A Bottom-up Approach to Dust Structure, Properties and Nucleation: Nano-silicates

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Bromley Institute of Theoretical and Computational

1 A Bottom-up Approach to Dust Structure, Properties and Nucleation: Nano-silicates Stefan T. Bromley Institute of Theoretical and Computational Chemistry, University of Barcelona, Spain

2 Astronomical dust formation and processing star + planet formation molecular cloud diffuse cloud low-mass stars (sun-like) diffuse cloud high-mass stars

3 Silicate dust grains Amorphous and crystalline silicates are the most abundant familiy of solids in space. Found in: interstellar clouds, circumstellar disks, main sequence/evolved stars, interplanetary and cometary dust and supernovae. Up to about 10% of interstellar Si could be in ultrasmall silicate grains (i.e. 3nm dia.) (Aigen & Draine,2001) Good models of ultrasmall silicate grains also imperative for the understanding of silicate dust formation via nucleation and dust destruction via shocks.

4 Elements of interest Al, Ti, Fe, Ca also of importance... Dark Clouds of the Carina Nebula. Credit: NASA, ESA, & Hubble Heritage Team (STScI/AURA),

5 The case for pure SiO nucleation SiO molecules are relatively abundant around oxygen rich giant branch stars (and to a lesser extent in supernovae). ü Conditions for SiO dust formation thought to only occur in stellar outflows at <500K but silicate dust formation observed at K (as in supernovae). x Recent SiO vapour pressure measurements and the possibility of vibrational disequilibration potentially allows for SiO grain condensation at higher temperatures...? Application of classical nucleation theory (J. Nuth et al. AstroPhys. J. 1, 732, 2011)?

6 Classical Nucleation theory Nuth and Ferguson, AstroPhys. J. 649, 1178, (2011): Having listed some of the problems with the application of classical nucleation theory to circumstellar environments, we must also admit that no appropriate substitute is yet available. Until one does come available, we must continue to use the modified version of the theory in an attempt to understand the formation of silicates in circumstellar outflows. Köhler, Gail and Sedlmayr, Astron. Astrophys. 320, 553 (1997): The method applied in this paper to calculate nucleation rates is free from arbitrary and unrealistic assumptions on which discussions of dust nucleation in circumstellar shells have been based up to now, especially compared to classical nucleation theory... (applied to MgO)

7 Bottom-up modelling approaches 1. Global optimisation using classical methods (e.g. interionic potentials) to give stable dust grain models. 2. Evaluate/refine properties using quantum mechanical methods (e.g. Density functional theory)

8 General methodology for probing the detailed properties of small dust grains Classical Atomistic and ab initio electronic structure methods Mature developed codes (e.g. parallelised DFT) General applicability (Silicates, Carbonaceous, SiC, TiO2.) Unprecedented detailed insights (otherwise unobtainable) In principle ab initio calculations have no adjustable fitting parameters Useful for calculating: Atomic and electronic structure Ionisation energies / electron affinities IR and UV/Optical emission/absorption spectra with assignments Chemical adsorption and reaction barriers Free energies of formation / thermal stability 1 ev =11600K / 1 kcal/mol=500k / 1 kj/mol =120K

Nanoclusters and Nucleation Chemical Society Reviews 9,

9 Modelling Nanoclusters of Inorganic Materials Approaching Nanoscale Oxides: Models and Theoretical Methods Nanoclusters and Nucleation Chemical Society Reviews 9, 2657 (2009). Physical Chemistry Chemical Physics Perspective 12, 786 (2010)

Obtaining the structure of low energy nanoclusters: global

reasonable cluster Isomers with increasing size (SiO2)7 Even for

>10 atoms) there are an astronomical number of possible isomers.

10 Obtaining the structure of low energy nanoclusters: global optimisation Exponential growth of the number of energetically reasonable cluster Isomers with increasing size (SiO2)7 Even for small clusters (e.g. >10 atoms) there are an astronomical number of possible isomers. Need global optimisation methods to search the energy landscape (e.g. Basin Hopping, Genetic Algorithms) Ground state

SiO dust formation from the bottom-up As dying stars expel their outer layers of gas into space the cooling expanding gas condenses into dust grains. Atomisation Si-O : 8.

11 SiO dust formation from the bottom-up As dying stars expel their outer layers of gas into space the cooling expanding gas condenses into dust grains. Atomisation Si-O : 8.21 ev energies per O-Si-O : 6.39 ev bond: Si-Si : 2.58 ev O-O : 2.58 ev Homogeneous nucleation would appear to prefer clusters of SiO and not SiO2 Cat Eye Nebula. Credit: NASA, ESA,.

12 (SiO)N cluster ground states N=1-7 SiO (SiO)2 (SiO)3 (SiO)5 (SiO)6 Ground states for (SiO)N N=1-7 well established by trial and error construction See e.g. W. C. Lu et al. J. Phys. Chem. A 107, 6936 (2003). (SiO)7 (SiO)4

13 Binding energy of (SiO)N Bulk SiO: >2.35 ev/sio ) indgery(v/so B SiO dimer: 1.05 ev/sio Initial stages of nucleation Number of SiO units (N) Input parameters for classical nucleation theory

Solids 320, 143 (2003) SiO2 Si (SiO)3 (SiO)12 SiO2 Si segregation occurs

14 Nano-segregation of (SiO)n TEM investigation on the structure of amorphous SiO K. Schulmeister, W. Mader J. Non-Cryst. Solids 320, 143 (2003) SiO2 Si (SiO)3 (SiO)12 SiO2 Si segregation occurs rapidly with (SiO)n cluster size increase problems for defining a surface energy S. T. Bromley, (2012) submitted (SiO)19

15 Formation of silicates - (SiO2)n? Hydrogen rich conditions: SiO + OH SiO2 + H SiO + H2O SiO2 + H Hydrogen poor conditions: SiO + O (SiO)2 (O rich regions in supernovae?) OR SiO + (SiO)n (SiO)n+1 Nanoscale segregation followed by Si / SiO2 fragmentation? (SiO2)N clusters SiO2 -rich SiO2 Si-rich SiO2 SiO2 (SiO)N nanoparticle

tetrahedra Pure silica dust not common but has been observed

16 The structure of bulk silica (SiO2) O O Si Si Si O O O O O O 1 nm of silica ~ 6 SiO2 units SiO4-groups Corner-sharing tetrahedra Pure silica dust not common but has been observed around T Tauri stars (Sargent et al. 2009) 3-D network of tetrahedra

17 Low Energy Clusters (SiO2)N N=1-5 (SiO2)N chains N=2-4 found in cluster beam experiments (L-S. Wang et al. Z. Phys. D 40, (1997), 36). (SiO2)N chains N=2-6 found by inspection and subsequent DFT energy minimisation of various clusters (S. N. Nayak et al. J. Chem. Phys. 109, (1998) 1245). (SiO2)2 N=2 (SiO2)3 Silanone-terminated two-ring chains ground state nanoclusters for (SiO2)N N=2-5 (SiO2)4 (SiO2)5 (SiO2)2 N=3 (SiO2)3 (SiO 2)4 (SiO2)5 (SiO2)2 N=4 (SiO2)3 (SiO2)4 (SiO2)5 For N>5? (SiO 2)2 N=5 (SiO 2)3 (SiO2)4 (SiO2)5

017 ev 1.02 ev N=8 Decreasing energetic stability E.

18 Low energy clusters (SiO2)N N= ev Theory: DFT B3LYP/6-31G* N= ev N= ev 1.02 ev N=8 Decreasing energetic stability E. Flikkema and S. T. Bromley J. Phys.Chem. B, 108, 9638 (2004) N= ev 0.33 ev

19 Low energy clusters (SiO2)N N=10-13 N= ev 0.70 ev 0.65 ev N=11 Decreasing energetic stability 0.05 ev Theory: DFT B3LYP/6-31G* N= ev E. Flikkema and S. T. Bromley JPCB, 108, 9638 (2004), S. T. Bromley, F. Illas, PCCP (2006) N= ev 0.66 ev

N=20 N=23 N=22 N=24 1D to 2D Transition/crossover from columnar to disk-like

20 Low energy clusters (SiO2)N N >13 N=14 N=16 N=18 N-odd anisotropic columnar growth pattern N-even anisotropic columnar growth pattern N=15 N=17 N=19 N=21 N=20 N=23 N=22 N=24 1D to 2D Transition/crossover from columnar to disk-like clusters N=26 S. T. Bromley and E. Flikkema Phys. Rev. Lett. 95, , nm N=25 N=27

0 Only 4.5 Two-rings? 4.0 3.5 VAPs (+ Two-rings)3.

21 Electronic Structure of Nanosilica (UV absorbers) 6.5 Silanones (+ Two-rings) 6.0 HOMO-LUMO energy gap (ev) Only 4.5 Two-rings? VAPs (+ Two-rings) Number of SiO2 units (N)

22 Mg-rich silicate grains Most silicate dust grains are Mg-rich and have the stoichiometry of pyroxene ( (MgO)n(SiO2)n ) or olivine ((MgO)n(SiO2)2n ) Observed magnesium-silicate dust grains appear to not be formed from elemental nucleation (Cherchneff & Dwek 2010). Bulk mixing of pure SiO2 and MgO energetically favoured but more energetically favourable than bulk for nano-pyroxene Bulk pyroxene (Clinoenstatite) ev Nano-olivine ev MgOSiO2 mixing energy Nano-pyroxene ev Bulk olivine (Forsterite) ev Size

23 Low energy (MgO)N nanoclusters Competition between tubular and cubic nanoclusters at small sizes. Magic cluster composition for (MgO)3N Bulk rocksalt structure becomes dominant for N 24 ~1 nm Bulk rocksalt N=6 N=15 N=24 N

24 Nucleation of SiO, H2O and Mg Metal addition Calculated Gibbs Free energy of the nucleation reactions at: T=1000K and p=0.1 Pa Oxidation Pyroxene F. Goumans and S. T. Bromley, MNRAS, 420, 3344 (2012). Olivine

25 Nucleation of SiO, H2O and Mg 1 O 2 3 SiO dimer Si 4 5 Mg 6 7 Pyroxene dimer F. Goumans and S. T. Bromley, MNRAS, 420, 3344 (2012).

26 Rules of silicate nucleation.... Admixing Mg and Si stabilizes the clusters w.r.t. the separate binary oxides A Mg atom can only be incorporated after an oxidation step For a fixed number of Mg+Si atoms, the fully oxidised cluster is the most favourable pure oxide cluster (no = nmg + 2nSi ) F. Goumans and S. T. Bromley, MNRAS, 420, 3344 (2012). Fully oxidised clusters can be favourably over-oxidised by water via surface OH formation Role in oxygen depletion in molecular clouds / initial stages of icy mantle formation F. Goumans and S. T. Bromley, MNRAS, 141, 1285 (2011)

27 Possible role of TiO2? Initial SiO dimerisation step found to be endogenic Perhaps silicate dust nucleates around non-silicate refractory cores? TiO2 seems to be capable of forming thermodynamically stable clusters under stellar outflow conditions (e.g. Jeong et al. Astron. Astrophys 2003) Ti is 300 times less abundant than Si and Mg in circumstellar environments but may act as a seed nuclei upon which silicates can start to nucleate. Does TiO2 assist silicate dust core formation? How much TiO2 is necessary?

28 Influence of a single TiO2 species One TiO2 monomer strongly exogenically reacts with SiO (-97 k/mol) +Mg SiO + TiO2 + H2O SiTiO3/ -97 SiTiO4 / -115 Many energetically downhill routes to add Mg, H2O, SiO to the SiTiO3 core A single TiO2 species can kickstart silicate dust nucleation closer to the star MgSiTiO3 / SiO Si2TiO4 / SiO + H2O +Mg Si2TiO5 / -164 MgSiTiO4 / Mg Si3TiO6 / -191 MgSi2TiO5 / -234 MgSiTiO5 / SiO + H2O +Mg Whether TiO2-initiated routes prevail over pure SiO + Mg + H2O routes depends on how these two routes compete with each other while depleting the metallic elements. + SiO + SiO + H2O MgSi2TiO4 / +86 +Mg + H2O MgSi2TiO6 / -272 Mg2SiTiO5 / Mg + SiO + H2O Mg2SiTiO6 / -376 Mg2Si2TiO6 / SiO MgSi2TiO7 / H2O + SiO Mg2Si2TiO7 / -216 MgSi3TiO8 / -474 F. Goumans and S. T. Bromley, Phil. Trans. R. Soc. A (2012) in press.

Other initial dust compositions: Al2O3, TiC, Dust formation (time,

29 Towards More Realistic (Nano)Astromineralogy No bulk crystalline order found for 60+ atoms larger grains? Other initial dust compositions: Al2O3, TiC, Dust formation (time, abundance) input data for kinetic modelling ~ 1 nm Pyroxene series: (MgO)N(SiO2)N N=2 N=8 Mg Si Olivine series: (MgO)2N(SiO2) N

30 Acknowledgements Edwin Flikkema Scott Woodley Fedor Goumans All of you for listening!

31 Energetics of nanosilica with increasing size Magic clusters 2.25 N= ) N= N= st energy difference (ev) Energy w.r.t. alpha quartz (ev/sio Bulk limit ev/sio Number of SiO2 units (N)

32 Relevance to Oxygen Depletion Oxygen depletion observed in cooling dust clouds. Up to 10% of Si in ultrasmall silicate grains (Aigen & Draine 2001) Relatively high surface area proportion and undercoordinated atoms. H and O absorb forming strongly bound OH groups (>2 ev per H2O) Likely initial absorbers of H and O (H2O) before ice formation? Mg4Si4O12 Mg4Si4O12(H2O ) OH + (2H,O): ev (compare ev for Hf of H2O)

33 Formation rates of relevant species

+ esioh ΔE = -178 kj/mol Highly reactive with atomic hydrogen - abundant in

34 Catalytic / Astrochemical Relevance? Possible limitations of the isolated SiO- picture: Creation of precursor NBO species not thermodynamically favoured? + H SiO- Where does the charge come from? + esioh ΔE = -178 kj/mol Highly reactive with atomic hydrogen - abundant in the interstellar medium Surface VAP site: + H Formed as an instrinsic low energy species NBO- Internally charged Non-reactive with atomic hydrogen Si15O30 Si15O30 H ΔE = +166 kj/mol + e-

35 Vertical optical excitations in low energy silica nanoclusters ΔRMS (w.r.t. CASPT for 3 lowest singlet excitations) Use of BB1K with 42% Hartree Fock-like exchange (HFLE) gives generally better results than B3LYP (20% HFLE) with respect to benchmark CASPT2 calculations. Improvement is defect dependent but may provide practical fix for accurate study of larger silica nanosystems. M. A. Zwijnenburg, C. Sousa, A. A. Sokol, S. T. Bromley, JCP, 35, 4156, (2008).

Vertical optical excitations in low energy silica nanoclusters Excited state of CNBO

typical localised Si=O and NBO excitations the CNBO excitations have greater

67 ev Remaining hole Transfered electron Charge transfer is known to be a problem for

CNBO vertical excitation: Greater localisation of the excited state?

36 Vertical optical excitations in low energy silica nanoclusters Excited state of CNBO results in separated NBO and a Si centres Silanone vertical excitation: Compared to typical localised Si=O and NBO excitations the CNBO excitations have greater chargetransfer character ev Remaining hole Transfered electron Charge transfer is known to be a problem for TD-DFT. Inclusion of a suitable proportion of HFLE can help why? CNBO vertical excitation: Greater localisation of the excited state? Improved asymptotics of the long range electrostatic interaction? 4.41 ev Remaining hole Transfered electron Likely large Stokes shift for PL M. A. Zwijnenburg, C. Sousa, A. A. Sokol, S. T. Bromley, JCP, 35, 4156, (2008).

37 Generic Nanoscale behaviour Large When in the bulk or scalable regime for a general property (G): G ( R ) = G ( ) + ar Small R, N 1 G(N,R) G(1) α G ( N ) = G ( ) + bn where R = radius N = number of atoms Medium β Scalable regime G( ) and where typically α=1 and β=1/3 R-α, N-β Quantum, size and surface effects ( Nano )

Amorphous Silica Nanoparticles For larger silica nanoparticles the ground state

in energetically low lying amorphous states Such amorphous nanoparticles also

nanoparticle O3 O1 Model of an amorphous silica nanoparticle (V. V.

38 Amorphous Silica Nanoparticles For larger silica nanoparticles the ground state structure is difficult to achieve due to the tendency for silica to get trapped in energetically low lying amorphous states Such amorphous nanoparticles also predicted to exhibit VAP defects Close-up of a VAP defect on a silica nanoparticle O3 O1 Model of an amorphous silica nanoparticle (V. V. Hoang, JPCB, 111, 12649, 2008) Slab model of an amorphous silica nanoparticle surface exhibiting VAP defects

Akihito Kumamoto, Tetsuya Miyashita, Chihiro Kaito and Yoshio Saito Ritsumeikan University

Akihito Kumamoto, Tetsuya Miyashita, Chihiro Kaito and Yoshio Saito Ritsumeikan University The workshop held from September 27 to October 1, 2010 at the Friedrich Schiller University Jena, Germany Dust