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XRD patterns after the first exothermic peak
contain the peaks from both oxidized and unoxi-
dized nanoclusters. Also, the ratio in the XRD
peak intensities of the oxidized nanoclusters to
those of the unoxidized nanoclusters is roughly
proportional to the ratio of the area of the first
exothermic peak to the remaining ones, supporting
the idea that the several exothermic peaks origi-
nated from an uneven thermal contact of metallic
nanoclusters with the oven.
The final products of the oxidation reaction
were identified by using both XRD patterns and
colors. The XRD patterns shown in Fig. 4A,B
indicate that the final products are monoclinic
MoO3 and monoclinic WO3 oxides for Mo and W
nanoclusters, respectively, irrespective of the initial
cluster sizes. The cell constants were determined to
estimated by using both average diameters
ð¼ꢀ 30 nmÞ observed in TEM micrographs and
3
n ¼ 0:68ðR=rÞ in which R and r are the cluster and
atomic radii, respectively [10,11].
In order to extract an oxidation enthalpy from a
DSC curve, we first drew a baseline of a DSC
curve from the initial to the final temperatures
obtained from a TG curve as previously described
in the experimental section and then estimated the
total area of exothermic peaks. The total area was
then converted into energy (kcal/mol), which was
then calibrated by using the oxidation enthalpy of
graphite powder as reference material [14]. The
calibrated oxidation enthalpies are schematically
plotted in Fig. 5a,b for Mo and W nanoclusters,
respectively. As can be seen in Fig. 5a,b, the oxi-
dation enthalpies decrease to the corresponding
bulk values with increasing cluster size.
ꢀ
ꢀ
ꢀ
be a ¼ 3:845 A, b ¼ 3:692 A, c ¼ 6:907 A, and
b ¼ 104:12° for the monoclinic MoO3 oxides
ꢀ
ꢀ
ꢀ
and a ¼ 7:294 A, b ¼ 7:516 A, c ¼ 7:676 A, and
b ¼ 91:13° for the monoclinic WO3 oxides, in
agreement with the literature values [16,17]. The
colors were white and light yellow for MoO3 and
WO3 oxides, respectively, also in agreement with
the literature colors [16,18].
In previous works, we observed that the cluster
size ðnÞ was such that n (amorphous) < n (fcc) < n
(bcc) [10,11]. That is, we found that the stable
structure of Mo and W nanoclusters depended on
the cluster size and varied as above. The above
order can be easily noticed from the full widths at
half maximum (FWHMs) of the XRD peaks (see
Fig. 4A,B) because the cluster size is inversely
proportional to the FWHMs according to Scher-
rer’s formula [19]. In the case of both fcc and bcc
nanoclusters, the TEM micrographs shown in
Fig. 2 clearly show that n (fcc) < n (bcc) for both
Mo and W nanoclusters. Cluster sizes were
roughly estimated to be 30, 7000, 106 for amor-
phous, fcc, and bcc W nanoclusters, respectively,
and 2000 and 106 for fcc and bcc Mo nanoclusters,
respectively. Here, cluster diameter ðdÞ for amor-
phous and fcc structures was estimated by using
the FWHMs of XRD peaks and by using Scher-
rer’s formula as done in previous works [10,11],
which are 4 nm for fcc Mo nanoclusters and 1
and 6 nm for amorphous and fcc W nanoclusters,
respectively. Cluster sizes for a bcc structure were
Fig. 5. The schematic energetic diagram for the oxidation re-
action and the formation enthalpy versus n of: (a) Mo and (b)
W nanoclusters. The energy barriers are arbitrarily drawn be-
cause the energy barriers do not affect the oxidation enthalpies.
The n scale is also drawn arbitrarily.