Isotope Effect on the Thermal Conductivity of Graphene

<table>(a) Phonon dispersions for <svg height="14.6" id="M35" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 22.112499 14.6" width="22.112499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">C</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.61,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">2</tspan>
</text>
</g>
</g>
</svg> graphene and (b) Grüneisen parameters of graphene as a function of <svg height="9.875" id="M36" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.9124999 9.875" width="7.9124999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
<g transform="translate(72,-64.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑞</tspan>
</text>
</g>
</g>
</svg> momentum for each vibration mode. <svg height="10.475" id="M37" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 9.3000002 10.475" width="9.3000002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.475)">
<g transform="translate(72,-63.62)">
<text transform="matrix(1,0,0,-1,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">Γ</tspan>
</text>
</g>
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</svg>M and <svg height="10.475" id="M38" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 9.3000002 10.475" width="9.3000002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.475)">
<g transform="translate(72,-63.62)">
<text transform="matrix(1,0,0,-1,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">Γ</tspan>
</text>
</g>
</g>
</svg>K represent armchair and zigzag directions of graphene. Phonon dispersion for graphene is calculated with PHON code [<a href="/journals/jnm/2010/537657/#B18">17</a>] for REBO carbon potential.</table>

Journal of Nanomaterials

Isotope Effect on the Thermal Conductivity of Graphene

Figure 3