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\begin{document}

\title{Comparison of biotite elastic properties recovered by spherical
nanoindentations and atomistic simulations - influence of nano-scale
defects in phyllosilicates}



\author[1]{Eril Suhada Lanin}%
\author[1]{Hiroki Sone}%
\author[1]{Zheng Yu}%
\author[1]{Qitong Liu}%
\author[1]{Bu Wang}%
\affil[1]{University of Wisconsin-Madison}%


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  \date{May 16, 2024}


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\begin{abstract}
Phyllosilicate minerals, due to their sheets structure and morphology,
are known to cause anisotropy in bulk rock properties and make the bulk
rock more compliant. Accurately characterizing the micromechanical
behavior of phyllosilicate minerals from laboratory observations, which
eventually translates to the bulk rock behavior, is still challenging
due to their fine-grained nature. Recent advances in atomistic
simulations open the possibility of theoretically investigating such
mineral mechanical behavior. We compare the elastic properties of
biotites recovered by spherical nanoindentation with those predicted
from density functional theory (DFT) simulations to investigate to what
extent theoretical predictions reproduce actual phyllosilicate
properties. Spherical nanoindentation was conducted using schist rocks
from Poorman Formation, South Dakota, USA, to recover continuous
indentation stress-strain curves. Loading in the layer-normal
orientation shows an average indentation modulus (M) of about 35 GPa,
while loading in the layer-parallel orientation gives a higher average
of about 95 GPa. To facilitate comparison, the elastic stiffness
constants (c\textsubscript{ij}) determined from DFT were converted to
indentation modulus (M) using solutions proposed in this study. The
majority of the nanoindentation modulus results are below the values
inferred from the simulation results representing ideal defect-free
minerals. We suggest that crystal defects present at the nano-scale,
potentially ripplocations, are the dominant cause of the lower
indentation modulus recovered from nanoindentation compared to those
inferred from DFT simulations. Results highlight the importance of
acknowledging the defects that exist down to the nano-scale as it
modifies the mechanical properties of phyllosilicates compared to its
pure defect-free form.%
\end{abstract}%



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