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denoting the energetic difference between crystal and liquid, and
S
m
/
R
, showing the
corresponding structural difference. The cited data in table 2 for
H
m
/
V
values are between 27
and 172 J/cm
3
, while those for
S
m
/
R
values are in the range from 0.064 to 0.568. Since
H
m
/
V
and
S
m
/
R
for one substance do not simultaneously take the largest values induced by different
T
m
, with the known fact that
H
m
=
T
m
S
m
, the real differences in γ
sl0
values are smaller than the
largest possible difference.
Let γ
sl0
of Eq. (2.13) be expressed as γ
sl0
=
c
1
hH
m
/
V
, there is
c
1
= 2
S
vib
/(3
R
). Because the
sizes of
S
vib
are different for crystals with different types of bonds and almost follow the
sequence of ionic bond, covalent bond, metallic bond, hydrogen bond, van der Waals force,
c
1
is component dependent. As shown in table 2, the sizes of
S
vib
vary from 9.22 J/g-atom for Sn
to 0.53 J/g-atom for Cis-decalin, which makes
c
1
in the range from 0.74 to 0.04. This range is
larger than that for
c
1
′ [11]. The reason can be illustrated as the followings: On one hand,
although γ′
sl0
in Eq. (2.3) is considered as the bulk solid-liquid energy, γ′
sl0
≈ γ
sl
(
D
n
,
T
n
) has
been implied [11,18-19] (it will be further demonstrated in Section 2.3), which makes the
maximum value of
c
1
′ is smaller than 0.74; On the other hand, molecular crystals are not
considered when Eq. (2.3) was proposed, thus the minimum value of
c
1
′ is larger than 0.04.
γ
sl0
(T
m
) for Intermetallic Compounds and Oxides
For intermetallic compounds and oxides listed in table 3, the predictions based on Eq.
(2.13) also correspond to the available theoretical results [57-59] with the absolute deviation
smaller than 6%. Although higher
T
m
and larger Δ
V/V
of these substances make
S
vib
comparable with those of elemental crystals, larger
H
m
and smaller
V
lead that their γ
sl0
(
T
m
)
values are larger than those of most of elemental crystals.
Table 3. Comparison of
γ
sl0
(
T
m
) between
γ
sl0
by Eq. (2.13) and other
theoretical results
γ′
for intermetallic compounds and oxides 57-59]
V
(cm
3
/g-
atom)
H
m
(kJ/g-
atom)
S
vib
(J/g-
atom K)
γ
sl0
γ′
h
(nm)
ρ
s
(g/cm
3
)
T
m
(K)
Δ
V
/
V
(%)
(mJ/m
2
)
651 620
0.277
6.27
8.1
28.2 2173
29
8.4
α-MoSi
2
538 509
0.460
6.32
8.0
22.9 2303
35
5.1
β-MoSi
2
0.193
WO
3
233 241
7.2
8.1
17.9
1743
18
6.8
29.1 2988
ZrO
2
491 500
0.223
5.89
7.0
15
6.6
Ref
57,60-61
56-57
56
56-57
57,62
The values of Δ
V/V
for MoSi
2
are calculated in terms of Eq. (5) of Ref. [57] and that of ZrO
2
is also taken
from Ref. [57]. Δ
V/V
of WO
3
is unavailable and assumed to be the average of those of ZrO
2
and Al
2
O
3
[62].
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