SIZE DEPENDENT INTERFACE ENERGY - Energy Research Developments: Tidal Energy, Energy Efficiency and Solar Energy - page 214

Table 6. Comparisons of γ sl0 (T m ) between γ sl (D n ,T n ) by Eq. (2.13)
and other theoretical results γ CNT deduced from γ CNT [101]

γ sl
( D n , T n )

γ CNT V

(cm 3 /g-
atom)

H m
(kJ/g-
atom)

S m S vib

h
(nm)

T m
(K)

Δ V / V
(%)

θ D n / h

(J/g-
atom K)

(mJ/m 2 )

LiF 101 124 0.125 4.9 1121 13.4 29.4 12.0 7.5 0.21 8.0
LiCl 72 86 0.257 10.0 883 10.0 26.2 11.3 7.1 0.21 8.0
LiBr 54 46 0.258 12.6 823 8.8 24.3 10.7 6.5 0.15 10.0
NaF 218 206 0.292 8.2 1269 16.8 27.4 13.2 8.9 0.22 9.0
NaCl 114 112 0.302 13.5 1074 14.1 25.0 13.1 8.9 0.23 9.0
NaBr 88 88 0.304 16.1 1020 13.1 22.4 12.8 8.8 0.23 9.0
KCl 86 82 0.328 18.8 1043 13.1 17.3 12.6 9.1 0.23 9.4
KBr 70 63 0.334 21.7 1007 12.6 16.6 12.6 9.1 0.23 9.4
KI 54 47 0.339 27.5 954 11.9 15.9 12.5 9.1 0.23 9.4
RbCl 61 57 0.326 22.0 996 11.8 14.3 11.9 8.7 0.23 9.0
CsF 61 46 0.288 18.5 976 11.3 11.6 8.8 0.23 9.0
CsCl 52 51 0.318 21.1 918 10.2 10.5 11.2 8.4 0.24 8.0
CsBr 64 66 0.329 24.0 909 11.8 13.0 10.2 0.26 9.0
CsI 81 69 0.342 28.1 900 12.9 14.2 11.4 0.23 12.0
Ref 44 56 29 29 44 29 101
S vib is determined by Eq. (2.10-a). Δ V/V for CsF, CsBr and CsI are unavailable and assumed to be equal to
that of CsCl since the differences of Δ V/V between different alkalis halides of the same family are small.

Solid-Solid Interface Energy

The Bulk Solid-solid Interface Energy γ ss0

For coherent or semi-coherent solid-solid interface, its interface energy can be
determined according to some classic dislocation models [102]. While for incoherent solid-
solid interface, which is the most case since even for semi-coherent interface, atomic diameter
misfit on the interface must be smaller than 0.15-0.25, γ ss0 remains challenge.
It is well known that a liquid may be regarded as a solid with such a high concentration of
dislocation cores that these are in contact everywhere [103]. Based on this consideration,
solid-solid interface energy γ ss0 at T m is considered to be twice of the solid-liquid interface
energy γ sl approximately [104], γ ss0 ( T m ) ≈ 2γ sl0 ( T m ). Combining with Eq. (2.13),

γ ss0 ( T m ) ≈ 4 hS vib H m /(3 VR ). (3.1)

As shown in table 7, the γ ss0 ( T m ) values based on Eq. (3.1) for eleven elemental crystals
(Cu, Ag, Au, Al, Ni, Co, Nb, Ta, Sn, Pb and Bi) and two organic crystals (Pivalic acid and
Succinonitrile) correspond to the available theoretical values γ′ ss0 [39,48-49,105-111]. In
addition, the data of γ′ ss0 and γ′ sl0 for Pivalic acid and Succinonitrile [48-49] determined by
the equilibrated grain boundary groove shapes also confirm the validity of γ ss0 ≈ 2γ sl0 with the
absolute deviation smaller than 5.5%. Thus, Eq. (3.1) can be used to quantitatively calculate
the γ ss0 values, at least for metals and organic crystals.