SIZE DEPENDENT INTERFACE ENERGY - Energy Research Developments: Tidal Energy, Energy Efficiency and Solar Energy - page 209

determined γ CNT values in terms of the CNT [11] are firstly listed in table 5. A good
agreement between them is shown. Thus, the obtained γ CNT values in the CNT are not γ sl0 ( T m )
values, but γ sl ( D n , T n ) ones. γ sl ( D n , T n ) < γ sl0 ( T m ) could be partly induced by different structures
between nuclei and bulk crystals although it is difficult to determine the nucleus structure.
The above argument can be further supported by considering the correlation of the incoherent
interface energy between adjacent crystals or grain-boundary energy γ ss0 with γ sl0 ( T m ), which
may be explained in detail in Section 3.1.

Table 5. The model predictions in terms of Eq. (2.26)
and the corresponding experimental results calculated from the
CNT [11] with relevant parameters listed in table 1

D n / h

γ sl ( D n , T n ) γ CNT θ n

(mJ/m 2 )

Co 248 234 0.187 11.0

Ni 283 255 0.185 11.6

Cu 200 177 0.174 12.0

Pd 211 209 0.182 10.8

Ag 137 126 0.184 11.2

Pt 243 240 0.181 11.2

Au 150 132 0.172 11.6

Pb 36 33 0.133 14.0

Mn 206 206 0.206 10.2

Fe 186 204 0.164 11.6

Hg 21 24 0.247 9.0

Al 110 93 0.14 12.0

Sn 62 55 0.208 12.0

Ga 61 54 0.25 10.8

Sb 109 101 0.15 12.6

Bi 45 54 0.166 9.6

Ge 201 181 0.184 11.0

Ref 11

Similarly, although γ sl0 ( T m ) of pure Si was reported to be 352±38 and 332 mJ/m 2 [39],
recent experiment has shown that γ CNT = 380 mJ/m 2 at θ = 0.21 [91]. Combining Eqs. (2.26-c)
and (2.27-c), the real γ sl0 ( T m ) value of pure Si should be 680 mJ/m 2 , which corresponds to
γ sl0 ( T m ) = 738 mJ/m 2 by Eq. (2.13) and γ TS = 672 mJ/m 2 by Eq. (2.14).
As shown in Ref. [39], the γ sl0 ( T e ) values of Solid Al-liquid Al-Cu, Solid Al-liquid Al-Si
and Solid Pb-liquid Pb-Sn systems are only a litter larger than the γ sl0 ( T m ) values of pure Al
and Pb where T e is eutectic temperature. However, γ sl0 ( T e ) of Solid Si-liquid Al-Si system is
much smaller than γ sl0 ( T m ) of pure Si. The possible reason can be explained as the following:
T e / T m for Al and Pb are about 0.90 and 0.76 while that for Si is 0.50. For the bulk crystals,
γ sl0 ( T e )/γ sl0 ( T m ) for Al and Pb are 0.97 and 0.92 while that for Si is 0.25 in terms of Eqs. (16-a)
and (16-c). Although it is inappropriate that Eqs. (2.26-a) and (2.26-c) for pure metals and