Serpentine polymorphism: A quantitative insight from first-principles calculations
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Single-walled chrysotile nanotubes [...] of increasing size (up to 5004 atoms per unit cell, corresponding to a radius of 205 Å) have been modelled at the Density Functional level of theory. For the first time, it is demonstrated that the (n, -n) and (n, n) series present a minimum energy structure at a specific radius (88.7 and 89.6 Å, respectively, referring to the neutral surface), corresponding to a rolling vector of (60, -60) and (105, 105), respectively. The minima are nearly overlapped and are lower in energy than the corresponding slab of lizardite (the flat-layered polymorph of chrysotile) by about 3.5 kJ mol-1 per formula unit. In both cases, the energy profile presents a shallow minimum, where radii in the range of 63 to 139 Å differ in energy by less than 0.5 kJ mol-1 per formula unit. The energy of larger nanotubes has a trend that slowly converges to the limit of the flat lizardite slab. Structural quantities such as bond distances and angles of nanotubes with increasing size asymptotically converge to the flat slab limit, with no discontinuities in the surrounding of the minimum energy structures. However, analysis of the elongation of a rectangular pseudo-unit cell along the nanotube circumference indicates that the main factor that leads lizardite to curl in tubes is the elastic strain caused by the mismatch between the lattice parameters of the two adjacent tetrahedral and octahedral sheets. It is also shown in this study that the curvature of the layers in one of the lately proposed models of antigorite, the "wavy-layered" polymorph of chrysotile, falls within the range of radii of minimum energy for the nanotubes. These findings provide quantitative insights into the peculiar polymorphism of these three phyllosilicates. They show also that chrysotile belongs to those families of inorganic nanotubes that present a minimum in their strain energy profile at a specific range of radii, which is lower in energy with respect to their flat equivalent.
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