= Solution
In terms of diameter $d$, the model is
$$
T_m(d)=1337\left(1-\frac{0.96\ \mathrm{nm}}d\right)\ \mathrm K.
$$
Thus \b[<melting> <temperature> rises toward the bulk value as diameter increases], with a depression proportional to $1/d$. The analytic sketch below includes the calculated point. It deliberately does not extrapolate the continuum expression down to a zero or negative <melting> <temperature>.
Facet-dependent energies, non-spherical shapes, size-dependent interfacial energies and <latent heat>, structural changes or magic cluster sizes can modify the trend. <Premelting> can broaden the transition. A substrate or encapsulating matrix changes interface energetics and can stabilize or destabilize the solid. <Ligands>, impurities, <strain>, <particle size distribution>s, coalescence during heating and nonequilibrium <temperature>/beam effects can shift the measured transition. These possibilities motivate separate thermal, structural and size controls rather than a fit to diameter alone.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2021/paper-2-gold-melting.png]
{title=Original Gibbs-Thomson model curve for gold with the three-nanometre estimate marked}
Back to article page
