Interfacial free energy and medium range order: Proof of an inverse of Frank's hypothesis

We study the relation of crystal-liquid interfacial free energy and medium range order in the quasicrystal-forming $\mathrm{T}{\mathrm{i}}_{37}\mathrm{Z}{\mathrm{r}}_{42}\mathrm{N}{\mathrm{i}}_{21}$ liquid from undercooling experiment and ab initio molecular dynamics (MD) simulation. Adding a small amount of Ag to the liquid significantly reduces the degree of undercooling, which is suggestive of small interfacial free energy, and thus very similar atomic configuration between the liquid and the icosahedral quasicrystal phases. Using ab initio MD study, we find that Ag atoms predominantly form a bond with Zr atoms in the short range and, further, Ag-Zr pairs are extended in the liquid, as a medium range order which is identical to the global structural feature reported recently [Liu et al., Phys. Rev. Lett. 105, 155501 (2010)]. This result may expect extremely small undercooling if the icosahedral medium range order exists in a liquid forming an icosahedral quasicrystal, which implies the ambiguity of clear distinction of heterogeneous and homogeneous nucleation.

Figure 1

Temperature-time curves for a $\mathrm{T}{\mathrm{i}}_{37}\mathrm{Z}{\mathrm{r}}_{42}\mathrm{N}{\mathrm{i}}_{21}$ liquid. The inset figures show the recalescence behaviors of each cycle. The spiked features in the temperature at the end of the plateaus and after the plateaus are caused by surface roughness due to crystallization. Case (I) is of (a), (d), and (e), and case II is of (b), (c), and (f).

Figure 2

Temperature-time curves of $\mathrm{T}{\mathrm{i}}_{37}\mathrm{Z}{\mathrm{r}}_{42}\mathrm{N}{\mathrm{i}}_{21}$ (a) and ${\left(\mathrm{T}{\mathrm{i}}_{37}\mathrm{Z}{\mathrm{r}}_{42}\mathrm{N}{\mathrm{i}}_{21}\right)}_{96}\mathrm{A}{\mathrm{g}}_4$ (b). Melting temperature of i-phase is indicated at 790 °C and 787 °C in (a) and (b), respectively. The melting temperature for Laves phase is 820 °C. Panel (a) shows only the recalescence behavior for each sample.

Figure 3

Calculated nucleation barriers and critical radii for Ti-Zr-Ni quasicrystals with and without Ag. Assuming $\mathrm{\Delta }{\mathbf{G}}_{\mathit{l}-\mathit{s}}\left(\mathbf{1}\right)=\frac{\mathrm{\Delta }\mathbf{T}\mathrm{\Delta }{\mathbf{H}}_{\mathit{f}}}{{\mathit{T}}_{\mathit{i}}}$.

Figure 4

Pair distribution function, $g\left(r\right)$, of supercooled $\mathrm{T}{\mathrm{i}}_{37}\mathrm{Z}{\mathrm{r}}_{42}\mathrm{N}{\mathrm{i}}_{21}$ and ${\left(\mathrm{T}{\mathrm{i}}_{37}\mathrm{Z}{\mathrm{r}}_{42}\mathrm{N}{\mathrm{i}}_{21}\right)}_{96}\mathrm{A}{\mathrm{g}}_4$ liquids at 757 °C. (a) Total $g\left(r\right)$. (b) Partial $g\left(r\right)$’s for the same atomic pairs. (c) Partial $g\left(r\right)$’s for different atomic pairs. (d) Partial $g\left(r\right)$’s with transition metal–Ag pairs. Inset in (d) shows the fitting curve for $g\left(r\right)$ of Ag-Zr pair with six Gaussian curves (the gray color is of total fitting curve).

Figure 5

Analysis of the $\mathrm{T}{\mathrm{i}}_{37}\mathrm{Z}{\mathrm{r}}_{42}\mathrm{N}{\mathrm{i}}_{21}$ and ${\left(\mathrm{T}{\mathrm{i}}_{37}\mathrm{Z}{\mathrm{r}}_{42}\mathrm{N}{\mathrm{i}}_{21}\right)}_{96}\mathrm{A}{\mathrm{g}}_4$ obtained from MD simulations using the Honeycutt-Anderson (HA) method with a cutoff, $r_{\mathrm{cutoff}}3.9\mathrm{\AA }$, which is the first minimum in $g\left(r\right)$ in Fig. 4.