$B_{2}$. One can compute the product of the theta functions via broken lines
and obtain

$\displaystyle\vartheta_{v_{1}}\vartheta_{v_{3}}$
$\displaystyle=1+\vartheta_{v_{2}},$
$\displaystyle\vartheta_{v_{2}}\vartheta_{v_{4}}$
$\displaystyle=(1+\vartheta_{v_{3}})^{2},$
$\displaystyle\vartheta_{v_{3}}\vartheta_{v_{5}}$
$\displaystyle=1+\vartheta_{v_{4}},$
$\displaystyle\vartheta_{v_{4}}\vartheta_{v_{6}}$
$\displaystyle=(1+\vartheta_{v_{5}})^{2},$
$\displaystyle\vartheta_{v_{5}}\vartheta_{v_{1}}$
$\displaystyle=1+\vartheta_{v_{6}},$
$\displaystyle\vartheta_{v_{6}}\vartheta_{v_{2}}$
$\displaystyle=(1+\vartheta_{v_{1}})^{2},$ (55)

where $v_{i}$ denotes the primitive generator of $l_{\gamma_{i}}$ for
$i\in\\{1,\dots,6\\}$ ordered cyclically. By [positive], Cheung and Magee
showed that the compactification of the cluster variety of type $B_{2}$ is the
del Pezzo surface of degree 6.

$l_{\gamma_{2}}$$l_{\gamma_{3}}$$l_{\gamma_{4}}$$l_{\gamma_{5}}$$l_{\gamma_{6}}$$l_{\gamma_{1}}$$M_{1}$$M_{2}$
Figure 11: The choice of a different branch cut for $X_{III}$.

To compare with the mirror constructed by Gross-Hacking-Keel, we take the
corresponding log Calabi-Yau pair $({Y},{D})$ with ${Y}$ the del Pezzo surface
of degree six. Since all del Pezzo surfaces of degree $6$ are isomorphic, we
will identify it with the blow up of $\mathbb{P}^{2}$ at three points, two
non-toric points on $y$-axis and one non-toric point on $x$-axis. The anti-
canonical divisor ${D}$ is the proper transform of the $x,y,z$-axis of
$\mathbb{P}^{2}$. Denote $H$ be the pull-back of the hyperplane class,
$E_{1},$ (and $E_{2},E_{3}$) be the exceptional divisor of the blow up on
$x$-axis (and $y$-axis).

######  Lemma 6.4.

There is an isomorphism of affine manifolds $B_{{\mathrm{GHK}}}\cong B$.

###### Proof.

From [GHK]*Lemma 1.6, toric blow-ups corresponds to the refinement of cone
decomposition but not change the integral affine structure. We will find a
successive toric blow-ups of $(\tilde{Y},\tilde{D})\rightarrow(Y,D)$ such that
not only the corresponding integral affine structure with singularity
coincides with $B$ but also its cone decomposition coincide with the chamber
structure bounded by the BPS rays. Such $\tilde{Y}$ is the ordered blow up the
intersection point of the $x,z$-axis, the proper transform of the $z$-axis and
the exceptional divisor, the proper transform of $y,x$-axis. Then we take
$\tilde{D}$ to be the pull-back of the $x,y,z$-axis. If we take the proper
transform of $y$-axis as $\tilde{D}_{1}$ and number the boundary divisors in
counter-clockwise order, then we have $\tilde{D}_{i}^{2}=-1$ if $i$ odd and
$\tilde{D}_{i}^{2}=-2$ if $i$ even.

Use (6.2), we have

$\displaystyle l_{\gamma_{1}}=$ $\displaystyle\\{\check{x}>0,\check{y}=0\\}$
$\displaystyle l_{\gamma_{2}}=$ $\displaystyle\\{\check{y}>0,\check{x}=0\\}.$

and we will identify $l_{\gamma_{1}}=\mathbb{R}_{>0}(1,0)$ and
$l_{\gamma_{2}}=\mathbb{R}_{>0}(0,1)$ and the rest of the proof is similar to
that in Lemma 5.9. ∎

Same argument of Lemma 5.22, we have a homeomorphism between $X_{III}\cong
Y\setminus D\cong\tilde{Y}\setminus\tilde{D}$ and $\tilde{Y}$ provides a
compactification of $X_{III}$. For the later discussion, we will replace
$(Y,D)$ by $(\tilde{Y},\tilde{D})$ for the rest of the section (see Remark
2.1). Similarly, we have the identification of the short exact sequence (50).

Next we need to compute the canonical scattering diagram for $(Y,D)$. Let
$D_{i}$ be the components of $D$ with $D_{i}$ are exceptional curves when $i$
even.

######  Lemma 6.5.

Under the identification of integral affine structures with singularities
$B\cong B_{\mathrm{GHK}}$, the canonical scattering diagram of Gross-Hacking-
Keel coincides with the scattering diagram in Theorem 6.1 via identification
$z^{[C_{i}]-\phi_{\rho_{i}}(v_{i})}=z^{\gamma_{i}}$ (or
$z^{[C^{j}_{i}]-\phi_{\rho_{i}}(v_{i})}=z^{\gamma_{i}}$) for $i$ is odd (or
even).

###### Proof.

We will first compute all the $\mathbb{A}^{1}$-curves of $({Y},{D})$, which is
standard and we just include it for self-completeness. Any irreducible curves,
in particular the irreducible $\mathbb{A}^{1}$ curves in $({Y},{D})$ are
either exceptional curves of blow-up from $\mathbb{P}^{2}$ or proper transform
of a curve $C\subseteq\mathbb{P}^{2}$. All the three exceptional curves are
$\mathbb{A}^{1}$-curves intersecting $D_{i}$ for $i$ odd. If $C$ is of degree
one and its proper transform is an $\mathbb{A}^{1}$-curve, then it either

  1. 1.

passes through two of the blow up points and its proper transform intersect
$\tilde{D}_{i}$ for $i$ odd. There are three such lines.

  2. 2.

passes through one blow up point and one intersection of toric $1$-stratum.
There are three such lines and intersect $\tilde{D}_{i}$ for $i$ even.

There are no higher degree curves with proper transform are
$\mathbb{A}^{1}$-curves and we draw the canonical scattering diagram and the
corresponding $\mathbb{A}^{1}$-curves in Figure 12.

Since $D\in|-K_{Y}|$ is ample, there is no holomorphic curves contained in
$Y\setminus D$. In particular, all the simple $\mathbb{A}^{1}$-curves are
irreducible and all the possible $\mathbb{A}^{1}$-curves are the multiple
covers of the above ones. The contribution of multiple covers of degree $d$ is
$(-1)^{d-1}/d^{2}$ by [GPS]*Proposition 6.1. Then the lemma follows from the
definition of the canonical scattering diagram [GHK]*Definition 3.3. Then the
function attached to the ray $\rho_{i}$ is

$\displaystyle
f_{i}=\begin{cases}(1+z^{[C_{i}]-\phi_{\rho_{i}}(v_{i})}),&\mbox{ if $i$ is
odd,}\\\ \prod_{j=1}^{2}(1+z^{[C_{i}^{j}]-\phi_{\rho_{i}}(v_{i})}),&\mbox{ if
$i$ is even,}\end{cases}$ (56)

where $C_{i},C_{i}^{j}$ are the $\mathbb{A}^{1}$-curve classes corresponding
to $l_{\gamma_{i}}$ in Figure 12. The assumption
$Z_{\gamma_{2}}=Z_{\gamma_{3}}$ implies that $z^{E_{2}]}=z^{[E_{3}]}$. Notice
that the monodromy of the only singular fibre shifts $\gamma_{i}$ to
$\gamma_{i+2}$. This implies that one would also need to identify

$\displaystyle z^{[E_{1}]}$
$\displaystyle=z^{[H-E_{i}]}=z^{[2H-E_{1}-E_{2}-E_{3}]}$ $\displaystyle
z^{[E_{i}]}$ $\displaystyle=z^{[H-E_{i}]}=z^{[H-E_{1}-E_{i}]},i=2,3.$

Equivalently, this corresponds to

$\displaystyle z^{[D_{i}]}=z^{[C_{i}]}=z^{[C_{i}^{j}]}=1.$

∎

$E_{1}$
---
$E_{i}$, $i=2,3$
---
$H-E_{i}$,
---
$i=2,3$
$H-E_{1}$
---
$H-E_{1}-E_{i}$, $i=2,3$
---
$2H-E_{1}-E_{2}-E_{3}$
---
$l_{\gamma_{1}}$
---
$l_{\gamma_{6}}$
---
$l_{\gamma_{5}}$
---
$l_{\gamma_{4}}$
---
$l_{\gamma_{3}}$
---
$l_{\gamma_{2}}$
---
Figure 12: The canonical scattering diagram and the $\mathbb{A}^{1}$-curves in
del Pezzo surfaces of degree $6$ (illustrated by a projection to
$\mathbb{P}^{2}$).

The GHK mirror can be computed via the spectrum of the algebra generated by
theta functions. The products of the theta functions

$\displaystyle\vartheta_{i-1}\vartheta_{i+1}$
$\displaystyle=z^{[D_{i}]}\prod_{j=1}^{2}\left(\vartheta_{i}+z^{[C_{i}^{j}]}\right)\quad\text{for
$i$ even,}$ $\displaystyle\vartheta_{i-1}\vartheta_{i+1}$
$\displaystyle=z^{[D_{i}]}\left(\vartheta_{i}+z^{[C_{i}]}\right)\quad\text{for
$i$ odd}.$

Again compare it with the analogue relations (6) from ${\mathcal{X}}$-cluster
algebra of type $B_{2}$, we conclude that the family Floer mirror $\check{X}$
corresponds to the particular fibre of the GHK mirror characterized by

$\displaystyle z^{[D_{i}]}=z^{[C_{i}]}=z^{[C_{i}^{j}]}=1.$

To sum up, we conclude the section with the following theorem.

######  Theorem 6.6.

The family Floer mirror of $X_{III}$ has a partial compactification as the
analytification of the $B_{2}$-cluster variety or the Gross-Hacking-Keel
mirror of $({Y},{D})$ described above Lemma 6.4. In particular, the family
Floer mirror of $X_{III}$ can be compactified as the analytification of a del
Pezzo surface of degree $6$.

##  7 Family Floer Mirror of $X_{IV}$

In this section, we will consider the case when $Y^{\prime}$ be a rational
elliptic surface with singular configuration $IV^{*}IV$ and $D^{\prime}$ is
the type $IV^{*}$ fibre. We claim that the family Floer mirror of $X$ is then
the del Pezzo surface of degree $4$. The argument is also similar to that in
Section 5. Such rational elliptic surface $Y^{\prime}$ has Weiestrass model

$\displaystyle y^{2}=x^{3}+t^{2}s^{4}.$ (57)

######  Theorem 7.1.

[L12]*Theorem 4.14 There exist
${\gamma_{1}^{\prime}},{\gamma_{2}^{\prime}},{\gamma_{3}^{\prime}},{\gamma_{4}^{\prime}}\in
H_{2}(X,L_{u})\cong\mathbb{Z}^{4}$ such that
$\langle{\gamma_{1}^{\prime}},{\gamma_{i}^{\prime}}\rangle=1$,
$\langle{\gamma_{i}^{\prime}},{\gamma_{j}^{\prime}}\rangle=0$ and
$Z_{{\gamma_{i}^{\prime}}}=Z_{{\gamma_{j}^{\prime}}}$, for
$i,j\in\\{2,3,4\\}$. Moreover, if we set

$\displaystyle\gamma_{1}$ $\displaystyle=-{\gamma_{1}^{\prime}},\
\gamma_{2}={\gamma_{2}^{\prime}},\
\gamma_{3}={\gamma_{1}^{\prime}}+{\gamma_{2}^{\prime}}+{\gamma_{3}^{\prime}}+{\gamma_{4}^{\prime}},\
\gamma_{4}={\gamma_{1}^{\prime}}+{\gamma_{2}^{\prime}}+{\gamma_{3}^{\prime}},$
$\displaystyle\gamma_{5}$
$\displaystyle=2{\gamma_{1}^{\prime}}+{\gamma_{2}^{\prime}}+{\gamma_{3}^{\prime}}+{\gamma_{4}^{\prime}},\
\gamma_{6}={\gamma_{1}^{\prime}}+{\gamma_{2}^{\prime}},\
\gamma_{7}={\gamma_{1}^{\prime}},\ \gamma_{8}=-{\gamma_{4}^{\prime}}.$

Then

  1. 1.

$f_{\gamma}(u)\neq 1$ if and only if $u\in l_{\gamma_{i}}$ and
$\gamma=\gamma_{i}$ for some $i\in\\{1,\cdots,8\\}$ .

  2. 2.

In such cases,

$\displaystyle
f_{\gamma_{i}}=\begin{cases}1+T^{\omega(\gamma_{i})}z^{\partial\gamma_{i}}&\mbox{
if $i$ odd,}\\\ (1+T^{\omega(\gamma_{i})}z^{\partial\gamma_{i}})^{3}&\mbox{ if
$i$ even.}\end{cases}$

  3. 3.

If we choose the branch cut between $l_{\gamma_{1}}$ and $l_{\gamma_{8}}$,
then the counter-clockwise mondoromy $M$ across the branch cut is given by

$\displaystyle{\gamma_{1}^{\prime}}$
$\displaystyle\mapsto-({\gamma_{1}^{\prime}}+{\gamma_{2}^{\prime}}+{\gamma_{3}^{\prime}}+{\gamma_{4}^{\prime}})$
$\displaystyle{\gamma_{2}^{\prime}}$
$\displaystyle\mapsto{\gamma_{1}^{\prime}}+{\gamma_{2}^{\prime}}$
$\displaystyle{\gamma_{3}^{\prime}}$
$\displaystyle\mapsto{\gamma_{1}^{\prime}}+{\gamma_{3}^{\prime}}$ (58)
$\displaystyle{\gamma_{4}^{\prime}}$
$\displaystyle\mapsto{\gamma_{1}^{\prime}}+{\gamma_{4}^{\prime}}.$ (59)

######  Lemma 7.2.

With suitable choice of coordinate $u$ on $B_{0}\cong\mathbb{C}^{*}$, we have

$\displaystyle
Z_{\gamma_{k}}(u)=\begin{cases}e^{\frac{5\pi}{6}i(k-1)}u^{\frac{2}{3}}&\mbox{if
$k$ odd,}\\\ \frac{1}{\sqrt{3}}e^{\frac{5\pi}{6}i(k-1)}e^{-\frac{\pi
i}{6}}u^{\frac{2}{3}}&\mbox{if $k$ even.}\end{cases}$ (60)

In particular, the angle between $l_{\gamma_{i}}$ and $l_{\gamma_{i+1}}$ is
$\frac{\pi}{4}$. See how the BPS rays position as demonstrated in Figure 13.

$\gamma_{1}=-{\gamma_{1}^{\prime}}$$\gamma_{2}={\gamma_{2}^{\prime}}$$\gamma_{3}=\gamma_{1}^{\prime}+\gamma_{2}^{\prime}+\gamma_{3}^{\prime}+\gamma_{4}^{\prime}$$\gamma_{4}=\gamma_{1}^{\prime}+\gamma_{2}^{\prime}+\gamma_{3}^{\prime}$$\gamma_{5}=2\gamma_{1}^{\prime}+\gamma_{2}^{\prime}+\gamma_{3}^{\prime}+\gamma_{4}^{\prime}$$\gamma_{6}={\gamma_{1}^{\prime}}+{\gamma_{2}^{\prime}}$$\gamma_{7}={\gamma_{1}^{\prime}}$$\gamma_{8}=-\gamma_{4}^{\prime}$
Figure 13: BPS rays near the singular fibre in $X_{IV}$. Note in Theorem 7.1,
we have $Z_{{\gamma_{i}^{\prime}}}=Z_{{\gamma_{j}^{\prime}}}$, for
$i,j\in\\{2,3,4\\}$.

###### Proof.

One can check that $Z_{\gamma}(u)=O(|u|^{\frac{2}{3}})$ and let
$Z_{\gamma_{k}}(u)=c_{k}u^{\frac{2}{3}}$. Using the relations between
$\gamma_{i}$ and straight-forward calculation show that

$\displaystyle c_{1}=1,c_{2}=\frac{1}{\sqrt{3}}e^{-\frac{\pi
i}{6}},c_{3}=e^{-\frac{\pi i}{3}},c_{4}=-\frac{i}{\sqrt{3}}$

after suitable normalization of the coordinate $u$. Then use the relation
$M_{\gamma_{i}}=\gamma_{i+4}$ to determines the rest of $c_{k}$. ∎

With the data above, the similar argument in Section 5.1 shows that the family
Floer mirror of $X_{IV}$ is gluing of eight copies of
$\mathfrak{Trop}^{-1}(\mathbb{R}^{2}\setminus\\{0\\})\subseteq(\mathbb{G}_{m}^{an})^{2}$
, with the gluing functions in Theorem 7.1. Similar to the argument of Section
5.3, we may change the branch cut in Figure 13 into two, as in Figure 14.

$\gamma_{1}=-{\gamma_{1}^{\prime}}$$\gamma_{2}={\gamma_{2}^{\prime}}$$\gamma_{3}=\gamma_{1}^{\prime}+\gamma_{2}^{\prime}+\gamma_{3}^{\prime}+\gamma_{4}^{\prime}$$\gamma_{4}=\gamma_{1}^{\prime}+\gamma_{2}^{\prime}+\gamma_{3}^{\prime}$$\gamma_{5}=2\gamma_{1}^{\prime}+\gamma_{2}^{\prime}+\gamma_{3}^{\prime}+\gamma_{4}^{\prime}$$\gamma_{6}={\gamma_{1}^{\prime}}+{\gamma_{2}^{\prime}}$$\gamma_{7}={\gamma_{1}^{\prime}}$$\gamma_{8}=-\gamma_{4}^{\prime}$
Figure 14: A choice of a different branch cut for $X_{IV}$

The scattering diagram of cluster type $G_{2}$ can be found in [GHKK]*Figure
1.2. One can show that the corresponding gluing functions of the
${\mathcal{X}}$ case are the same as those in Theorem 7.1 under suitable
identification. Then the family Floer mirror of ${X}_{IV}$ can be partially
compactified to gluing of eight tori (up to GAGA) with the gluing functions
same as the ${\mathcal{X}}$-cluster variety of type $G_{2}$.

Next we will construct a log Calabi-Yau pair $(Y,D)$ such that the
corresponding Gross-Hacking-Keel mirror corresponds to the family Floer mirror
of $X_{IV}$. We will take

  1. 1.

$Y$ to be the blow up of $\mathbb{P}^{2}$ at $4$ points, three of them are the
non-toric points on $y$-axis and one non-toric point on $x$-axis.

  2. 2.

$D$ is the proper transform of $x,y,z$-coordinate axis.

Let $\tilde{Y}$ be the successive toric blow up of $(Y,D)$ at the intersection
of $x,z$-axis, the proper transform of $z$-axis and the exceptional divisor,
the two nodes on the last exceptional divisor and then the proper transform of
$y,z$-axis in order. Then take $\tilde{D}$ to be the proper transform of $D$.
Denote $H$ to be the pull-back of the hyperplane class on $\mathbb{P}^{2}$,
$E_{1}$ (and $E_{2},E_{3},E_{4}$) to be the exceptional divisor of the blow up
on the non-toric point on the $x$-axis (and $y$-axis).

Similar to the argument Section 5.2 we have the following lemma.

######  Lemma 7.3.

The complex affine structure on $B_{0}$ together with $l_{\gamma_{i}}$ is
isomorphic to the integral affine manifold $B_{\mathrm{GHK}}$ of
$(\tilde{Y},\tilde{D})$. Moreover, the BPS rays $l_{\gamma_{i}}$ give the
correoding cone decomposition on $B_{\mathrm{GHK}}$ from
$(\tilde{Y},\tilde{D})$, the wall function with restriction
$z^{[D_{i}]}=z^{[E_{i}]}=1$ and the identification $d$ coincide with the
functions in Theorem 7.1

We then can compute the canonical scattering diagram for $(Y,D)$. Actually all
the simple $\mathbb{A}^{1}$-curves contributing to the scattering diagram are
toric transverse in $(\tilde{Y},\tilde{D})$, which are depicted in Figure 15
below.

$E_{1}$
---
$E_{i}$, $i=2,3,4$
---
$H-E_{i}$,
---
$i=2,3,4$
3
---
2
---
3
---
1
---
$H-E_{1}$
---
$H-E_{1}-E_{i}$
---
$H-(\sum_{i=1}^{4}E_{i})$
---
$2H-E_{1}-E_{i}-E_{j}$,
---
$3H-2E_{1}-E_{2}-E_{3}-E_{4}$
---
$\\{i,j\\}=\\{2,3,4\\}$
---
Figure 15: The scattering diagram of Gross-Pandharipande-Siebert [GPS] and the
$\mathbb{A}^{1}$-curves corresponding to $X_{IV}$ (illustrated by a projection
to $\mathbb{P}^{2}$).

We conclude the section with the following theorem.

######  Theorem 7.4.

The family Floer mirror of $X_{IV}$ has a partial compactification as the
analytification of the $G_{2}$-cluster variety or the Gross-Hacking-Keel
mirror of a suitable pair $({Y},{D})$.

##  8 Further Remarks

Here we consider the family Floer mirror of $X$ without the geometry of its
compactification. Following the idea of the Gross-Hacking-Keel as summarized
in Section 2.1, one would need to use the theta functions, the tropicalization
of the counting of Maslov index two discs, to construct a (partial)
compactification of the original mirror. Assuming that $X=X_{*}$ in the
previous sections admit a compactification to a rational surface with an anti-
canonical cycle at infinity. Moreover, assume that the there is certain
compatibility between the compactification and the asymptotic of the metric
behaviour. Then one can follow the similar argument in the work of the second
author [L14] and prove that the counting of the Maslov index two discs with
Lagrangian fibre boundary conditions can be computed by the weighted count of
broken lines. However, the authors are unaware of such asymptotic estimates of
the metrics in the literature.

One can further construct the pair $({Y},{D})$ such that the corresponding
monodromy is conjugate to the monodromy of the type
$IV^{*},III^{*},II^{*},I_{0}^{*}$. For instance, the case of $I_{0}^{*}$ can
be realized by a cubic surface with anti-canonical cycle consisting of three
$(-1)$-curves [ghks_cubic]. The authors would expect that the family Floer
mirror of $X=Y\setminus D$ coincides with a particular fibre in the mirror
family constructed by Gross-Hacking-Keel. Moreover, the families of Maslov
index zero discs emanating from the singular fibres in $X$ are one-to-one
corresponding to the $\mathbb{A}^{1}$-curves of the pair $({Y},{D})$. This may
help to understand the Floer theory of more singular Lagrangians. In this
case, the wall functions are algebraic functions and the GAGA can still apply.
Although the walls are dense, it is likely the mirror can be covered by
finitely many tori up to some codimension two locus. In general, the wall
functions may not be algebraic a priori and GAGA may not apply directly. The
authors will leave it for the future work.

## References

Man-Wai Cheung
Department of Mathematics, One Oxford Street Cambridge, Harvard University, MA
02138, USA
e-mail<EMAIL_ADDRESS>
Yu-Shen Lin
Department of Mathematics and Statistics, 111 Cummington Mall, Boston, Boston
University, MA 02215, USA
e-mail<EMAIL_ADDRESS>


# Effect of Ag doping on structural, optical, and photocatalytic properties of
ZnO nanoparticles

S. M. Hosseini  I. Abdolhosseini Sarsari  P. Kameli  H. Salamati  a)
Department of Physics, Isfahan University of Technology, Isfahan, 84156-83111,
Iran

###### Abstract

Silver-doped ZnO nanoparticles were successfully fabricated at
$400\,^{\circ}\mathrm{C}$ via a simple and rapid method based on short time
solid state milling and calcination of precursor powders. The effect of Ag
dilute doping on the structural, optical, and photocatalytic properties of ZnO
nanoparticles was investigated by X-ray diffraction (XRD), UV-vis
spectrophotometer and photoluminescence (PL) spectroscopy. X-ray analysis
revealed that Ag doped ZnO solidified in hexagonal wurtzite structure. The
intensity of deep level emission was reduced with increasing silver doping in
PL measurement. The X-ray photoelectron spectroscopy (XPS) measurement
predicted that Ag was mainly in the metallic state and ZnO was in the wurtzite
structure. This metallic state accompanied by unique zinc oxide properties
decolorized the methyl violet, efficiently. The first-principles calculation
represented Ag deep level in ZnO with an n-type behavior, while in ZnO
structure with grain boundary p-type nature via shallow states is dominant
same as powder samples as studied in this present work. It was suggested that
these Ag-doped ZnO nanoparticles may have good applications in
optoelectronics, spintronics and wastewater treatment.

ZnO nanoparticles, Silver doping, p-type ZnO, Optoelectronic, Density
functional theory

##  I INTRODUCTION

Multifunctional materials come on stage accompanied with magnetic properties
in diluted magnetic semiconductors (DMS), in which non-magnetic ions replace
some of the magnetic and non-magnetic cations. The origin of ferromagnetic
properties in diluted semiconductors has been studied, both theoretically and
experimentally 1; 2, however, still there is no broad consensus on this issue
.

Among DMS materials, ZnO-based DMS has remarkable features: i) Direct wide
band gap $3.37~{}eV$ at room temperature, ii) Access to the large bulk and
high-quality single crystals of ZnO and iii) Large exciton binding energy of
$60~{}meV$. The latter is useful for having lasers with high efficiency at
room temperature 3; 4. In addition, ZnO is useful in solar cells and sensors
as transparent conductive and piezoelectric 5.

Pure ZnO nanostructures show weak optical features that are resulted from
point defects such as oxygen vacancy or interstitial Zn; therefore, they can
not be used directly in the industry 5. As a result, doping ZnO with a
convenient element is a method for engineering optical and magnetic
properties. Furthermore, in order to make optoelectronic devices, n-type and
p-type states are needed. It is relatively difficult to achieve p-type doping
and this limitation is considered an obstacle in using ZnO in these
instruments 6. Although the elements V, I, and IB groups have been studied for
p-type doping 7, silver has been reported as the best candidate because of its
high solubility, larger ionic size, and minimum orbital energy 8.
Theoretically, Volnianska et al. 9 reported that, among the elements of group
IB, copper, and especially Au, ionization energy was higher than Ag and caused
silver to be the best case for achieving p-doping in ZnO. Recently, Thomas et
al. 10 combined experimental approaches and theoretical calculations and
revealed that the majority of Ag was doped (substitution) into the ZnO
structure. Furthermore, Ag 4d and O 2p states were overlapped to form an
impurity band, which shifted the Fermi level toward the valence band maximum
and induced p-type properties in ZnO. Electrical properties of the Ag-doped
ZnO nano-wires showed that their p-type properties depended not only on Ag
content, but also on other conditions such as electrochemical growth and post-
annealing conditions.

Silver ions have two characteristic features and can be used in the places of
substitution and interstitial; hence, they can act as an acceptor in ZnO 11.
However, previous studies on Ag-doped ZnO by Yan et al. 8 suggested that
substitutional sites were more energetically favourable than interstitial
sites. Most studies have examined the effects of silver doping on the
photocatalytic activity and antibacterial properties of ZnO 12; 13; 14; 15. It
is also possible to form a dilute magnetic semiconductor by silver doping in
ZnO wurtzite structure and ferromagnetic behavior of the compound has been
investigated experimentally 16 and theoretically 17, which can be used in
spintronic applications by both degrees of freedom of electron spin and
charge. The ferromagnetic properties are due to the formation of impurity band
which interacts with the d orbital of nonmagnetic element 18. However, the
origin of ferromagnetic properties is still under investigation.

In the studies on the nanostructures of Ag-doped ZnO, different methods such
as sol-gel 19, sonochemical 20, and coprecipitation 21 have been used, all of
which require harsh conditions of sample preparation, high temperature, and
high costs. However, in this paper the structural, optical, and photocatalytic
properties in $Zn_{1-x}Ag_{x}O$ ($x=0,0.02$, and $0.07$) nanoparticles
synthesized by a simple and low-cost method, called thermal treatment of ball-
milled precursors were investigated. The aim of this work was to produce
p-type doping of the nanoparticles to be used in practical applications.
Optical measurements showed that the synthesized nanoparticles were of p-type.

##  II EXPERIMENTAL

###  II.1 Substances and their provision

Nanoparticle samples of $Zn_{1-x}Ag_{x}O$ were prepared by a simple and low-
cost method. In this method, zinc acetate dehydrate
$[(CH_{3}COO)_{2}Zn*2H_{2}O]$ with $95\%$ purity and citric acid
$[C_{6}H_{8}O_{7}]$ were initially combined at the molar ratio of $1:1$. Then,
various concentrations (x=$0$, $0.02$ and $0.07$ called A, B, and C,
respectively) of silver nitrate $[AgNO_{3}]$ were used for preparing the doped
samples. The powders were mixed and ground for 90 min at room temperature and
the milled powders were ultimately calcined in air at
$400\,^{\circ}\mathrm{C}$ for 2 h 22.

###  II.2 Photocatalytic studies

The photocatalytic performances of the samples were evaluated by the
decomposition of methyl violet in the solution under UV light. In order to
prepare the samples for the photocatalytic analysis, first, 0.05 gr of MV with
$C_{24}H_{28}N_{3}Cl$ chemical formula was weighed. The 50ppm solution of
methyl violet dye and 0.1 gr of the catalyst, ZnO, and Ag-doped ZnO, in a
quartz tube were prepared for the photo reactor system. First, the solution
was placed in the dark mood for 30 min and then, under UV irradiation
(wavelength=254 nm, power =15 W) at several stages. Afterwards, absorption
spectra of the samples were taken. The solution was analyzed by Lambda 25
UV/VIS spectrophotometer ( Perkin Elmer).

The degradation rate was calculated using the following formula:

$Degradation~{}percent=\frac{C_{0}-C(t)}{C_{0}}\times 100(\%)$ (1)

where $C_{0}$ is the primal concentration of methyl violet solution and C(t)
is concentration at different UV irradiation times.

###  II.3 Characterization of samples

Structural analysis was carried out using X-ray diffractometry (XRD) (XPERT
model, $CuK_{\alpha}$ radiation, $\lambda=1.5405\AA$ at room temperature). The
morphologies of the prepared nanoparticles were recorded by a Hitachi S4160
field emission scanning electron microscope (FE-SEM). X-ray photoelectron
spectroscopy (XPS) analysis was carried out for assessing purity of materials
and examining the composition and characteristics of defects by an ESCA/AES
system. The system was equipped with a concentric hemispherical analyzer (CHA,
Specs model EA10 plus). An $AlK\alpha$ line at 1486.6 eV was utilized for
exciting the X-ray photoelectrons. This analysis was done using high-
resolution scan of the O(1s), Zn(2p), Zn(3d) and Ag(3d) spectral regions. In
the XPS spectra, all the binding energies were calibrated by taking the carbon
peak (284.8 $eV$) as the reference. Formation of ZnO wurtzite phase and
available molecular bonds was investigated by the measurement of FTIR
absorption spectrum of $Zn_{1-x}Ag_{x}O$ samples using a BRUKEN TENSOR 27
spectrophotometer. The FTIR analysis was carried out at room-temperature in
the range 400-4000 $cm^{-1}$ using KBr as the reference. To investigate the
optical properties of these nanoparticles, the absorbance spectra of the
samples were measured on a Perkin Elmer Lambda 25 UV/VIS spectrophotometer
using ethanol as the reference. The UV-vis absorption spectrum was recorded in
the range of 300-800 nm. Room temperature photoluminescence spectra of the
samples were acquired from Perkin-Elmer LS55 spectrometer using xenon flash
lamp laser as the excitation source within the range of 340 to 500 nm and
excitation wavelength of 210.5 nm.

##  III RESULTS AND DISCUSSION

###  III.1 Structural properties

Fig. 1 shows a broad and enlarged view of X-ray diffraction patterns of the
$Zn_{1-x}Ag_{x}O$ nanoparticles. All the intensity data were appropriately
normalized to 1. The XRD pattern of pure ZnO displayed wurtzite crystal
structure (JCPDS NO. 01-079-2205), without any other crystalline phases. There
were three additional peaks at $2\theta$ of 38.14, 44.48, and 64.47o in ZnO
doped with Ag values 0.02 and 0.07, which could be attributed to metallic Ag
fcc phase, and indicate the formation of Ag as the second phase clusters.
Also, a consistent increase in the intensity of silver peaks can be noted by
the increase in the concentration of Ag from 2 to 7 $mol\%$. It should be
noted that the formation of metallic silver and the crystalline phase of ZnO
begins at about $400\,^{\circ}\mathrm{C}$ 23. By increasing Ag concentration,
peak position is shifted toward lower values, as shown in Table 1. This shift
suggests the partial substitution of $Ag^{+}$ ions at the ZnO lattice and
increase in the lattice parameters a and c, as expected 24; this issue is
presumably related to the ionic size difference between the $Ag^{+}$ (0.126
nm) and $Zn^{2+}$ (0.074 nm) ions. But, in this work, rietveld analysis showed
a slight decrease in the a and c lattice parameters and cell volume, which can
be explained by the formation of silver nano-collection 25 and the part
substitution of $Ag^{+}$ ions in the system, respectively. The substitution
did not cause any increase in the lattice parameters via very small percentage
of silver doping.

To study the effect of silver doping on the crystal size, the mean crystal
size was estimated from the Debye-Scherrer equation as follows:

$D=\frac{k\lambda}{\beta\cos\theta}$ (2)

where, $\beta=FWHM$, $\theta$ is Bragg angle, $\lambda=1.54\AA$ (X-ray
wavelength) and $k=0.9$. The crystalline size of A, B and C samples are
estimated as 23.12, 24.44 and 25.46 nm, respectively.

Figure 1:  (color online) XRD patterns of A, B and C samples. The inset of it pointed the enlarged view of XRD patterns by $2\theta=30-40$. Table 1:  Geometric parameters of un-doped and Ag-doped ZnO nanoparticles.  Compound | 2Theta | (hkl) | Crystal size ”D” (nm)
---|---|---|---
A | 31.78 | (100) | 23.12
B | 31.67 | (100) | 24.44
C | 31.65 | (100) | 25.46

Information such as grain size and shape can be obtained by FE-SEM analysis.
Surface morphology of the undoped and silver-doped ZnO nanoparticles is shown
in Fig. 2. The particle sizes were clearly of the order of nanometers and
shape of particles was quasi-spherical. Formation of the quasi-spherical
nanoparticles in the size range of 20-150 nm is shown in Fig.2. Using silver
doping, significant changes were not observed in the size of nanoparticles.

Figure 2:  The FE-SEM morphologies of (a) undoped, (b) $2\%$ and (c) $7\%$ Ag
doped ZnO nanoparticles.

###  III.2 FT-IR studies

FT-IR spectra for different concentrations of silver doping in the range of
300-4000 $cm^{-1}$ were recorded and the results can be seen in Fig. 3.
Enlarged position of the first absorption band is shown in the inset. Sharp
peak was observed in 440 $cm^{-1}$ , which could be attributed to the Zn-O
stretching vibration mode 26. A wide peak was in the range of 3020-3650
$cm^{-1}$ that was related to the presence of hydroxyl ions (OH) in the ZnO:Ag
system. The symmetric and asymmetric bending modes of C=O bonds were in 1580
and 1410 $cm^{-1}$, while the peak located at 2860 and 2950 $cm^{-1}$ was
related to symmetric and asymmetric C-H stretching bonds, respectively 22.
There were some bands originated from the presence of water moisture and
carbon dioxide in the air in the process of making pellet. The absorption band
at 1020 $cm^{-1}$ could be attributed to bending vibrational modes 27.
According to Fig. 3, a slight shift with increasing silver (Ag) is visible.
The shift in the position of the band toward lower frequencies can be
associated with changes in bond length due to the partial substitution of
$Ag^{+}$ ion at the ZnO lattice 28.

Figure 3:  FTIR spectra for undoped and silver doped ZnO. the inset shows the enlarged view of first absorption band location.  Table 2:  Binding Energy$(eV)$ and Area size of $Zn(2p_{1/2})$, $Zn(2p_{3/2})$, $O(1s)(I)$, $O(1s)(II)$, $Ag(3d_{3/2})$ and $Ag(3d_{5/2})$ in XPS analysis of morphology of ZnO and A and C samples.  | Binding Energy$(eV)$@ Area
---|---
Sample | $Zn(2p_{1/2})$ | $Zn(2p_{3/2})$ | $O(1s)(I)$ | $O(1s)(II)$ | $Ag(3d_{3/2})$ | $Ag(3d_{5/2})$
A |<EMAIL_ADDRESS>|<EMAIL_ADDRESS>|<EMAIL_ADDRESS>|<EMAIL_ADDRESS>| - | -
C |<EMAIL_ADDRESS>|<EMAIL_ADDRESS>|<EMAIL_ADDRESS>|<EMAIL_ADDRESS>|<EMAIL_ADDRESS>|<EMAIL_ADDRESS>

###  III.3 XPS results

To determine the elements and chemical-bonding state of the compounds in the
$Zn_{1-x}Ag_{x}O$ nanoparticles, the XPS analysis of the samples was studied.
It should be noted that the XPS curves were fitted using XPSPEAK 4.1 software.
The survey and core-shell level XPS spectra of Zn-2p, O-1s, and Ag-3d as well
as valance band of ZnO and $7\%$ silver-doped ZnO nanoparticles are shown in
Fig. 4. In the survey scan spectrum, Zn, O, C, and Ag peaks were
characterized, as can be seen in Fig. 4 (a). The carbon present in the samples
was presumably due to acetate vestige 29 and/or carbon adsorption process
present in ambient conditions 30; 31.

Symmetrical peaks are visible in Fig. 4(b) located at 1044.81 and 1021.67 $eV$
for the sample of pure zinc oxide ascribed to $Zn(2p_{1/2})$ and
$Zn(2p_{3/2})$, respectively 32. The splitting of Zn-2p states was about 23
$eV$ which was induced from the powerful spin-orbit coupling. These numbers
were different from the binding energy quantity of stoichiometric ZnO (1045.1
$eV$ for $Zn(2p_{1/2})$ and 1022.1 $eV$ for $Zn(2p_{3/2})$), which can be
attributed to the change of charge transfer from $Zn^{2+}$ to $O^{2-}$ due to
the existence of vacancies 33. According to Table 2 and Fig. 4(b), the
location of peaks was shifted toward the lower binding energy by silver
doping. These peaks could confirm the wurtzite structure and $Zn^{2+}$ mode of
Zn atom on the samples 34. Therefore, due to the charge transfer in the
binding energy of XPS spectrum, it can be deduced that the Zn-2p peak shift
indicates that oxygen deficiency is the dominant factor versus Zn deficiency
in the doped samples in contrast to the pure one 33.

Fig. 4(c) shows the internal levels of oxygen in both of the nanoparticles. It
is clearly seen that the O-1s curve was asymmetric; hence, they were fitted
with two Gaussian peaks (as I and II) symmetrically. There were two different
types of oxygen groups in the samples. The peak (I) was located in the lower
binding energy in comparison with the peak (II), which was dedicated to
$O^{2-}$ ions of $Zn-O$ bonding at crystal lattice 35. The peak (II) was
related to the hydroxyl group adsorption due to structural defects 30; these
groups could play a major role in the photocatalytic activity and increase the
photocatalytic activity 36 because of preventing from the recombination of
electron-hole pairs. Silver doping in ZnO led to a shift in the O-1s spectrum
toward lower binding energy. The atomic ratio of hydroxyl group (II) to total
oxygen was calculated for pure ZnO, which was equal to $51\%$ and increased by
$16\%$ using Ag doping. So, the photocatalytic activity should be increased by
silver addition process. Also, decreasing the binding energy of the Zn-2p and
O-1s levels with silver doping could be due to the reduction of oxygen
vacancy. Decrease in the ratio of $Zn/O$ in the present XPS results for the
doped samples compared to the pure sample confirmed the reduced the density of
oxygen defects 37.

The chemical state of Ag element was characterized by examining Ag-3d levels
in Fig. 4(d). The $Ag(3d_{3/2})$ and $Ag(3d_{5/2})$ peaks were split to about
the $\sim$6 $eV$ that showed the metallic condition of silver in the present
synthesised samples 38; 39. Lupan et al. 11 and Khosravi et al. 40 have
revealed the presence of two different components, which could be attributed
to either metallic Ag or $Ag_{2}O$ and to a Ag-Zn-O ternary compound.
Interestingly, the binding energy of Ag-3d for the doped sample compared to
the binding energy of silver bulk sample (368.3 $eV$ for $Ag(3d_{5/2})$ and
374.3 $eV$ for $Ag(3d_{3/2})$ 41) was significantly shifted towards lower
binding energy. Thongsuriwong et al. 42 observed a similar behavior in Ag 3d
spectra for Ag-doped ZnO thin films. This shift showed the electron movement
from metallic Ag levels to ZnO nanoparticles and the formation of silver with
unit valance. The interaction between silver and ZnO nanoparticles was also
proposed, which could regulate the position of Fermi level of silver and zinc
oxide nanoparticles and result in the formation of a new Fermi level for
metallic silver. Free electrons above the new Fermi level might be tunnelled
to the conduction band, because the conduction band of ZnO was empty 37. As
mentioned before, in the present XPS patterns, Ag-3d binding energy was
shifted to lower binding energy which can be explained by two processes: the
first process is that the binding energy of the unit valance silver is much
lower than the zero valance silver 29 and the second one is due to the
formation of an oxide layer on the surface of silver particles 33, which can
be identified by the XRD analysis. Due to the high electronegativity of Ag
than Zn, electron transfer was assumed to occur from Zn to the Ag particles,
suggesting that the chemical bond between ZnO and Ag is one reason for silver
effect in controlling defects at ZnO crystal lattice.

Figure 4:  (Color online) XPS spectra of A and C samples: (a) The survey scan
spectrum; (b) Zn(2p) spectrum; (c) O(1s) spectrum and (d) Ag(3d) spectrum.

###  III.4 Optical studies

Optical absorption spectra of the $Zn_{1-x}Ag_{x}O$ samples were measured by
UV-vis spectrophotometer in the range 300-800 nm. UV-vis absorption spectrum
primarily represents the available change in the energy gap 43. Fig. 5 shows
the UV-vis spectra of the ZnO:Ag nanoparticles. Pure ZnO nanoparticles
indicated the strong UV absorption edge at 374 nm that could be related to the
wurtzite crystal structure of ZnO 31. Silver adding to the ZnO nanoparticles
moved the absorption edge toward the major wavelength (red shift). Changes in
the absorption peaks, due to doping, showed changes in the band structure. The
shift of the absorption edge represented the change in the particle energy gap
44.

The optical energy gap of the nanoparticles was obtained from drawing the
graph of $(Ah\nu)^{2}$ versus energy, according to $A=\frac{[k(h\nu-
E_{g})^{\frac{n}{2}}]}{h\nu}$ equation. In this relation, A is absorption, k
is constant, h is Planck’s constant, $\nu$ is light frequency, n = 1 for
direct electronic transition, n = 4 for indirect electron transition and
$E_{g}$ is energy gap 45.

The A sample’s optical energy gap was 3.25 $eV$ that was smaller than the
energy gap of the bulk samples of ZnO. With increasing the amount of silver,
the energy gap decreased from 3.25 $eV$ for the pure sample (x=0) to 3.18 $eV$
for the Ag-doped sample (x=0.07), as shown in Table 3. The increase of the
energy gap for ZnO doped with donor is commonly observed, while reducing the
energy gap of ZnO doped with acceptor has been reported 46. Decreasing the
energy gap can be related to the presence of p-type conductivity in the
silver-doped ZnO nanoparticles. Silver doping in ZnO provides the impurity
band in the energy gap, which could be due to the formation of the p-type in
this substance. It should be mentioned that this reduction in energy gap led
to increase efficiency in the use of these materials in optoelectronic devices
46.

Figure 5:  UV-visible absorption spectra of pure and doped ZnO nanoparticles.  Table 3:  UV–vis absorption data for the undoped and doped ZnO nanoparticles.  Sample | $\lambda(nm)$ | Band gap$(eV)$
---|---|---
A | 374 | 3.25
B | 384 | 3.21
C | 380 | 3.18

Further information about the optical properties of ZnO can be received from
PL spectra. Information about the crystal modality, structural defects such as
oxygen vacancy, Zn interstitials,… and surface properties of particles can be
obtained from PL spectra 23.

Fig. 6 shows the PL spectra of ZnO doped with silver and pure ZnO
nanoparticles. A radiation band at the center of the UV spectral range around
418 nm for all the samples can be observed. The UV radiation is usually
attributed to the near band edge (NBE) emission due to free exciton
recombination 32. No significant change was observed in the position of this
ultraviolet band with silver doping. The decrease in UV intensity was due to
the interactions between the excited ZnO nanoparticles and Ag particles in the
grain boundaries. These kinds of interactions via the Schottky contact, metal-
semiconductor diode effect, decrease the recombination of electrons and holes
generated from UV light irradiation 47; 23 and improved the photocatalytic
activities 48.

On the other hand, reduction in the intensity of UV radiation was due to the
interstitial Ag atoms at ZnO lattice and created a large amount of defects, as
confirmed by Zeferino et al. 49. Dissimilar results for the annealing effect
on the PL properties of Ag-doped ZnO nanowires were reported by Yong et al.
50. They observed the increase in UV intensity that was attributed to the
substitution of Zn atom sites by Ag atoms. The present experimental results in
Fig. 6 displayed deep level emissions (DLE) at about 480 nm in the visible
region. This multicomponent visible emission in ZnO has been frequently
ascribed to several intrinsic and extrinsic defects. DLE or blue radiation is
due to electron recombination in oxygen vacancy with a hole in the valence
band 51. By increasing Ag concentration, the intensity of DLE decreased. The
reduction of DLE with Ag doping represented a decline in the defects and
improved crystallization ZnO 12; 32.

Figure 6:  (color online) PL spectra of the pure ZnO and Ag doped ZnO
nanoparticles.

To better understand the role of Ag doping in the optical properties, Gaussian
fitting was performed on PL spectra. Multiple PL peaks in the energy region of
the absorption edge were observed in many ZnO nanostructures. Understanding
the origin of the PL peak was required to study the optical properties of ZnO
nanostructures and sketch ZnO-based opto-electronics tools. PL spectra’s
Gaussian fitting for pure and silver-doped ZnO nanoparticles is shown in Fig.
7. The first band on 2.58 $eV$ as a blue irradiance was reported due to the
electron transition between Zn interstitials and Zn vacancy states 52; 49
which was in agreement with the calculated energy levels of defects in ZnO by
Kohan et al. 53 and showed the existence of Zn vacancies in the samples, while
oxygen defects constitute deep donor levels in the band gap 54. Band located
at 2.74 $eV$ was blue radiation that was attributed to the Zn vacancy defects
55. Radiant bands on 2.95, 2.88, and 2.81$eV$ were violet radiation. The
mechanism of this radiation can be questioned: the emission mechanism is still
unknown and researchers have related it to defects of Zn interstitials or Zn
vacancy defects 52. The two peaks located at 3.24 and 3.12 $eV$ were UV near
absorption edge radiation due to free exciton recombination. The NBE emission
in UV region was shifted which represented the variation of the band gap.

Figure 7:  (color online) Gaussian fitting of the A, B and C samples in the
visible and UV region.

###  III.5  Studying photocatalytic activity

The purpose of this analysis was the degradation of methyl violet. In the
industry, methyl violet is entered as a pollutant into groundwater and its
destruction helps to remove pollutants. When ZnO nanoparticles are used to
remove indissoluble chemicals in diverse applications, surface properties such
as surface area, oxygen vacancy, and hydroxyl ions play an important role 56.

The results of photocatalytic measurements of the ZnO:Ag nanoparticles are
shown in Fig. 8. Pure ZnO nanoparticles showed a significant photocatalytic
activity. It can be seen that the photocatalytic activity of the ZnO
nanoparticles was improved by silver doping with optimum 2 $\%$, which may be
related to the oxygen vacancy defect concentration in different samples. In
the C sample compared with the B one, the Zn vacancies were more dominant than
the oxygen vacancies due to Ag presence on grain boundaries and consequently
lack of Zn atoms in the bulk region. So, increasing Zn vacancies accompanied
by oxygen vacancies could be responsible for the degradation process.
According to these studies, it can be concluded that the photocatalytic
activity of the ZnO nanoparticles increases by Ag doping and thereby incurs
the increased surface area and increased oxygen defects. The reaction between
conduction-band electrons and oxygen in the solution could generate the
reactive oxygen species which is responsible for the color decolorisation 13
and its value increases with silver doping. As a result, the increase of
silver improves the photocatalytic activity of the ZnO nanoparticles .

Figure 8:  (Color online) MV degradation curves of A, B and C samples under UV
irradiation.

Fig. 9 schematically explains the mechanism of photocatalytic process on
ZnO:Ag nanoparticles. In the dark, by dispersing ZnO:Ag nanoparticles in the
MV solution, the surface electrons of the Ag nanoparticles were transferred to
the MV dye 37. The valance band electrons in these nanoparticles under UV
radiation with the photons of energy greater than or equal to ZnO band gap
($e^{-}$) can be excited to the conduction band producing the equal number of
holes ($h^{+}$) in the valance band, simultaneously. Because the conduction
band energy level of ZnO nanoparticles is higher than that of the Fermi level
of ZnO:Ag nanoparticles, electrons can flow from ZnO nanoparticles to Ag
nanoparticles 57. So, oxygen vacancy defects and Ag nanoparticles on the
surface of ZnO nanoparticles trap electrons and prevents the recombination of
$e^{-}-h^{+}$ pairs 14. Also, UV radiation excites the dye molecules ($MV^{0}$
to $MV^{+}$). These MV molecules transfer electrons to the conduction band
(CB) of ZnO ($MV^{+}$ to CB of ZnO) and the Fermi level of Ag ($MV^{+}$ to
Ag). Then CB electrons react with dissolved oxygen in the solution to produce
superoxide radicals($.O_{2}^{-}$), while the valance band (VB) holes react
with hydroxide ions for the production of hydroxyl radicals($.OH^{-}$). Both
of these radicals are responsible for the decolorization of MV dye 15; 58.
Also, the energy barrier of the Ag-semiconductor junction prevented electron-
hole recombination to separate photogenerated charges, effectively 47.

Figure 9:  Schematic mechanism of photocatalysis process on ZnO:Ag
nanoparticles under UV irradiation.

###  III.6 Ab initio calculation of Ag-doped ZnO

A 32 orthorhombic wurtzite supercell of ZnO:Ag (16 oxygen atoms, 15 Zinc atoms
and an atom of silver substituting Zn) corresponding to a nominal Ag doping
concentration of 6.25 $\%$ was studied by the density of states. First
principles calculations based on density functional theory were carried out
using the HSE hybrid exchange-correlation functional at the level of HSE03 59.
Sampling a 8$\times$8$\times$6 $\Gamma$-centered $k$-points mesh in the
Brillouin zone was done for the calculation. Hybrid functional correction in
these calculations was seen to slightly reduce $E_{3d}$ from 6.98 eV in the
density functional theory (DFT) ground state to 6.01 eV in the HSE, while
forbidden gap was improved to 2.24 eV compared to 0.78 eV in the conventional
GGA-DFT calculations.

The present HSE calculations showed a deep level in the band gap of the single
crystal which explained the n-type conductivity due to Ag doping.
Hybridization between Ag-4d and O-2p levels led to this deep level above the
valance band maximum (VBM). Indeed, this deep level originated from
Ag($d_{z^{2}}$)-O(2p) repulsion which pushed the Ag $d_{z^{2}}$ orbital to
higher energies around 0.6 eV above VBM. So, the existence of the deep levels
was n-type conductivity formation proof in pure Ag-doped ZnO, while grain
boundaries in the powder samples can prepare shallow levels as acceptor p-type
conductivity centers as found in these samples 60.

Figure 10:  (Color online) The total and partial DOS of ZnO doped with Ag
calculated via the HSE method. Fermi level is set to zero.

##  IV Conclusion

In conclusion, the optical, structural and photocatalytic properties of Ag-
doped ZnO nanoparticles were checked. XRD analysis showed that the samples
were in the hexagonal-wurtzite phase. Also, the XRD and XPS measurements
confirmed the presence of silver metallic phase in the nanoparticles. The
density functional theory calculation predicted a deep level in the band gap
of the single crystal which explained the n-type conductivity due to Ag
doping. In general, in the powder samples, the grain boundary and metallic Ag
on the grain boundaries were found to prepare shallow levels as a smoking gun
for p-type conductivity. Optical absorption measurements indicated a red shift
in the absorption band edge by silver doping. This study suggested that silver
doping reduced the energy gap and controlled the luminescence properties;
thus, it produced the p-type conductivity. This p-type nature can be used in
the optoelectronic industry.

The photocatalytic activity of the ZnO nanoparticles were improved by Ag
doping that was confirmed by XPS analysis. Also, decolorisation efficiency of
methyl violet depended on the amount of silver.

##  V ACKNOWLEDGMENTS

The authors would like to thank Dr. Mehdi Ranjbar, Dr. Mehran Ghiaci and
Isfahan University of Technology for supporting this project.

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