model and the experimental spectrum at low pressures. Fig- ure 6.8(b) shows oxygen cluster UPS spectra as a function of the doping pressure. As the doping pressure increases, it can be seen from the fits that the

62 feature at the bulk energy (black) increases drastically. This is expected, since at some point, the Ar host cluster will become liquid, and oxygen molecules will, in principle, be able to migrate freely in the Ar host. At lower doping pressures, the oxygen molecules does not penetrate into the bulk at all, but stay in the surface and interface layers. In general, the results of this paper agrees well with how one would expect that oxygen behaves when doped on Ar by considering its van der Waals interaction potential. That no band formation is observed is a fact that can allow UPS to be used as a structural probe in many other mixed cluster experiments with similar properties. The results of this study indicate that a high degree of control of the radial structure and diffusion behavior of molecules adsorbed on inert host clusters can be achieved. Paper V presents a doping study, using XPS of Ar clusters doped with Kr and Xe. This technique has the great advantage that it provides a (in principle) linear relation between the observed spectral intensity and the actual composition of the sample. This is a modiﬁed truth, because of issues regarding the electron effective attenuation length of electrons in the cluster [45, 46]. Figure 6.9 shows XPS spectra of the two systems, at different doping conditions. One can clearly see the evolution of the dopant features in these spectra. For Kr, there is a clear radial structuring, where most of the Kr ends up on the surface of the cluster, in contrast to the co-expanded case, where Kr atoms are mostly found in the bulk, and Ar atoms are mostly found on the surface [73, 74].

Ar 2p−1 XPS, hω eV Kr 3d−1 XPS, hω eV 3/2 ¯ = 270 5/2 ¯ = 115 −1 −1 Ar 2p3/2 XPS, ¯hω = 270 eV Xe 4d5/2 XPS, ¯hω = 112 eV surface

bulk surface Doped: 2 mbar Doped: 2 mbar

bulk doped doped Doped: 40 mbar Doped: 40 mbar co-exp co-exp co-exp co-exp Intensity [arb.units] Intensity [arb.units] Intensity [arb.units] pure pure pure pure

0.0-0.5 -1.0 0.0 -0.5 -1.0 0.0 -1.0 0.0 -1.0 Relative binding energy [eV ] Relative binding energy [eV ] Relative binding energy [eV ] Relative binding energy [eV ] (a) XPS spectra of Ar clusters doped and (b) XPS spectra of Ar clusters doped and co-expanded with Kr. co-expanded with Xe. Figure 6.9: XPS spectra of Ar/Kr and Ar/Xe clusters.

For Xe, the situation is more complex. At low doping pressures, the dopant remains in the surface layer, with a polarization screening that can be traced to the Ar matrix. For higher doping pressures, the Xe XPS feature looks very much like the pure Xe clusters, which are also shown in the ﬁgure. This has been interpreted as island formation on the Ar surface; a schematic picture of this is shown in ﬁgure 6.10. This is also very different from what is seen from

63 the co-expanded case, where there is a clear interface feature in the spectra, indicating a very high radial segregation [72].

Low doping pressures High doping pressures

Figure 6.10: A schematic picture of how Xe forms islands as it aggregates on the Ar clusters.

The main conclusion is that it is, indeed, possible to create free clusters by post-expansion doping that do not have a thermodynamically favorable structure, such as has been predicted in, for example, [68]. The other method of creating mixed rare-gas clusters, co-expansion, gives a cluster distribution in which clusters have a much more thermodynamically favorable structure [72, 73, 74]. This is not surprising, considering that the cluster flight distance from the expansion nozzle to the probing region is in the order of several cm, allowing the clusters time to cool down and minimize their energy by attaining a more stable configuration. In the doped case, the situation is such that the host clusters have time to cool down even before the doping takes place. Thus the doping process might or might not heat the host cluster up to the melting temperature, allowing for control of the radial distribution of the dopant atoms in the Ar host. Another subject about which very little is known is the structure of molecular clusters. These clusters can be formed by a combination of a wide range of inter-molecular forces, such as van der Waals forces, dipole interactions or hydrogen bonds. In paper VI, the structure of CH3Br clusters was studied by XPS and UPS spectroscopy. The polarization screening shift value trend in both XPS and UPS follow a similar pattern; the orbitals that are localized on the methyl group have a larger polarization screening shift, while the ones that are localized on the bromine atom have a smaller polarization screening shift. States involving orbitals that are delocalized over the molecule have a polarization screening shift in between the two. Figure 6.11 shows UPS and XPS spectra from large bromomethane clusters. The shift values are marked in the figure. These shift values tell us that the bromine end of molecules are mostly screened by methyl groups, which have a small polarizability compared to bromine atoms. It also tells us that the methyl carbon is mostly screened by bromine atoms, which are highly polarizable. All things considered, this is strong evidence for a packing in the cluster matrix similar to that of the bulk material [78], and to that which has been proposed for the bromomethane dimer [58]. Recent calculations on the local structure of bromomethane clusters also support these findings [79].

64 h tutr fnurlfe lsesi adt eemn sn experiments, using determine to of hard help the is with clusters but free neutral of structure The Conclusions 6.2.1 6.11: Figure 3 Br clusters. bromomethane the in of edges spectra XPS (a) ple ocutr fohrplrmlclst netgt oa emtyand geometry local investigate the to molecules characterize be polar can packing. to other reasoning same of used the clusters been molecules; to polar also applied of final has consisting the cluster XPS a influences of system. what structure cluster of the atoms picture of clear rare-gas these more structure of using a studied behavior been giving the has together, hosts work, techniques cluster this rare-gas on nano- In adsorbed of clusters. molecules and structure as the such investigating objects when scale advantage surface- distinct inherently are a techniques give the sensitive that fact The information. accurate give Intensity (a. u.) Intensity (a. u.) (b) XPSC1s (a) XPSBr3d Molecule Molecule 87 76 77 78 293 3d P n P pcr rmpr rmmtaeclusters. bromomethane pure from spectra UPS and XPS ≈0.94eV 3/2 Binding Energy(eV) Binding Energy(eV) 292 ≈1.25eV 3d ≈0.94eV 5/2 binitio ab 291 d 75 n 1 C and Cluster Cluster 290 n Dcluain,XSadUSsetacan spectra UPS and XPS calculations, MD and 74 s b P pcr fte1 the of spectra UPS (b) ec ttso rmmtaeclusters. bromomethane of states lence Intensity (a. u.) Intensity (a. u.) 18 (a) UPS (b) UPS Molecule 11.0 17 Molecule 10.5 614 16 Binding Energy(eV) Binding Energy(eV) ≈1.1eV 009.0 10.0 ≈0.9eV 15 e 17 9.5 1010.0 11.0 ,3 16 a 1e ≈1.0eV 1 2e 10.5 n 2 and 13 15 14 12 Cluster Cluster 8.5 3a e 13 1 va- 65 6.3 Laser excited metal vapors Papers VII and VIII deal with x-ray photoelectron spectroscopy on vapors of laser-excited sodium and potassium, respectively. In photoemission, there is a type of processes known as electron shake. These shake processes can be classified as either shake-off, shake-up or shake-down. Figure 6.12 shows a schematic picture of the final states in each of these processes. In a shake-off type process, the outgoing photoelectron loses enough energy to the valence electronic configuration to cause valence ionization. Thus the final state consists of a photo-electron, a shake-off electron and a doubly charged ion. A shake-up process is similar to the shake-off in that the outgoing photoelectron loses energy to the valence electrons. It does not, however, cause ionization, but rather a valence excitation; i.e. a valence electron is excited into an unoccupied orbital. Both of these processes reduce the kinetic energy of the outgoing photoelectron [80]. The third possibility, shake-down, is only possible when photo-ionizing an excited state. In this case, the photoelectron does not lose energy to the valence electrons, but rather gains energy while a de-excitation of the initial state takes place.

Ground state shake Excited state shake

hν hν

Ground state Shake-up Shake-oﬀ Excited state Shake-down

Figure 6.12: Three different shake processes. On the left hand side, shake-up and shake-off from the ionized ground state, on the right shake-down from the ionized excited state.

The ﬁrst experimental observations of the shake-down process are presented in paper VII. The relative simplicity of the sodium atom (only s and p orbitals, and only one electron in the valence shell) and the fact that the 3s − 3p gap is in the optical range (588.995 nm, 2.1 eV) makes it an ideal candidate for studies of the shake-down process itself. It turned out to be possible to directly compare the direct photoemission lines from the ionization 2p63s + hν → 2p53s + e− to the shake-down photoemission lines, 2p63p + hν → 2p53s + e−. The difference in kinetic, and thus binding energy of the

66 two kinds of photoelectrons was shown to be 2.1 eV, corresponding to the excitation energy of the laser light.

2.1 eV 2.1 eV 45 degree 3 a) P fit 2 atomic shake-down -1 cluster direct 2p

1 3 P 1 P1 3 P 3 2 P 0 1 P1 3 P intensity (arb. units) 3 1 Intensity (arb. units) P0 3 1 P ÷100 P1 2

39 38.5 38 37.5 37 36.5 36 35.5 36.5 36.4 36.3 36.2 36.1 36 35.9 35.8 35.7 binding energy (eV) binding energy (eV) (a) XPS spectrum which shows both the (b) A closeup of the shake-down spec- ground-state spectral features and those tral features. The dotted line represents from shake-down satellites. the direct photoemission from the Na2 molecule. Figure 6.13: Overview and detailed decomposition of the shake-down features of laser-excited Na atoms.

Figure 6.13(a) shows the measured 2p XPS spectrum. At higher binding energy, the ground state multiplet features can be seen, at higher energies are the shake-features; these are, as expected, a shifted copy of the ground state multiplet lines. As can be seen from figure 6.13(b), there is another feature overlapping the shake-down lines, this is attributed to the ground state 2p photoemission from the Na2 molecule, as was discussed in paper III. To con- serve parity between the initial and final states, it turns out to be necessary that the outgoing 2p photoelectron wave is p-symmetric, and that the excited 3p electron undergoes a dipole transition to the 3s orbital. It was also possible to probe the alignment of the excited atoms; it is described well by the framework of linear dichroism [81]. The most prominent part in the description of the dichroism in this case is the term which is independent on the relative po- larizations between the laser light and the synchrotron light. This shows that the photoelectrons are primarily emitted in the direction of atomic alignment. Figure 6.14(a) shows the shake feature measured at different polarization angles, and figure 6.14(b) shows the fitted dichroism function. Shake-down was studied also in paper VIII, but with the purpose of char- acterizing final states that are only weakly excited in direct photoemission. In this case, 3p photoemission from potassium atoms was examined. For the laser part of the experiment, the exciting radiation was tuned to 769.9 nm, 2 → 2 1.61 eV. This pumped the K 4s S1/2 4p P1/2 transition. In the direct 3p photoemission from potassium, there is a significant configuration interaction between the 3p54s and 3p53d states. There are also a number of extra final states from the 3p53d configuration, namely the 3p53d 3F states. The ground state of potassium is S-symmetric, and thus one would not expect to see F-symmetric final states in the direct p-photoelectron emission. Even so,

67 o 3 0 shakedown P2 o b) 45 shakedown o 90 shakedown 3 o P 135 shakedown 2 -1 1 1 P cluster direct 2p P 1 1 Intensity (arb. units) Intensity (arb. units)

36.5 36.4 36.3 36.2 36.1 36 35.9 35.8 35.7 0 306090120150 180 binding energy (eV) Angle (deg) (a) XPS spectra of the shake-down fea- (b) The measured intensity as a function ture at various laser polarization angles. of polarization angle. Figure 6.14: Angle dependence of the shake-down spectral features. such states are visible. Figure 6.15(a) shows the ground state 3p photoelectron spectrum. The observed F-symmetric features stem from conﬁguration interaction, shake-up photoemission or higher-order photoemission.

ground state K 1 3 P P

5 3 3p 4s P K 3p PES 2 × 200 intensity (arb. units)

5 3p 3d 25.5 25 24.5 5 1 3 3p 4s P F4 1 laser excited K 3 F 5 13 3 3p (3d 4s) P 3 3 F2

intensity (arb. units) F intensity (arb. units)

25.5 25 24.5 24 24 23.5 23 binding energy (eV) binding energy (eV) (a) Ground state K 3p direct photoe- (b) Comparison between the shake-down mission spectrum. The dashed line is features (lower panel) and the direct 3p the same spectrum as the solid line, but photoemission. The relative intensity of scaled by a factor of 200 to show the very the F-symmetric final states to the P- weak F-symmetric final state features. symmetric final states varies drastically between the two cases. Figure 6.15: XPS spectra of the K3p level.

We have also observed the 3p53d 1,3D lines in the direct photoemission spectrum. In the shake-down spectra, a difference in excitation scheme from the direct photoemission case (in direct photoemission, the 3d excited final states can only be reached via shake-up or by configuration interaction with the 4s states, whereas in the shakedown process, both the 4s and the 3d final states are excited via the shakedown of the 4p electron) changes the ratio between the 3d and 4s excited states drastically. Figure 6.15(b) shows the 3p spectrum from the laser excited initial state. The 3d final states are much more

68 likely to be populated in the excited case. By studying the variations in intensity ratio between features from the same final states in direct photoemission and from shakedown, it was thus possible to quantify which final states that are likely to have an electron in the 3d orbital, and which final states have an electron in the 4s orbital. The shake-down structure of potassium is considerably much more complex than that of sodium, which is not surprising considering the larger number of electrons.

6.3.1 Conclusions The combination of synchrotron and laser radiation has been utilized to perform spectroscopy on excited metal atoms. This excitation and probing scheme allowed for observation of the shake-down process, which is observable only from excited states. The difference in decay pathway between the single photoionization and the shake-down process allows characterization of the ﬁnal states in a complex system such as potassium, even though the ﬁnal states in the two cases are the same. For sodium, it was seen that an aligned ensemble of excited atoms were created during the laser excitation, through performing a study of the linear dichroism. These results provide a good basis from which it is possible to begin to interpret other laser-induced effects in similar spectra.

7. Future outlook

The synchrotron has facilitiated an almost exponential growth of knowledge in the surface science community. New facilities and lightsources will continue to open up new possibilities for new types of experiments and for experiments on systems that have, hithterto, been impossible to investigate for various reasons. The type of experiments that have been performed in this thesis will beneﬁt greatly from these developments, since today, they are really touching on the limits of what is possible. The combination of synchrotron radiation and lasers is especially promising, because of the unique ability to study the core electron structure of systems that are involved in a lot of processes in nature. A few such very interesting prospects are the studies of atmospheric photochemistry, chemical catalysis and various biological systems. The knowledge about such systems today is very limited, and there are almost endless possibilities to imagine new ways of studying them in the future. The continued development of theory goes hand-in-hand with the experiments, and is progressing at a quicker pace than ever before; on one hand, computers are getting faster and faster, allowing for studies of larger systems with “brute force” methods, on the other hand, very extensive work is being performed in the areas of paralellization and algorithmic science, speeding up computations by orders of magnitude in the best cases. Quantum molecular dynamics is also becoming more usable because of these facts, which is especially useful for systems such as clusters. The interdisciplinary aspect of work like this is also highly fruitful, bringing together the communities of biology, chemistry and physics to tackle questions that span these subject matters. As for the close future, the cluster studies at the Uppsala group serve not only as interesting systems in themselves, but also as ﬁnite model systems for the development of an understanding of processes that take place in liquid systems; a key point if biologically important systems are ever to be studied by techniques like the ones employed in this thesis. It is the belief of many, including myself, that atomic, molecular and cluster science has a very bright future, considering the need for minaturiza- tion and development occuring in the nano-science and technology areas.

8. Acknowledgments

The number of people involved in bringing this thesis work to its conclusion is large, and I thank each and everyone who has, in some way, contributed to it. There are, of course, people who deserve special mention. First and foremost, I would like to thank my supervisors, Olle, Gunnar and Maxim for always being available to answer questions about all things practical and for all their encour- agement over the years. I would also like to thank Svante, for his unflagging confidence in his graduate students and for all our discussions. Joachim, thank you for the laser work, it was a pleasure even if it was sometimes frustrating. All of my fellow Ph. D. students, who provided fun and joy and a positive atmosphere everyday at work, thank you. Especially, Andreas, with whom I spent most of my time, writing, teaching, traveling and discussing. I would like to thank the Finnish group from Oulu, and the Bergen group, for allowing me to join in their beamtimes, and for allowing me to visit their universities for experiments and course work. All of the people at Fysikum, for providing an open and productive working environment, thank you! Also, thanks to the MAX-lab staff, who provided the most odd bits and pieces for the experiments to run smoothly. I would also like to thank all of my friends, none mentioned, none forgotten, for making living life a joy each day and for always being there when there was a rough patch. Wherever and whenever you are around, there is always fun to be had. All of the people working on a non-profit basis, producing the fantastic stage shows known as spex, in which I have taken part over the years, thank you. All members of HKF, who are just as deranged as one should be, and who keep coming up with the most brilliant get-rich-quick-schemes all the time. How come we’re not rich yet? Finally, I’d like to thank my family, Mamma, Pappa, Mia and Sanna, for being who you are, and for always encouraging me to do what I wanted to do.

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