102
6 Atomic Chains, Clusters, and Nanocrystals
from 0 to −6% [15]. These observations evidence the shortening and strengthening
of bonds between undercoordinated atoms.
The S 2s and the S 2p band of ZnS and CdS nanosolids exhibit each three components [16, 17]. These components correspond to the outermost capping layer, the
surface layer, and the core of the nanosolid. The capping and the surface layer are
each 0.2–0.3 nm thick. Particle size reduction enhances the intensities of the capping and the surface components rendering the intensity of the core component,
which follows the size-dependence of the surface-to-volume ratio of a nanosolid.
These observations evidence that cluster size reduction enhances globally the
CLS for nanostructures, regardless of composition or structure phase of the
nanocrystals [5].
An incorporation of the BOLS-NEP scheme to STM/S, PES, APECS, and ZPS
measurements as well as DFT calculations leads to consistent understanding of the
performance of atomic clusters and nanocrystals from the perspective of local bond
contraction, quantum entrapment, and nonbonding (valence) electron polarization.
6.2 BOLS-TB Formulation
The size dependent CLS of a nanocluster follows the core-shell configuration [18,
19]:
E ν (K ) − E ν (12)
E ν (12) − E ν (0)
=
H (τ, m, K ) (B O L S)
B ν
K
(Measurement)
⎧
⎨
⎩
H (τ, m, K ) =
i≤3
γ i (C
−m
i
− 1) ( perturbation)
γ i = τ C i K
−1
(sur f ace-to-volume)
(1)
The perturbation H is bond nature m, cluster size K, and geometrical shape τ
dependent. The B ν is the slope of the linearization of the measured size dependent
CLS for nanocrystals. The perturbation counts the weighted contribution of the outermost three atomic layers. The C
−m
i
− 1 term is exact what used for defects and
solid skins with different z values. Therefore, nanostructure is an extension of the
point defects and solid skins of varied curvatures and core-shell configuration.
The following illustrates how to resolve the cluster size dependent CLS when
the τ , m, E ν (12), and E ν (0) are yet to be known. Firstly, one can obtain the E ν (12)
by linearizing the measurements E ν (K) = b + B
/K. The intercept at the vertical
axis is the E ν (12). Equaling the BOLS prediction to the measurement yields, H =
B ν /K and B ν = τ
i≤3 C i
C
−m
i
− 1
. One can determine the m, τ , and E ν (0) from
measurements using this relationship with the known C i (z) given in Eq. (1) and the
known z i in Eq. (1). The accuracy of quantities estimated from analyzing the XPS
data for nanostructures is often one order lower with respect to that derived from
skin XPS analysis as the former is subject to the accuracy and uniformity of particle
sizes. The following shows typical examples.
6 Atomic Chains, Clusters, and Nanocrystals
from 0 to −6% [15]. These observations evidence the shortening and strengthening
of bonds between undercoordinated atoms.
The S 2s and the S 2p band of ZnS and CdS nanosolids exhibit each three components [16, 17]. These components correspond to the outermost capping layer, the
surface layer, and the core of the nanosolid. The capping and the surface layer are
each 0.2–0.3 nm thick. Particle size reduction enhances the intensities of the capping and the surface components rendering the intensity of the core component,
which follows the size-dependence of the surface-to-volume ratio of a nanosolid.
These observations evidence that cluster size reduction enhances globally the
CLS for nanostructures, regardless of composition or structure phase of the
nanocrystals [5].
An incorporation of the BOLS-NEP scheme to STM/S, PES, APECS, and ZPS
measurements as well as DFT calculations leads to consistent understanding of the
performance of atomic clusters and nanocrystals from the perspective of local bond
contraction, quantum entrapment, and nonbonding (valence) electron polarization.
6.2 BOLS-TB Formulation
The size dependent CLS of a nanocluster follows the core-shell configuration [18,
19]:
E ν (K ) − E ν (12)
E ν (12) − E ν (0)
=
H (τ, m, K ) (B O L S)
B ν
K
(Measurement)
⎧
⎨
⎩
H (τ, m, K ) =
i≤3
γ i (C
−m
i
− 1) ( perturbation)
γ i = τ C i K
−1
(sur f ace-to-volume)
(1)
The perturbation H is bond nature m, cluster size K, and geometrical shape τ
dependent. The B ν is the slope of the linearization of the measured size dependent
CLS for nanocrystals. The perturbation counts the weighted contribution of the outermost three atomic layers. The C
−m
i
− 1 term is exact what used for defects and
solid skins with different z values. Therefore, nanostructure is an extension of the
point defects and solid skins of varied curvatures and core-shell configuration.
The following illustrates how to resolve the cluster size dependent CLS when
the τ , m, E ν (12), and E ν (0) are yet to be known. Firstly, one can obtain the E ν (12)
by linearizing the measurements E ν (K) = b + B
/K. The intercept at the vertical
axis is the E ν (12). Equaling the BOLS prediction to the measurement yields, H =
B ν /K and B ν = τ
i≤3 C i
C
−m
i
− 1
. One can determine the m, τ , and E ν (0) from
measurements using this relationship with the known C i (z) given in Eq. (1) and the
known z i in Eq. (1). The accuracy of quantities estimated from analyzing the XPS
data for nanostructures is often one order lower with respect to that derived from
skin XPS analysis as the former is subject to the accuracy and uniformity of particle
sizes. The following shows typical examples.