Supplementary Information:

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1 Supplementary Informaton: Vsualzaton-based analyss of structural and dynamcal propertes of smulated hydrous slcate melt Bjaya B. Kark 1,2, Dpesh Bhattara 1, Manak Mookherjee 3 and Lars Stxrude 4 1 Department of Computer Scence, 2 Department of Geology and Geophyscs, Lousana State Unversty, Baton Rouge, Lousana 783, U.S.A. 3 Bayersches Geonsttut Unverstät Bayreuth, Bayreuth D-9544, Germany 4 Department of Earth Scences, Unversty College London, London WC1E 6BT, U.K. We have provded three types of supplementary materals: Three tables: T1 to T3 Ten fgures: F1 to F1 One descrpton: Hydrogen dffuson process (D1). T1. Set of pressures (n GPa), volumes (V X = Å 3 ) and temperatures (n kelvns) condtons at whch smulatons are performed for the hydrous melt. The numbers n the parenthess are for the anhydrous melt. The pressure for low (5 wt%) water content s 1.6 GPa at 3 K. V/V X P (at 2 K) 1.1 P (at 25 K) 1.7 (1.5) P (at 3 K) 2.3 (1.8) P (at 4 K) 3.1 (3.3) P (at 6 K) 6.4 (7.5) (24.7) (31.7) (41.) (135.2) (154.9)

2 T2. Calculated postons (n Å) of the frst peak (R P1 ), the mnmum (R M ) after the frst peak, and the second peak (R P2 ) for three caton-anon dstrbuton functons. The mean coordnaton numbers (CN) are also gven. The expermental results for hydrous (hy) melt at 2 GPa (Yamada et al. 27) and anhydrous (anhy) melt at ambent pressure (Waseda and Togur 199) are shown. The numbers n the parenthess n the frst column are pressures n GPa. S-O Mg-O H-O R P1 R M R P2 CN R P1 R M R P2 CN R P1 R M R P2 CN V = V X 2 K K K (2.3) K Expt-hy Expt-anhy V =.7V X 3 K (17.6) V =.5V X 3 K (77.5) V =.45V X 4 K (127.1) K (149.8)

3 T3: The calculated mean coordnaton numbers of 16 types at dfferent condtons. The rows marked wth and are, respectvely, the results for lower (5 wt%) water content and larger (168 atoms) supercell. Also shown s GGA results at V X and 3 K. 3

4 F1: RDF matrx (symmetrc) plot. The vertcal lnes mark the crtcal dstances, such as the frst peak poston (red lne) and the mnmum poston (blue lne). 4

5 Mg S O H Mg S O H Speces: Mg S O H C αβ (t) = F2: Coordnaton matrx plot. In each entry, spheres show atomc speces pars nvolved n coordnaton. The color of centered spheres encodes coordnaton value, C αβ (t). The atomc speces are represented by dfferent szes and dfferent colors. The cutoff dstances (r mn values) used are from the RDF matrx plot. For hydrous MgSO 3 melt, there are 16 possble coordnaton types. We hghlght some nformaton. For example, almost all slcon atoms are tetrahedrally coordnated wth oxygen atoms; the S-O coordnaton plot shows wth 11 slcon atoms n four-fold coordnaton state (cyan spheres) and only one slcon atom n three-fold coordnaton state (green sphere). The absence of black spheres n the Mg-Mg coordnaton plot means that Mg atoms form a complete network whereas the S-S network s not complete snce the correspondng plot contans three black spheres (free S atoms). Also, the absence of the black spheres n the H-O plot suggests that every hydrogen atom s bonded to one or more oxygen atoms whereas a large number of black spheres n the O-H plot suggest that many oxygen atoms do not partcpate n hydrogen bondng. 5

6 F3: MSD versus tme plots for all four atomc speces of the hydrous melt at dfferent condtons. The calculated partal MSDs, n general, show two temporal regmes. The frst s the ballstc regme (for relatvely short tmes) n whch the atoms move wthout nteractng strongly wth ther neghbors and MSD s proportonal to t 2. The second one s the dffuson regme (for long tmes) n whch MSD s proportonal to t. However at lower temperatures and hgher compresson, an ntermedate regme appears where MSD ncreases rather slowly due to the so-called cage effect n whch the atoms are temporarly trapped wthn the cages made by ther neghbors. Note that countng statstcs decreases towards the end of the smulaton run so the MSD curve tends to be less smooth at large t. In the calculaton of dffusvty, we gnore 1 % of the total number of steps both n the begnnng (so that that the dffusve regme s reached) and n the end (so that countng statstcs s suffcently large) of the smulaton. 6

7 S: Large spheres O: Medum spheres H: Small spheres (yellow) Mg: Ponts (green) Cαβ (t) = F4: Coordnaton ncrease through transformaton of free oxygen (NPO) to non-brdgng oxygen (NBO) as marked. A four-fold coordnated slcon (cyan sphere) atom turns nto the fve-fold coordnaton state (blue sphere) by pckng an Mg-bound oxygen atom (black sphere) up. Now the oxygen atom also becomes sngly coordnated wth slcon (ts color changed to red). At a later tme a dfferent O atom leaves the coordnaton shell thereby changng the coordnaton to four-fold state. The oxygen s a BO, whch pcks a hydrogen atom up before the S-O bond breaks. An NPO s always bonded wth hydrogen so an OH attack results n breakng S-O-S brdgng. The snapshots are for VX and 3 K. S: Large spheres O: Medum spheres H: Small spheres (yellow) Mg: Ponts (green) Cαβ (t) = F5: Coordnaton ncrease through transformaton of non-brdgng oxygen (NBO) to brdgng oxygen (BO) as marked. A four-fold coordnated slcon atom (cyan sphere) turns nto a fve-fold coordnated slcon atom (blue sphere) by formng a bond wth the oxygen atom (red sphere) already bonded to the neghborng slcon atom (cyan sphere), and the oxygen atom now becomes doubly coordnated (yellow sphere). At a later tme, a dfferent oxygen atom leaves the coordnaton shell. Thus, the overall effect s an exchange of oxygen atoms surroundng a slcon atom va a transtonal fve-fold coordnaton state. The snapshots are for VX and 3 K. 7

8 S: Large spheres O: Medum spheres H: Small spheres (yellow) Mg: Ponts (green) C αβ (t) = F6: Coordnaton ncrease through brdgng oxygen (BO) as marked. A fve-fold coordnated slcon atom (blue sphere) s bonded wth a BO (yellow sphere) to become a sx-fold coordnated slcon atom (magenta sphere), and the oxygen atom s now n the three-fold coordnaton state (green sphere). Snce ths reacton does not consume any BO, the overall number of brdgng oxygen keeps on ncreasng on compresson at the rate of formaton of BO n the second reacton (F4). The snapshots are for.5v X and 3 K. 8

9 O: Large spheres H: Small spheres Mg: Ponts (green) S: Ponts (blue) C αβ (t) = F7: Snapshots of mxed H-O and O-H coordnaton (left), and H-H coordnaton (rght) at V X (upper) and.5v X (lower) for 3 K. In left, the hydrogen atoms (small spheres) are mostly red (one-fold coordnated wth oxygen) at V X whereas they are mostly yellow (two-fold coordnated wth oxygen) at.5v X. Also note one green sphere for hydrogen n three-fold coordnaton state at.5v X. Many oxygen atoms (large black spheres) are free at both compressons. More yellow (large) spheres and even green (large) sphere mply the domnance of hgher coordnaton O-H speces at hgh compresson. In rght, the lnes are shown between two H-atoms, whch are wthn the cutoff dstance, and the color of H atom ndcates ts coordnaton state. Note that these lnes do not represent H-H bondng,.e., stable H 2 molecules do not exst. The H-H par n near the center (upper rght fgure) represents a water molecule. The second type represents the pars n whch two H atoms are bonded to two dfferent O atoms belongng to the same specaton or dfferent specaton. The trplet near the bottom represents three hydroxyls. At.5V X, the exstence of hgher coordnaton speces mples that H atoms tend to form large clusters at hgh compresson, compared to solated small structures at the equlbrum volume. The large cluster represents three structures. 9

10 F8: Dstrbutons of Mg-O and S-O bond lfetmes at V X, 3 K (crcles) and.5v X, 3 K (damonds) for the hydrous melt. O: Large spheres H: Small spheres S-O coordnaton: Polyhedra Mg: Ponts (green) C αβ (t) = F9: Stages of the H transfers from NPO to PO (top) and from PO to NPO (bottom) marked by crcles. The ntermedate stage n both the cases nvolves a four-atom speces. In the smplest (but the 1

11 most common) case, the reactants are the source polyhedral hydroxyl (preferably, NBO-H) and the destnaton non-polyhedral hydroxyl (top-left). PO-H.NPO-H PO-H-NPO-H PO..H-NPO-H The ntermedate stage must nvolve water-lke group (about Mg atom), wth one H shared between PO and NPO, and other H attached only to NPO (top-center). Ths four-atom structure s qute abundant at low compresson. The PO-H bond eventually breaks thereby formng an Mg-bound water molecule (H-NPO-H) as shown n top-rght. Ths reacton may be subsequently followed by another reacton n whch the newly formed water molecule loses one of ts H atoms to a dfferent PO (bottom): H-NPO-H.PO H-NPO-H-PO H-NPO..H-PO Note that the source NPO must be a water group for t to be able to loose one H atom. If source or destnaton n the PO-to-NPO reacton contans water, the ntermedate state can nvolved a fve-atom structure even nvolvng a hydronum. O: Large spheres H: Small spheres S-O coordnaton: Polyhedra Mg: Ponts (green) C αβ (t) = F1: Transfer of a hydroxyl group between polyhedral and non-polyhedral unts. The H-O bond remans stable durng ts transfer from one caton to another. D1 Hydrogen dffuson process: The drect H transfer mechansm nvolvng PO and NPO can be consdered occurrng together wth hydroxyl/water transfer mechansm. The mxed mechansms allow the possblty of transton between hydroxyl and water molecule as well as between polyhedral and non-polyhedral assocaton durng the dffuson process. To llustrate the general nature of hydrogen dffuson, we follow the trajectory of a randomly selected hydrogen atom (labeled as H*) over a perod of about 1 ps startng at the 2219 th step. At the start, ths hydrogen atom forms polyhedral hydroxyl (S-O*-H* or smply PO*-H*). After 9 steps, the polyhedral hydroxyl forms 4-atom structure wth another polyhedral hydroxyl and steals ts hydrogen thereby formng polyhedral water at the 2234 th step: PO-H PO*-H* PO-H-PO*-H* PO. H-PO*-H* 11

12 Wthn the next 1 steps, the S-O bond breaks and PO thus becomes NPO to form nonpolyhedral water (H-NPO*-H*). The orgnal O*-H* bond remans unbroken up to the 2553 th step exstng mostly as a non-polyhedral hydroxyl although four-atom structures wth other hydrogen attached to dfferent PO or NPO or molecular water appear/dsappear a few tmes. Long structure nvolvng as many as sx atoms (NPO-H-NPO*-H-NPO-H) s formed at the 25 th step, whch soon (wthn 16 steps) reduces to NPO*-H*. Later, ths hydroxyl turns nto molecular water whch forms bond wth another nonpolyhedral hydroxyl before the orgnal bond (NPO*-H*) breaks (between 2538 and 2553 steps): H-NPO*-H*. NPO-H H-NPO*-H*-NPO-H H-NPO* H*-NPO-H In effect, the orgnal hydrogen s now transferred to another NPO. The non-polyhedral water soon reduces to a non-polyhedral hydroxyl, whch lasts for another 165 steps. At the 2556 th step, t turns nto a polyhedral hydroxyl (H*-PO) by formng S-O bond. Ths s the second tme H* s bonded wth PO (of course, a dfferent oxygen atom than orgnal O). The polyhedral hydroxyl s stable for another 4 steps before t loses H* to another PO va edge-decoraton. The newly formed polyhedral hydroxyl remans stable untl the 2875 th step and then t loses H* to non-polyhderal hydroxyl thereby formng molecular water: PO-H* NPO-H PO-H*-NPO-H PO. H*-NPO-H The water molecule loses/exchanges the other hydrogen a few tmes before H* s transferred to PO at the 312 th step: PO H*-NPO-H PO-H*-NPO-H PO-H* NPO-H Durng the next 37 steps, H* moves from PO to PO three tmes (twce va polyhedral brdgng and once va edge decoraton) before t turns nto a nonpolyhedral hydroxyl (at the 3472 th step). Ths hydroxyl turns nto a polyhedral hydroxyl at the 3564 th step and H* mantans ts polyhedral assocaton over next 8 steps nvolvng 11 PO-to-PO transfers. Then H* s transferred to a NPO and so on. 12