Size dependence of thermal expansion of nanostructures

A theory for the size dependence of the coefficient of thermal expansion (CTE) of nanostructures is developed. The theory predicts that the fractional change in the CTE from the bulk value scales inversely with the size of the nanostructure. An explicit relation for the intrinsic length scale that governs the size dependence is derived. The theory is tested against full-scale molecular dynamics simulations and excellent agreement is found. Further, it is shown that the CTE can rise or fall with size depending on the properties of the bounding surfaces of the nanostructure. The theory has the potential to be used as part of a predictive tool for the design of nanostructures.

Figure 1

(Color online) Size dependence of coefficient of thermal expansion $\alpha$. Top: Results for LJ slabs bounded by (100) crystal planes of thickness $h$. Bottom: Results for LJ square (side $h$) bars bounded by (100) crystal planes. The lines indicated as “Fit” correspond to fits of simulation data to Eq. (7).

Figure 2

(Color online) Variation of CTE with thickness of Al[20] slabs bounded by (100) crystal surface. This surface is known to have a negative biaxial modulus. The line indicated as “Fit” correspond to fits of simulation data to Eq. (7).