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The structural and optical constants of Ag2S semiconductor nanostructure in the Far-Infrared

  • 1, 2Email author,
  • 3,
  • 1,
  • 1,
  • 2,
  • 4 and
  • 2
Chemistry Central Journal20159:28

  • Received: 13 December 2014
  • Accepted: 15 April 2015
  • Published:



In this paper a template-free precipitation method was used as an easy and low cost way to synthesize Ag2S semiconductor nanoparticles. The Kramers–Kronig method (K–K) and classical dispersion theory was applied to calculate the optical constants of the prepared samples, such as the reflective index n(ω) and dielectric constant ε(ω) in Far-infrared regime.


Nanocrystalline Ag2S was synthesized by a wet chemical precipitation method. Ag2S nanoparticle was characterized by X-ray diffraction, Scanning Electron Microscopy, UV-visible, and FT-IR spectrometry. The refinement of the monoclinic β-Ag2S phase yielded a structure solution similar to the structure reported by Sadanaga and Sueno. The band gap of Ag2S nanoparticles is around 0.96 eV, which is in good agreement with previous reports for the band gap energy of Ag2S nanoparticles (0.9–1.1 eV).


The crystallite size of the synthesized particles was obtained by Hall-Williamson plot for the synthesized Ag2S nanoparticles and it was found to be 217 nm. The Far-infrared optical constants of the prepared Ag2S semiconductor nanoparticles were evaluated by means of FTIR transmittance spectra data and K–K method.

Graphical Abstract image
Graphical abstract

The Far-infrared optical constants of Ag2S semiconductor nanoparticles.


  • Nanostructures
  • Semiconductors
  • Raman spectroscopy
  • Infrared spectroscopy
  • Crystal structure
  • Optical properties


In recent years, nanometer-sized chalcogenide semiconductors have drawn attention as a component of nanotechnology, mainly due to their physical and chemical properties, heavily dependent on their shape and size. The Ag2S is found amongst the most important chalcogenides and because of its unique optoelectronic properties. It have been extensively studied due to its many potential applications in optical and electronic devices such as infrared detectors, photoconductive cells, magnetic field sensors and photoconductors, amongst others [15]. Ag2S is an effective semiconductor material due to a large absorption coefficient and a direct band gap of 0.9 to 1.05 eV. It is a coinage mineral undergoes a structural phase transition. Above 183 °C, Ag2S appear with a cubic structure known as argentite (α-Ag2S). At room temperature, Ag2S have a monoclinic structure named acanthite, space group P21/c and Z = 4 (β-Ag2S) [6, 7]. The α-Ag2S behaves like a metal (dσ/dT < 0) while β-Ag2S behaves like a semiconductor (dσ/dT > 0, with activation energy of 1.3 eV) [810]. Several methods have been developed for the synthesis of Ag2S nanoparticles such as solvothermal method, hydrothermal route, and single-source precursor routes [11]. Yu et al. synthesized sub-micrometer Ag2S particles thru a simple hydrothermal method but it is difficult to control the size and shape of the nanoparticles for the large-scale synthesis of high-quality nanoparticles [12]. Qin et al. successfully synthesized Ag2S nanorods by a biomimetic route in the lysozyme solution at physiological temperature and atmospheric pressure [4]. In another work, Wang et al. synthesized spherical silver sulphide nanoparticles (Ag2S) at 205 °C under N2 atmosphere by a direct reacting silver acetate with n-dodecanethiol [13]. Therefore, there is a considerable challenge for the synthesis of Ag2S nanoparticles on a large scale through a simple and low-cost approach.

In this paper, a template-free precipitation method was used to prepare nanometric powders of Ag2S. The structural and optical constants of the prepared Ag2S nanometric powders in Far infrared were calculated and are presented for the first time.

Experimental section

Synthesis and characterization of Ag2S nanoparticles

Nanocrystalline Ag2S was synthesized by a wet chemical precipitation method. Initially 0.1 mmol of AgNO3 (Aldrich, Germany) was dissolved in 50 ml of distilled water. The obtained solution was added drop wise into 50 mL 0.1 M Na2S solution. Finally, the as prepared precipitated nanocrystalline powder was collected and dried after centrifugation at 80 °C during a 3 h period. The schematic diagram for the experimental set up and chemical reaction is shown in Fig. 1. The structure and morphology of the sample was studied by X-ray diffraction (Shimadzu XRD-6000, Tokyo, Japan) and Scanning Electron Microscopy (SEM, SU-70, Hitachi). The study of the optical properties of the samples was carried out by UV–visible (Perkin-Elmer, Lambda 35) and FT-IR spectrometry.
Fig. 1
Fig. 1

Schematic diagram of experimental set up

Results and discussion

Phase and compositional study (XRD)

Figure 2 shows the X-ray diffraction pattern for synthesised Ag2S particles. A Rietveld refinement analysis was performed after x-ray diffraction pattern acquisition. The refinement of the monoclinic β-Ag2S phase yielded a structure solution similar to the structure reported by Sadanaga and Sueno [8]. No impurity phase was observed in the X-ray diffraction pattern. However, the refined structure from this study showed a slight deviation in the xyz coordinates for Ag and S atom. The refined parameters are listed in Table 1, and the Rietveld refinement diffraction pattern of β-Ag2S structure is shown in Fig. 2.
Fig. 2
Fig. 2

X-Ray Diffraction patterns and Rietveld refinement plot for Ag2S nanoparticles powder

Table 1

Structural details and refined parameters obtained by Rietveld refinement

Basic structural details


Space group


P 21/c

Lattice parameters (in Å) and angle (in °)







Vol. (Å3)








Atomic coordinates parameters





















Anisotropic displacement parameters, in Å2


U 11

U 22

U 33

U 12

U 13

U 23






















Other parameters

R p

R wp

R exp

R b

R f

χ 2









Goodness of fit

D-W statistics (d)

QD = expected (d)

S (goodness of fit) = Rwp/Rexp




To determine the strain and size effect associated to the synthesized Ag2S particles, Hall-Williamson method was used as the estimation of the particle size. This is explained by the Scherrer equation not taking in consideration for the broadening due to lattice strain presence. Generally, the observed peak broadening Bo can be attributed to
$$ {\mathrm{B}}_{\mathrm{r}} = {\mathrm{B}}_{\mathrm{o}} - {\mathrm{B}}_{\mathrm{i}} $$
where Bo is the observed peak broadening in radians, Bi is the instrumental broadening in radians, and Br is the broadening due to the small particle size and lattice strain. Using the Scherrer equation, the broadening caused by small crystallite size may be expressed as:
$$ {B}_C = \frac{k\lambda }{d\ cos\theta} $$
where: B is the broadening solely caused by small crystallite size, k is a constant whose value depends on particle shape and is usually taken as unity, d is the crystallite size, θ is the Bragg angle and λ is the wavelength of the incident X-ray beam (1.5418° A). Similarly, according to Wilson, the broadening caused by lattice strain is expressed as:
$$ {B}_s=4\varepsilon \tan \theta $$
where: B is the peak broadening caused by the lattice strain, ε the strain distribution within the material and θ is the Bragg angle [14]. The instrumental broadening was estimated performing a XRD to a pure strain-free silicon standard under identical conditions. The total broadening excluding the instrumental broadening of the peak is expressed as the sum of eqn (2) and (3) [15]:
$$ {B}_r=\frac{k\lambda }{t\ Cos\theta} + 4\ \varepsilon\ tan\theta $$
$$ \frac{Br\ Cos\theta}{\lambda }=\frac{k}{t} + \varepsilon\ \frac{4 Sin\theta}{\lambda } $$
The plot of Br cos(θ)/λ versus 4sin(θ)/λ is a straight line with slope equal to ε and hence the particle size can be estimated from the intercept. A typical Hall-Williamson plot for the synthesized Ag2S nanoparticles is shown in Fig. 3.
Fig. 3
Fig. 3

W-H analysis of Ag2S particles

The crystallite size of the synthesized particle was found to be 217 nm. A small non uniform lattice strain (0.039 %) was observed in the sample. The non-uniform strain and the crystallite size was calculated from the slope and the y-intercept of the fit, respectively.

Morphology study (SEM)

Figure 4 (left) depicts the SEM image of Ag2S nanoparticles. Formation of agglomerated spherical Ag2S nanoparticles can be seen from this Figure. Therefore it is difficult to estimate the real particles size. Energy dispersive X-ray spectroscopy (EDS) was also performed to determine the chemical composition of the prepared Ag2S nanoparticles (shown in Fig. 4 (right)). The obtained EDS results confirmed the presence of Ag and S in the final products.
Fig. 4
Fig. 4

SEM image (left side) of and EDS analysis of the Ag2S nanoparticle (right side)

The absence of extra peaks, besides the expected ones for nanocrystals, suggests that the obtained powders are very pure.

UV–VIS reflectance

The UV–VIS reflectance spectrum of the sample is presented in Fig. 5a. The Kubelka–Munk function was used to convert the diffuse reflectance into the absorption coefficient and spectrum is presented in Fig. 5b.
Fig. 5
Fig. 5

UV–VIS reflectance spectrum of Ag2S nanoparticles a reflectance and b absorption coefficient

$$ \alpha =\frac{k}{s}=\frac{{\left(1-{R}_{\infty}\right)}^2}{2{R}_{\infty }}\equiv F\left({R}_{\infty}\right) $$

where S and K are the scattering and absorption coefficients; the reflectance R is equal to: \( \frac{R_{sample}}{R_{S \tan dard}} \) [16].

Bulk Ag2S is a semiconductor with a direct band gap of 0.9 to 1.05 eV [17]. The following equation was used to determine the band gap of Ag2S nanoparticles [18]:
$$ \alpha =A{\left(h\nu -{E}_g\right)}^n/h\upsilon $$

where A is constant, Eg is the absorption band gap, α is the absorption coefficient, and n depends on the type of transition, n may assume the values 1/2, 2, 3/2 and 3 respectively corresponding to allowed direct, allowed indirect, forbidden direct and forbidden in direct transitions [19].

Since Ag2S nanoparticles have direct allowed transitions so we choose n = 1/2. The band gap of Ag2S nanoparticles was determined by extrapolating the function of (αhυ)2 in term of as shown in the Fig. 6 and it was found that the band gap of Ag2S nanoparticles is around 0.96 eV, which is in good agreement with previous reports for the band gap energy of Ag2S nanoparticles (0.9–1.1 eV) [1921].
Fig. 6
Fig. 6

hν)2 versus hν for Ag2S nanoparticles

FT-IR analysis

Figure 7 shows FT-IR spectrum of Ag2S nanometric powders. The characteristic vibration of Ag–S appears located at 500–600 cm−1 while the broad and small peaks located at 3400 and 1600 cm−1 can be attributed to the stretching and bending vibrations of the O–H bond of the adsorbed H2O molecules on the surface of Ag2S [22, 23].
Fig. 7
Fig. 7

FT-IR spectrum of the Ag2S nanoparticles

Optical constants of Ag2S nanoparticles

The K–K method was used to determine the Far-infrared optical constants of the prepared Ag2S semiconductor nanometric powders by using FT-IR transmittance spectral data. The absorption (A) can be obtained from transmittance according to Lambert’s law [24]:
$$ A\left(\omega \right)= log\frac{I_0}{I}=lo{g}_{10}\frac{1}{T\left(\omega \right)}=2-lo{g}_{10}\left(T\left(\omega \right)\%\right) $$
$$ R\left(\omega \right)=100-\left[T\left(\omega \right)+A\left(\omega \right)\right] $$
where R(ω) is the reflectance in the particular wave number. The reflective index n is an important physical quantity in optical design and generally is a complex quantity:
$$ \tilde{n}\ \left(\omega \right)=n\left(\omega \right)+ik\left(\omega \right) $$
where n(ω) and k(ω) are the real and the imaginary parts of complex refractive index respectively, and can be obtained by the following equations:
$$ n\left(\omega \right)=\frac{1-R\left(\omega \right)}{1+R\left(\omega \right)-2\sqrt{R\left(\omega \right)} \cos \varphi \left(\omega \right)} $$
$$ k\left(\omega \right)=\frac{2\sqrt{R\left(\omega \right)} \cos \left(\varphi \right)}{1+R\left(\omega \right)-2\sqrt{R\left(\omega \right)}\mathrm{cosb}\ \varphi \left(\omega \right)} $$
Here, φ(ω) is the phase change between the incident and the reflected signal at a particular wavenumber ω. This phase change can be calculated from the K–K dispersion relation [25]:
$$ \varphi \left(\omega \right)=\frac{-\omega }{\pi }{\displaystyle \underset{0}{\overset{\infty }{\int }}}\frac{LnR\left({\omega}^{\hbox{'}}\right)-LnR\left(\omega \right)}{\omega^{\hbox{'}2}-{\omega}^2}\ d{\omega}^{\prime } $$
This integral can be precisely evaluated by Maclaurin’s method [26]:
$$ \varphi \left({\omega}_j\right)=\frac{4{\omega}_j}{\pi}\times \varDelta \omega \times {\displaystyle \sum_i}\frac{ \ln \left(\sqrt{R\left(\omega \right)}\right)}{\omega_i^2-{\omega}_j^2} $$

here Δω = ω j + 1 − ω j and if j is an even number then i=1, 3, 5, 6,,…j − 1, j + 1, ….. while if jis an odd number then i =2, 4, 6,…j − 1, j + 1, …..

In addition, the dielectric function can be obtained by the square of the refractive index. Therefore, the real and imaginary parts of the complex dielectric function are:
$$ \overline{\varepsilon}={\left[\tilde{n}\left(\omega \right)\right]}^2={\left[n\left(\omega \right)+ik\left(\omega \right)\right]}^2 $$
$$ \Rightarrow\ {\varepsilon}^{\prime }+i{\varepsilon}^{{\prime\prime} }={n}^2\left(\omega \right)-{k}^2\left(\omega \right)+2 in\left(\omega \right)k\left(\omega \right) $$
$$ \Rightarrow\ \left\{\begin{array}{c}\hfill {\varepsilon}^{\prime}\left(\omega \right) = {n}^2\left(\omega \right)-{k}^2\left(\omega \right)\kern6.5em \hfill \\ {}\hfill {\varepsilon}^{{\prime\prime}}\left(\omega \right)=2n\left(\omega \right)k\left(\omega \right)\kern7.75em \hfill \end{array}\right. $$
The Far-infrared optical constants of Ag2S semiconductor nanoparticles was calculated by the above equations and the spectrums are presented in Fig. 8a and 8b.
Fig. 8
Fig. 8

The Far-infrared optical constants of Ag2S semiconductor nanoparticles a refractive index and extinction coefficient, b real and imaginary parts of dielectric functions


We have successfully prepared Ag2S semiconductor nanometric powders by using a simple and low cost wet chemical precipitation technique. The micro-structural analysis of the sample was done through XRD pattern analysis and Rietveld refinement analysis. No impurity phase was observed in the X-ray diffraction pattern. The crystallite size of the synthesized particles was obtained by Hall-Williamson plot for the synthesized Ag2S nanoparticles and it was found to be 217 nm. The Far-infrared optical constants of the prepared Ag2S semiconductor nanoparticles were evaluated by means of FTIR transmittance spectra data and K–K method.



Reza Zamiri would like to thank the Foundation for Science and Technology of Portugal (FCT) and Universiti Putra Malaysia Postdoctoral research fellow program (R.Z.) for the financial support under the grant references, SFRH/BPD/76185/2011 and NSR-8978 (G.P.D.).

Authors’ Affiliations

Department of Physics, Faculty of Science, Universiti Putra Malaysia, Serdang, Selangor, 43400 UPM, Malaysia
Department of Materials and Ceramic Engineering (DEMaC), University of Aveiro, Campus Santiago, Aveiro, 3810-193, Portugal
Department of Chemistry, Faculty of Science, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Iran
TEMA-NRD, Mechanical Engineering Department and Aveiro Institute of Nanotechnology (AIN), University of Aveiro, Aveiro, 3810-193, Portugal


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