Figure 1

(Color online) Molar Gibbs energy diagram illustrating the method to calculate onset driving forces for the beginning of the precipitation of two new phases $\alpha$ (solid solution) and $\epsilon$ (line compound) from an undercooled liquid for the composition $x_B^L$. The dotted line represents the common tangent (equilibrium), and the dashed lines show the tangents to the Gibbs energy curve of the liquid phase at the composition $x_B^L$, and to the Gibbs energy curve of $\alpha$ at the composition $x_B^{\alpha }$. $G_A^L$ and $G_B^L$ are the chemical potentials of A and B atoms, respectively, in the liquid phase of composition $x_B^L$ and at the temperature $T$. Vertical arrows represent the onset driving forces for the precipitation of $\alpha$ $\left({\mathrm{ODF}}^{\alpha }\right)$ and $\epsilon$ $\left({\mathrm{ODF}}^{\epsilon }\right)$, respectively.Reuse & Permissions

Figure 2

Calculated onset driving forces of various crystalline phases for ${\mathrm{Ca}}_{55}{\mathrm{Mg}}_x{\mathrm{Zn}}_{100-x}$ alloys versus Mg content at $390\mathrm{K}$. The circles represent the alloy compositions studied. Their critical thicknesses are indicated.Reuse & Permissions

Figure 3

Calculated onset driving forces of various crystalline phases for ${\mathrm{Ca}}_{60}{\mathrm{Mg}}_x{\mathrm{Zn}}_{100-x}$ alloys versus Mg content at $390\mathrm{K}$. The circles represent the alloy compositions studied. Their critical thicknesses are indicated.Reuse & Permissions

Figure 4

Calculated onset driving forces of various crystalline phases for ${\mathrm{Ca}}_{(100-x)}{\mathrm{Mg}}_x{\mathrm{Zn}}_{20}$ alloys versus Mg content at $390\mathrm{K}$. The circles represent the alloy compositions studied. Their critical thicknesses are indicated.Reuse & Permissions

Figure 5

Complete two-dimensional plot of the onset driving forces (ODF) calculated for the full composition space in the Ca-Mg-Zn system at $390\mathrm{K}$. The two ODF minima are identified by arrows.Reuse & Permissions

Figure 6

Correlation between ODF and GFA indicators (a) $T_{rg}=T_g∕T_l$, (b) $\alpha =T_x∕T_l$, (c) $\gamma =T_x∕(T_g+T_l)$, (d) $T_{rgx}=T_g{T}_x∕T_l{T}_m$, and (e) $\Delta T_{xg}=T_x-T_g$ for 11 Ca-Mg-Zn alloys given in Table . The trendlines and corresponding regression coefficients $\left(R^2\right)$ are shown.Reuse & Permissions

Figure 7

Correlation between the critical thickness $\left(\lambda \right)$ and GFA indicators (a) $T_{rg}=T_g∕T_l$, (b) $\alpha =T_x∕T_l$, (c) $\gamma =T_x∕(T_g+T_l)$, (d) $T_{rgx}=T_g{T}_x∕T_l{T}_m$, and (e) $\Delta T_{xg}=T_x-T_g$ for 11 Ca-Mg-Zn alloys given in Table . The trendlines and corresponding regression coefficients $\left(R^2\right)$ are shown.Reuse & Permissions

Figure 8

(a) Correlation between the critical thicknesses $\left(\lambda \right)$ and the calculated onset driving force normalized by the gas constant $R$ and absolute temperature $T$ (ODF/RT) for 11 Ca-Mg-Zn alloys given in Table . (b) The same data set arrayed into three groups, with alloys forming $\mathrm{Ca}{\mathrm{Mg}}_2$ (1st group), CaZn (2nd group) and ${\mathrm{Ca}}_5{\mathrm{Zn}}_3$ (3rd group) phases during the onset of crystallization of the undercooled liquid (see Figs. 1, 2, 3).Reuse & Permissions

Figure 9

Correlation between the critical thickness $\left(\lambda \right)$ and the fragility index $D$. The trendline and corresponding regression coefficients $\left(R^2\right)$ are shown.Reuse & Permissions

Figure 10

Correlation between the critical thickness $\left(\lambda \right)$, the fragility index $D$ and the calculated onset driving force normalized by the gas constant $R$ and absolute temperature $T$ (ODF/RT) for 11 Ca-Mg-Zn alloys given in Tables . Values of the critical thicknesses are indicated in millimeters in the black sphere for each alloy composition. The data are well fitted by the meshed plane drawn. Its equation and regression coefficient are also shown.Reuse & Permissions