Large Melting-Point Hysteresis of Ge Nanocrystals Embedded in ${\mathrm{SiO}}_2$

The melting behavior of Ge nanocrystals embedded within ${\mathrm{SiO}}_2$ is evaluated using in situ transmission electron microscopy. The observed melting-point hysteresis is large ($\pm 17\%$) and nearly symmetric about the bulk melting point. This hysteresis is modeled successfully using classical nucleation theory without the need to invoke epitaxy.

Figure 1

Diffraction patterns and integrated intensity plots obtained during measurements of the Ge melting point. 1308 K is 97 K above the bulk melting point of Ge, and diffraction rings are clearly observed.

Figure 2

Intensity of the 111, 202, and 113 Ge diffraction rings as a function of temperature during heating (solid symbols) and cooling (open symbols). Both superheating and supercooling are clearly observed. The solid curve is the prediction of the kinetic theory presented in the text. All temperature measurements are uncertain to $\pm 15\mathrm{K}$.

Figure 3

(a)–(d) The kinetic pathway used to compute the transformation rate. A spherical particle of Ge is embedded in an ${\mathrm{SiO}}_2$ matrix. The nanocrystal is shown in cross section and is assumed axially symmetric about an axis pointing from left to right. (e) Free energy curves associated with melting (solid line) and solidification (dashed line) at the kinetically determined melting points for a nanocrystal with $r=2.5\mathrm{nm}$. The $x$ axis represents the volume fraction of the nucleating phase. (f) The predicted melting (solid line) and solidification (dashed line) points plotted vs nanocrystal radius.