AUXILIARY MATERIAL
Calcium silicate (C-S-H) samples with Ca/Si ratio of 1.00 were prepared using
stoichiometric amounts of CaO and amorphous silica mixed at a water-solids weight ratio of
about 12.9. The reactants were placed in high-density polyethylene (HDPE) bottles that were
continuously rotated (16 rpm) for two weeks, and then they were left to continue hydrating for
three months.
The HDPE bottles were purged with inert gas to minimize the effects of
carbonation. Excess water was removed by filtration in a He filled glove box, and material was
dried under vacuum for 4 days. The hydrated tricalcium silicate (hyd-C3S) sample was made by
mixing distilled water and pure tricalcium silicate in a mass ratio of 0.5. The sample was cured in
a sealed container to avoid carbonation for 2 months when the sample was finely ground for the
experiment. Note the two hyd-C3S measurements were performed during different experimental
runs to the C-S-H measurements. Due to re-positioning of the beamstop between the
measurements the C-S-H low-Q limit is slightly lower than the hyd-C3S measurement.
X-rays with incident wavelength 0.01075(5)nm were used. Samples were mounted in a
2mm diameter kapton tube with 0.1mm wall thickness. At this x-ray energy, the sample
container attenuation length is 55mm, therefore, no attenuation corrections were made. The
MAR345 image plate detector was placed perpendicular to the incident beam at a distance of
319(1)mm from the sample, providing a 4-220nm 1 Q range. The SX(Q) used here refers to the
observable structure factor [19]. The position of the low-Q (basal) peak in the synthetic C-S-H(I)
is centered at a d-spacing of 1.1(1)nm has previously also been observed in [20-22], although
higher basal spacings have also been reported in [23, 24].
The Fourier back-transforms after removal of the r < 0.1nm features shown in figure 1(a)
neglected the O-H separation expected around 0.095nm due to it is small ~2% weighting). The
slight intensity refinement in figure 1(b) is justified as the measured Hyd-C3S pattern was not a
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good powder average. For the comparison in figure 2 a small scaling factor ( ˆ
5% ) was applied to
the measured g(r), such that the SiO peak area corresponded to tetrahedral coordination,
effectively correcting for density and Sx(Q) normalization uncertainties. To account for damping
of the distribution function, and equivalently size broadening of the diffraction pattern, the data
in figure 3 was modified prior to refinement using the upper blue dash curve plotted in figure 2
(as this Gaussian represents size broadening effects). The middle curves are the distribution
functions of 1.1nm tobermorite before and after refinement to fit the measured data.
The RMC simulation was initiated from the Hamid 1.1nm tobermorite crystal structure
(H atoms were neglected). The simulation box was approximately square with a side length
around 4.4nm, and contained 5952 atoms.
Since the initial crystal structure was already
remarkably similar to the measured CSH(I), small (0.0025nm) atom moves were used. Also to
maintain the nearest neighbor SiO and CaO structural units, their initial structure factors were
used as constraints for r<0.3nm in the refinement. This is valid given the CSH(I) measurements
and crystal structures are already in near perfect agreement in this r<0.3nm region. The structure
refinement is then essentially asking the question: Can these SiO and CaO units be easily
reorganized into a structure that matches the CSH(I) measurements.
To account for the small compositional difference between C-S-H(I) and tobermorite, a
fraction of the bridging Si-O tetrahedra were removed at random in the RMC model. This is
preferred to the addition of jennite-like regions as removal of bridging Si results in the model
being consistent with the measured SiO chain lengths of C-S-H(I). Prior to fitting the measured
distribution function was modified using the damping curve shown in Fig. A (upper blue dashed
curve). This approximately removes the damping in the measurements which is present due to
averaging of the structure across many nano-grains.
One key difference between atomistic simulation methods and distribution function
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measurements is that simulations are typically limited to describing the system with a few
thousand atoms. The experimental distribution function, however, is the average of  1020 atoms.
This is especially important when comparing simulation results on nano-crystalline systems, as
the experimental distribution functions are the result of averaging over  1016 nano-crystals,
whereas a simulation may only encompass one. The broadened crystal patterns in figure A were
therefore obtained by applying an equal width Gaussian broadening to each Bragg peak. This is
valid for this setup because the Q < 40 nm 1 region corresponds to  < 2 , i.e., cos( )  1 to
within 1%, therefore, the Scherrer equation reduces to constant broadening in Q . Figure B
shows the final refined structure that is consistent with the measured data.
Figure A. The X-ray structure factors of synthetic C-S-H(I) (top line), and the reported
crystal structures (grey spikes) with a constant Q broadening to simulate nano-crystal size
effects. From top to bottom the crystal structures are: 1.1nm tobermorite (blue = Merlino et al
[16], grey dash = Hamid [15]) , jennite [25], and 1.4nm tobermorite [26]. The intensity of the
broadened crystalline patterns has been scaled for convenient comparison.
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Figure B. The final structure that is refined to be consistent with the measured data.
Green polyhedra = CaO, blue tetrahedra= SiO, red spheres = inter layer O (water), green spheres
= interlayer Ca.
Additional References :
19. Egelstaff, P.A. 'Introduction to the Liquid State' 2nd edition, Oxford University Press (1994).
20. Black, L., Garbev, K., Beuchle, G., Stemmermann, P. & Schild, D. J. Cem. Conc. Res. 36 (2006)
1723.
21. Matsuyama, H. & Young, J. F. J. Mater. Res. 14 (1999) 3379.
22. Cong, X. & Kirkpatrick, R.J.. J.Cem. Conc.Res. 25(6) (1995) 1237.
23. Merlin, F., Lombois, H., Joly, S., Lequeux N., Halary, J-L & Van Damme, H. J. Mater. Chem. 12
(2002) 3308.
24. Suzuki, S. & Sinn, E. J. Mater. Sci. Lett. 12 (1993) 542.
25. Bonaccorsi, E., Merlino, S. & Taylor, H. F. W. Cement and Concrete Res., 34 (2004) 1481
26. Bonaccorsi, E., Merlino, S. & Kampf, A. R J. Am. Ceram. Soc. 88 (2005) 505.
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