Structural features of PbSe nanoparticles produced within the silicate glasses
V. S. Gurin
Research Institute for Physical Chemical Problems, Belarusian State University, Minsk, Belarus
G. E. Rachkovskaya, G. B. Zakharevich
Belarusian State Technological University, Minsk, Belarus
S. E. Kichanov, Yu. E. Gorshkova
Joint Institute of Nuclear Research, Dubna, Russia
PbSe-doped silicate glasses were studied through wide-angle X-ray diffraction (WXRD) and
small-angle neutron scattering (SANS). PbSe nanoparticles in the glasses were produced due to the
secondary heat treatment at different temperatures and their appearance was established by
WXRD, SANS, and TEM techniques with the results for particle sizes in accordance to our recent
optical studies of this material. The simulation of SANS measurements revealed new structural
features of the PbSe nanoparticles. They form fractal aggregates as several overlapping spheres up
to ~30 nm in full size.
Quantum-sized semiconductor nanoparticles incorporated into solid matrices are of great interest
for design of novel optical materials, non-linear optical units, etc. Optical glasses belong to
perspective type of such materials and with lead chalcogenide nanoparticles possess many
advanced features for infrared technology, solar energy converters, cutting filters for a range of IR
and visible spectra, etc. [1-4]. Lead chalcogenides (PbS and PbSe) are featured by explicit
manifestation of quantum size effects through wide size range because they possess the large
values of the Bohr exciton radii (18 and 46 nm, respectively) and small effective masses of
electron and holes ( _______________, respectively).
The nanoparticles can be successfully stabilized within a glass matrix of various type
(silicate, phosphate, borate). For the size range of 2-10 nm their excitonic absorption peaks enter
the near IR range that is of great interest for application in lasers for telecommunication and
medicine [5,6]. Meanwhile, the nanoparticles synthesized through soft chemistry methods
(colloidal, sol-gel, etc.) may have typically the less size and more tuned particle properties with the
optical absorption also in the visible range up to UV. In contrast to colloidal chalcogenides, a
material with particles within glass matrices is more stable with respect to environment as well to
intense laser irradiation that provides pathways to use glasses as non-linear optical media with
proper control of spectral properties via the variation of lead chalcogenide particle state (size,
concentration, aggregation, etc.). However, detailed structural studies of nanoparticles in glass are
troubled because low particle concentration and background effects due to matrix. Also, any
extraction of particles from glass is impossible without their essential modification. Thus, more
adequate technique to reveal structural information on nanoparticles is to be non-destructive, e.g.
scattering of X-rays and neutrons. Small-angle neutron scattering (SANS) results in versatile
structural information on composite nanosystems at different scales as far as neutrons are scattered
on various structural inhomogeneities ranging from atomic sizes through tens of nanometers. In the
present paper, we combine SANS and wide angle X-ray diffraction (WXRD) for exploration of
silicate glasses with PbSe nanoparticles in order to shed a light onto their structural features those
influence also optical response of these glasses. The latter are of interest for application as new
optical materials for non-linear optical elements, IR-filters, mode-locking units of IR-lasers [ ].
To date, there is no detailed knowledge of structure of such nanocomposite materials since the
glass matrix is rather complicated multicomponent system with several oxides, and semiconductor
dopants can perturb the glass structure rather significantly as well more structuring of
nanoparticles is possible resulting in change of mechanical and optical properties.
Principal optical properties of these glasses are provided by doping with lead chalcogenides.
They were presented by us earlier  and some similar glasses with PbS and PbSe were described
by the other authors [4,8-11]. The doped glasses after the heat treatment at the temperatures near
Tg during rather prolonged procedure (20-150 h) reveal the pronounced excitonic absorption as
familiar feature of quantum-sized semiconductor nanoparticles in different media. Spectral
position of the excitonic absorption is varied in the near IR-range in correspondence with
numerical data of the band structure calculations of the nanoparticles in . The PbSe-doped
glasses heated at 480oC during 50-60 h correspond to beginning particle growth steps, while the
treatment at 525oC exhibits the pronounced peaks in the range of λ > 2 µm. Thus, within the
framework of the present study we consider the couple of samples with different steps of
nanoparticles formation and various structural features are expectable to be detected with SANS.
2. Experimental: preparation of glasses and measurement techniques
The samples of PbSe glasses were fabricated according to the technique described earlier . It is
based on the conventional two-step method used for semiconductor-doped glasses: (1) The
melting-cooling cycle of glass-forming oxides (SiO2, Na2O, ZnO, Al2O3, and PbO) with addition
of NaF. Elemental Se was used as selenium source. The synthesis temperature was kept
1400 ± 50ºC during 2 h with the temperature increase rate about 300oC/h. (2) The secondary heat
treatment near Tg of the glass (480-530oC). PbSe nanoparticles in this system are nucleated and
growing during the second step through a complex mechanism with auxiliary participation of ZnO
. Temperature and duration of this step in this protocol is a tool to control final state of the
nanoparticles-glass system and its optical features.
XRD patterns for the glasses were recorded using a DRON-7 diffractometer with CuKα
radiation and Ni-filter. TEM study was performed by the method of carbon film replica with
extraction. This method provided a view of both particles and glass matrix surface across the
sample particular area.
SANS measurements were made using a time-of-flight spectrometer UMO at a IBR-2 reactor
(Dubna, Russia). The scattering parameter range covered 0.05-2.5 nm-1 allowing to get information
on structures at the various scale, 2-100 nm. Raw data of SANS were corrected taking into account
thickness of samples and absorption in them and scattering from support and were processed with
SASfit software .
]Table 1. Composition of the glass under study
F (NaF) 2.03
3. Results and discussion
The diffraction patterns for the three PbSe-doped glass samples for different conditions of their
heat treatment are given in Fig. 1. There are explicit diffraction maxima those can be assigned to
appearance of PbSe nanocrystalline phase (JCPDS 06-0354), however, they are of rather low
intensity because concentration of PbSe within glasses is low and the nanometer-range particle size
provides broadening. This is also a reason that only principal peaks appear, and another possible
peaks at 2θ > 50 deg are not revealed. Also, amorphous glass matrix can mask good diffraction
pattern. Nevertheless, the XRD data depicted in Fig. 1 can be considered as sufficient to conclude
on formation of PbSe nanocrystals since they are at close positions to the reference data. Another
possible nanocrystalline phases in this system those may be supposed with Pb, i.e. metallic Pb,
PbO and PbSe2 do not fall in correspondence with observed data. The weaker peaks at about
21 deg for the sample 525/50 are assignable to partial crystallization of SiO2 (cristobalite phase,
JCPDS 39-1425). The assignment of these patterns for the cubic (rocksalt) PbSe phase is given by
the reflections (111), (200) for both samples and else (222) for the sample 525/50. The reference
positions are 25.16; 29.14 and 41.68 deg, respectively. A comparison of the XRD data for the
glasses under study with similar research published in [8-11] indicates good agreement and
confirm conclusion on formation of nanocrystalline PbSe with conventional rocksalt lattice.
However, in our case we can see the slight shift in position of the (111) peak while the other ones
are better coincident with the reference of bulk PbSe. This observation can argue on small
distortion of the nanoparticles structure from the perfect cubic lattice assigned to this space group
(Fm-3m, No. 225). While, under ambient conditions only this phase of PbSe is stable, the
transitions to the other structures is well known under high pressures and elevated temperatures
. The restricted number of diffraction peaks available in the present experiment, their low
intensity and broadness do not allow to proceed accurate refinement procedures to decode the
distorted lattice of the nanoparticles, however, one can assume the effect of glass matrix in which
the particles tightly fixed in the result of melting-cooling cycles. E.g. in the PbS-TiO2 system
where the concentration of PbS nanoparticles is higher to resolve the structure through
electronographic measurements [ ], the distortion of PbS cubic lattice has been established and
simulated by DFT calculations. In our case, the particle-matrix interaction may be even stronger
due to the high temperature of the glass preparation and multi-oxide composition of glass. Such
interaction is expected to result in strong stabilization of nanoparticles that is of interest for non-
linear optical application of these materials.
The full range XRD patterns in the appropriate scale include also broad haloes in the 2θ
interval of 20-30 deg that is typical for silicate glasses of different composition and assigned to
features of silicate amorphous structure (due to slightly varied Si-O distances) rather than a
crystalline doping phase.
Approximate particle sizes from these XRD patterns can be evaluated through the conventional
Scherrer method estimating the peaks width, and the average diameter of particles is about 10 nm.
A low intensity of the peaks in these patterns does not allow to conclude certainly on difference of
the particle size for two samples using this approximate method, but little variations may not be
excluded (not more than 1-2 nm). Meanwhile, the difference of XRD diffraction patterns for the
two samples consists in more clear appearance of the peaks (~29 and ~41 deg) for the sample
525/50. That can be due to more number of nucleated particles under the higher temperature rather
than their larger size. This factor can influence the structural organization of particles contributed
into results of SANS measurements and their interpretation (below).
The raw data of SANS measurements (Fig. 2) display the scattering curves for the two samples
under study. These scattering curves appear to be rather different in the full experimental range of
scattering parameter Q that should be taken into account in elaboration of models for each glass. A
search of possible models corresponding to the scattering data for these glasses issued from the
knowledge of their structure as near-spherical nanoparticles distributed in low concentration (low
amount of Pb and Se in the precursors, Table 1) within the amorphous glass matrix.
In order to find adequate models applied throughout the full range of these SANS
measurements we consider separately three intervals of Q: Q<0.02, 0.02≤Q≤0.1 and 0.1<Q<0.3.
The fitting of a single model in the full range of Q was not successful. Within the framework of
capabilities of SASfit software  we incorporated into the simulation both fractal aggregates of
overlapping spheres and isolated spheres. For fractal aggregates the scattering function the
following expression including the form-factor (spherical particles in this model) and structural
factor (general form now for some aggregates):
I Q g R R QR
QR dR( ) ( ) sin( )
The function g(R) describes the aggregates through the diameter, 2, that characterizes the
dimension of space (d=3 in this model), and D is the value of fractal dimension. g(R) function is
defined for this type of aggregates as
g(R) = RD-d((1+R/4)(1-R/2)2) for R<2
g(R) = 0 for R≥2.
The fitting of experimental data for the two samples under study to this model is presented in
In the next range of scattering parameters, 0.02≤Q≤0.1, we use the Guinier approximation
I(Q) = (4π2N2/3)exp(-Q2Rg2/3),
where N is particle concentration and Rg is the gyration radius which is related to particle radius
for the spherical case as R=(5/3)1/2Rg. The result of this fitting is given in Fig. 2b,d (the part of
smaller Q, QR<1) and decoded as presence of spherical particles of certain radius (R).
The fitting at the larger Q in these plots corresponds to the generalized Porod law [ ] in which
we account both surface fractals (Ds) and mass fractals (D) in the scattering intensity:
I(Q) = c0 + c4QDs-2D
where c4 is the fitting constants and the term c0 accounts the background. In our case we obtain by
the simulation the exponent Ds-2D close to the value -4, i.e. the Porod law if to consider only one
value for the dimension parameter. Taking into account possibility of different Ds and D, the
surface fractal dimension Ds appears to be different for the two samples since the mass fractal
dimension, D, covered two values (Table 2) for these two samples. For the first sample, 480/56,
Ds=1.84 that means the almost smooth surface for scattering objects, while, in the case of the
sample 525/50 the surface features are more complicated, Ds=1.06. These results can evidence that
the temperature-stimulated modification of PbSe nanoparticles affects the particle-glass interface.
The effect may be associated with pre-melting the glass matrix at the T>Tg with slight growth of
the nanoparticles size providing changes at the glass-particle interface.
Table 2. Parameters of the models obtained through fitting procedures of SANS data for two
samples of PbSe-doped glasses
Sample , nm D Ds Rg, nm R, nm
480/56 27.6 2.92 1.84 6.13 7.9
525/50 24.5 2.53 1.06 8.11 10.5
Table 2 summarizes the data obtained through the above analysis of SANS data for two glass
samples. They indicate that structure of glasses may be presented as combination of single
particles (Rg~6-8 nm) and fractal aggregates of different dimension. The size of aggregates is of
the order of tens of nanometers and comprised of several particles of the size range R~8-10 nm.
The value D is close to 3 (dense aggregate) for the 480/56 sample while the 525/50 sample reveals
formation of less dense aggregates and possesses more complicated surface. That can means slight
growth of PbSe nanoparticles under the temperature rise (480/56 → 525/50) accompanied by
disintegration of aggregates.
A typical micrograph of nanoparticles within glass (480/56 sample) is presented in Fig. 4. We
observe both single particles of the size range of 5-20 nm and little amount of aggregates those are
comprised of two or several particles. Locations of each particle or aggregate demonstrate specific
areas around them those may be associated with changes in glass matrix during the cooling process
as far as the melting temperature of PbSe is higher than Tg for the glass. This picture is typical for
different semiconductor-doped glasses with the glass matrix of similar composition (alkali-silicate)
doped with CdTe, CdSe, PbS, CuInSe2, etc.), since usually a semiconductor material and glass
matrices have different thermal expansion features. Inhomogeneous density of glass can contribute
slightly into the above neutron scattering patterns, however, it is hardly decodable from the
experimental data together with PbSe nanoparticles since the scattering cross section by the latter
is much higher than any contribution due to matrix density variations. Thus, the size range and
morphology of these particles due to PbSe-doping in the results of TEM, in general, are in
consistence with the above conclusions from SANS data simulation.
In this work, we studied the PbSe-doped silicate glasses in which PbSe nanoparticles have been
formed due to the secondary heat treatment at different temperatures. Appearance of the
nanoparticles localized within glass matrix was established by WXRD, SANS, and TEM
techniques with results in accordance to previous optical studies of this material. The size range of
the particles from the measurements with different techniques is evaluated in the range of 5-10 nm.
The simulation results of SANS reveal new structural features of the PbSe nanoparticles: they form
fractal aggregates as several overlapping spheres up to ~30 nm in full size. Thus, the glasses under
study are not simple ‘particle-in-a-matrix’ material. An effect of the structuring upon optics and
the nature of aggregation are the subject of our future research.
1. Lagatsky A.A., Leburn C.G., Brown C.T.A., Sibbett W., Zolotovskaya S.A., Rafailov E.U.
Progr. Quantum Electron. 34, 1 (2010).
2. Reisfeld R. J. Alloy Comp. 341 , 56 (2002).
3. Mazzoldi P., Righini G.C. In: Insulating Materials for Optoelectronics: New Developments.
World Sci. Publ. Co., 2015. Ch.13, P. 367.
4. Onushchenko A.A., Golubkov V.V., Zhilin A.A. Adv. Mater. Res. 39/40, 31 (2008).
5. Liu Ch., Heo J. Intern. J. Appl. Glass Sci. 2013 I, 1 (2013).
6. Malyarevich A.M., Yumashev K.V., Lipovskii A.A. J. Appl. Phys. 103, 081301 (2008).
7. Loiko P.A., Rachkovskaya G.E., Zacharevich G.B. et al. J. Non-Cryst. Solids 358, 1840 (2012).
8. Xu K., Heo J. Physica Scripta T139, 014062 (2010).
9. Kolobkova E.V., Polyakova A.V., Abdrshin A.N., Nikonorov N.V., Aseev V.A.
Glass Phys.Chem. 41, 127 (2015).
10. Kolobkova E.V., Kuznetsova M.S., Nikonorov N.V. Optics and Spectroscopy. 123,344 (2017).
11. El-Rabaie S., Taha T.A., Higazy A.A. Mater.Sci.Semicond. Process. 34, 88 (2015).
12. Ma D.-W., Zhang Y.-N., Xu Zh.-S., Cheng Ch. J. Am. Ceram. Soc. 97, 2455 (2014).
14. Bencherif Y., Boukra A., Zaoui A., Ferhat M. Mater. Chem. Phys. 126, 707 (2011).
Fig. 1. Diffraction patterns for two samples of the PbSe-doped glasses labeled by temperature and
time of the second heat treatment.
Fig. 2. Raw data of SANS measurements for two samples of the PbSe-doped glasses labeled by
temperature and time of the second heat treatment.
Fig. 3. Fitting of the SANS data for two samples of PbSe-doped glasses through different ranges of
the scattering parameter, Q: (a-b) 480/56 and (c-d) 525/50 (temp, oC/time of treatment, h)
Fig. 4. Transmission electron microscopy image of the PbSe-doped glass, the 480/56 sample.