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Baking nanoparticles: Linking the synthesis parameters of CdS nanoparticles in a glass matrix with their size and size distribution
Journal of Non-Crystalline Solids 529 (2020) 119781
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Baking nanoparticles: Linking the synthesis parameters of CdS nanoparticles in a glass matrix with their size and size distribution
T
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I.D. Popova, , B. Sochorb, B. Schummerb,c, Yu.V. Kuznetsovaa, S.V. Rempela,d, S. Gerthc, A.A. Rempela,e a
Institute of Solid State Chemistry, UB RAS, Pervomayskaya 91, 620990 Ekaterinburg, Russia Würzburg University, Chair for X-Ray Microscopy, Josef-Martin-Weg 63, 97074 Würzburg, Germany c Development Center X-Ray Technology EZRT, Flugplatzstraße 75, 90768 Fürth, Germany d Ural Federal University, NOC “Nanotech”, S.Kovalevskoy 7a, 620002, Ekaterinburg, Russia e Institute of Metallurgy of the Ural Branch of the Russian Academy of Sciences, Amundsena 101, 620016, Ekaterinburg, Russia b
A R T I C LE I N FO
A B S T R A C T
Keywords: Nanoparticle Semiconductor Cadmium sulfide Nanocomposite Glass SAXS
CdS nanoparticles in a glass matrix are attractive material for applications in numerous fields, especially optics. However, the growth kinetics of such nanoparticles and its effect on optical properties is still under investigation. Here, the influence of the heat treatment on the nanoparticles was investigated using SAXS and WAXS. The CdS nanoparticles are formed when heat treatment temperature is higher than the glass temperature of the matrix. Nanoparticles with a mean size from 1 to 10 nm are gradually formed followed by linear growth. Thus, the heat treatment time is the key tool to control the nanoparticle size, while the temperature may be used to adjust size distribution. Further heating of samples at 700 °C has led to the formation of nanoparticles with D < 15 nm with hexagonal crystalline structure. Different definitions for particle size and size of coherent scattering region were applied to explain shape and size differences.
1. Introduction Semiconductor nanoparticles (NPs) recently attracted interest in various fields of science. Such materials are successfully developed for applications in different areas: biology [1], solar cell industry [2,3] or laser engineering [4]. Numerous techniques were described [5,6] for the synthesis of NPs in liquids with desirable size using different types of stabilizers. The stabilization is typically based on matrices, micelles or shells around the NPs using organic molecules like proteins, polymers or surfactants. The type of stabilizer determines the particular field of potential application. Liquid colloidal solutions are subject to aging [7,8], while these disadvantages can be solved using nanocomposites based on dielectric matrices, such as glass. These materials show outstanding storage time and resistance to chemical and physical treatment [9]. The NPs synthesis in glass is based on the precipitation process during heat treatment [10]. The heat treatment time and temperature are the defining parameters for this directed synthesis [11]. However, it is still unclear how the synthesis conditions influence the exact size and size distribution of the NPs, which are essential for optical properties. Their unique optical properties provide the possibility of applications in
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optoelectronic devices [12]. The potential applications of such glasses are quantum dot lasers [13], solar concentrators [14], LEDs, optical switches [15] etc. The production process of such materials is well known since it is used for manufacturing of color cut-off filters [9]. However, the lack of knowledge still exits concerning the growth kinetic of NPs, its effect on optical properties and efficiency of the devices mentioned above. The mean size and size distribution of NPs are triggered by the kinetics of growth. Typically, the growth of particles is considered with several competitive processes: nucleation, linear growth and coarsening. The kinetics of semiconductor NPs in glass were described [16,17] by the domination of coarsening process, which means, that the particle growth occurs due to the dissolution of smaller ones. This theory was developed by Lifshitz and Slyozov for supersaturated solid solutions [18]. However, the nucleation kinetics and initial growth remains undescribed for NPs up to 10 nm in size, which show attractive luminescent properties. We considered that the kinetics of NP growth in glass is comparable to the kinetics of precipitation in liquid solution. The growth kinetics of NPs was studied using small-angle-x-ray-scattering (SAXS) and wide-angle-x-ray-scattering (WAXS).
Corresponding author. E-mail address: [email protected] (I.D. Popov).
https://doi.org/10.1016/j.jnoncrysol.2019.119781 Received 13 September 2019; Received in revised form 5 November 2019; Accepted 10 November 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
Journal of Non-Crystalline Solids 529 (2020) 119781
I.D. Popov, et al.
Table 1 Heat treatment conditions of samples, size distribution, volume fraction and number of CdS nanoparticles obtained by SAXS. Sample
A B1 B2 B3 B4 C D E
Heat treatment temperature, °C
time, h
Mean Dnp, nm
FWHM, nm
Relative volume, cm4∙10−6/cm3
Total number of nanoparticles, 1015/cm3
Eg, eV
– 580 580 580 580 595 610 700
– 3 5 15 24 3 3 23
– 2.1 ± 0.1 2.2 ± 0.1 2.8 ± 0.1 3.0 ± 0.1 2.6 ± 0.1 4.0 ± 0.1 5.2 ± 0.1 19.4 ± 0.1
– 0.3 0.4 0.3 0.3 0.3 0.6 1.9 12.2
– 6.71 ± 0.12 7.57 ± 0.23 23.55 ± 0.07 24.95 ± 0.07 10.87 ± 0.06 19.19 ± 0.04 0.72 ± 0.04 25.44 ± 0.04
– 203 246 234 205 157 64 1.13 1.18
4.10 3.03 2.98 2.85 2.82 2.92 2.70 2.43
2. Experimental
3. Result and discussion 3.1. Optical absorption of nanocomposite The optical absorption of the samples is shown in Fig. 1 that demonstrates the effect of heat treatment. The spectra were normalized due to the different sample thicknesses, nanoparticle concentrations and attenuation coefficients caused by changing nanoparticle sizes. The normalization was done to the values at the first maximum to improve comparability of the data sets. The reference sample A has an optical absorption edge at 4.10 ± 0.02 eV, which indicates the absence of CdS NPs. The heat treatment leads to a shift of the absorption edge of all samples proving the formation and growth of CdS NPs in the glass. The oscillations in the inter-band absorption spectrum appear due to dimensional quantization of the energy states of electrons and holes. This quantization is caused by the restriction of their motion at the boundaries of the nanocrystal [24]. The formation of the first absorption peak is a result of the most probable exciton transition 1S3/2-1Se. The blueshift of the absorption indicates the small size of the obtained CdS NPs. In addition, the narrow peak shape and sharp optical absorption edge show the narrow size distribution of the NPs. By using a heat treatment at 580 °C,(samples B1-B4) the optical absorption edge shifts while the shape of first absorption peak remains unchanged. This is a clear sign for the gradual growth of NPs in the glass matrix. Heat treatment at 595 °C still leads to the absorption peaks formation and shifts optical absorption edge (sample C). After heat treating the samples at 610 °C, the first absorption maximum begins to disappear, which may be associated with a softer confinement and increasing particle size
Table 2 The first- and second-nearest coordination of Cd atoms in NPs. Number of atoms
Average coordination number Cd–S Cd–Cd
Occupancy fraction in coordination sphere First Second
1 2 4 6 8 10 20
22 160 1324 4498 10,658 20,848 16,669,038
2.46 3.24 3.63 3.75 3.81 3.85 3.91
0.62 0.81 0.91 0.94 0.95 0.96 0.98
4.91 8.35 10.14 10.76 11.07 11.26 11.59
0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
The data was modelled using particle populations represented by spheres with a log-normal size distribution [23]. Least squares method was used for fitting. Chi squared (χ2) was used as correlation coefficient. The value of χ2 significantly depends on number of data points. In current work values of χ2 for all data fits were in the range from 128 to 333 that was accepted to be appropriate.The error bars represent a combination of random (poison noise) and systematic (solid angle correction) errors. Both influences were treated in thoroughly and to the existing standards described in literature [24]. Log-normal size distribution was used since the effect of many factors (temperature, time, local chemical composition, diffusion, etc.) may be accumulated during the nucleation and growth of NPs. Additionally, such distribution law takes into account critical or minimal size of particles which must be considered during the particle nucleation process. WAXS patterns represent the intensities of the integrated detector images that were scaled taking the samples thickness, X-ray transmission, detector accuracy and setup geometry into account [24]. Bragg peaks on WAXS pattern were modelled using pseudo-Voight functions by means of Retvield refinement. The instrumental parameters of widening were determined using a Standard Reference Material (NIST 660c, LaB6), which is intended for the calibration of diffraction line positions and line shapes.
Glass synthesis by charge melting of raw oxides and sulfides was described in our previous report [19]. Glass temperature for the used type of glass Tg = 546 ± 1 °C. The NPs nucleation and growth was controlled by secondary heat treatment at distinct temperatures (see Table 1), which start the ion diffusion. Subsequently, the samples were polished and their thickness was reduced. The optical absorption of samples were measured using FS-5 Spectrofluorometer equipped arc Xe-lamp (450 W) and Si photodiode with a maximum absolute error of ± 0.01 absorbance units. The measurements were carried out with spectral resolution of 1 nm and 0.1 s of integration time per every point. Bandgap energy of samples was determined using method developed by Tauc [20]. SAXS and WAXS methods give information about the investigated samples on different scale. SAXS might be used for the evaluation of the size and shape of the nanoparticle, which is usually on the scale of 1 to 100 nm. WAXS on the other hand gives information about the crystalline structure in the atomic (Angstroms) scale. All SAXS/WAXS measurements were carried out at a setup build by Fraunhofer EZRT at the Chair of X-ray Microscopy (University Würzburg, Germany). It consists of a Rigaku MicroMax-007 HF as a source and a Dectris Eiger R 1 M as a detector. The sample-detector distance can be varied between 6 cm and 3.5 m, which corresponds to possible Q-values between 0.005 and 5 Å−1. The complete setup is operated in a vacuum below 0.1 mbar to reduce air scattering. The samples were positioned perpendicularly to the X-ray beam and had the thickness of around 100 µm. The presented experiments were done at sample-detector distances of 46.90 mm for WAXS measurements, 280.59 mm and 977.22 mm for SAXS measurements with an integration time of 2 h each. All distances were calibrated using Silver behenate as a standard. Additionally, all data was calibrated in terms of absolute intensities with Glassy Carbon using the secondary calibration standard method [21,22]. Finally, the scattering data was reduced taking the samples thickness, X-ray transmission, detector accuracy and setup geometry into account. To correct for the glass/reference scattering, glass without nanoparticles was used as a reference (sample A, see Table 2). For SAXS data analysis, the Igor Pro macros IRENA was used.
DNP, nm
± ± ± ± ± ± ± ±
0.41 0.69 0.85 0.89 0.92 0.94 0.97
2
Journal of Non-Crystalline Solids 529 (2020) 119781
I.D. Popov, et al.
Fig. 1. Evolution of the optical absorption depending on heat treatment temperature (a) and time (b). Each spectrum was normalized to the value of the first absorption peak. All samples are described in Table 1. Sample A and E demonstrate the optical absorbtion properties of the pure glass matrix and NPs with properties of bulk CdS. The normalization was done due to the different thickness of samples, concentration of NPs and attenuation coefficients due to size changing.
and Cd-S pairs in NPs. The calculations were carried out using the following simplifications: the NPs are in vacuum, have spherical shape and a perfect wurzite (B4 type) crystalline structure. The Radial distribution function for a S-S pair is the same as for a Cd-Cd pair due to the wurzite structure symmetry. Furthermore, the first and second average coordination number of Cd was calculated. Using these coordination numbers we can evaluate the fraction of Zn and O atoms, which are bound to the NP surface. The average first coordination number changes from 2.46 to 3.91 with increasing NP diameter from 1 to 20 nm (Table 2). By increasing the NP size, the average coordination number approach 4 and 12, for the first and second coordination number, respectively. At the same time, the occupancy fraction for NP with D = 1 nm shows, that up to 38% of atoms in the first coordination sphere can be located onto the surface of the NP. Thus, up to 38% of first nearest neighbor of Cd might be O atoms taking into account chemical composition of glass. Hereby, the oxygen might be found as the nearest neighbor of Cd due to the presence of the presence of the glass-nanoparticle interface rather than due to impurities in nanoparticle volume. Additionally, O can be observed in first coordination sphere due to the presence of Cd outside the NPs, because it is dissolved in glass matrix and oxidized. With these results, we can neglect changes in the local density of the matrix and chemical composition of NPs, which is important for SAXS data handling. In other words, the scattering contrast between CdS NPs and glass is assumed to be constant. Consequently, the increasing scattering intensity is caused by the growth of NPs.
distribution (sample D). Comparing all the samples, E shows the strongest optical absorption and has a bandgap at Eg = 2.43 ± 0.02 eV. Thus, increasing the heat treatment temperature up to 700 °C during 23 h will lead to the formation of large particles with optical properties of bulk CdS. 3.2. Before SAXS data handling The nanocomposite samples show a significant difference in the scattering intensity compared to the pure glass matrix (sample A). This change in intensity points out the presence of CdS NPs in dielectric matrices. We have suggested two reasons for the increasing scattering intensity with rising of heat treatment temperature (Fig. 2a). First, an increased scattering intensity can be caused by a larger particle size and/or number or, second, by changing the scattering contrast between NPs and the dielectric matrix. During the growth of NPs, modifications of their chemical composition can arise due to impurities and defects of the crystalline structure during the heat treatment, where the presence of light atoms mainly leads to a lower contrast. Hence, dielectric matrices, which are based on oxides including ZnO, have a significant influence on the atomic structure of NPs. As a result, a solid substitution solution Cd(1-x)ZnxS can exist with a certain number of O ions. The presence of O and Zn was shown by EXAFS in other works [25–27]. Here, the increasing heat treatment temperature and time changed the occupancy ratio of the first-nearest coordination from 50:50 up to 75:25 for S and O, respectively. Consequently, the larger the NP size is, the less O are in the nearest coordination of Cd atoms since heat treatment leads to increasing NP mean size. A similar result was observed for Zn atoms in the second-nearest coordination of Cd [25]. However, EXAFS fails to determine the Cd bounds in the NPs or with the dielectric matrix. Moreover, when the particle size is less than 10 nm, the ratio of atoms at the surface and in the particle volume increases accordingly. Thus, the average coordination number of nearest neighbors for each Cd atom is significantly less than 4 due to dangling bonds. However, the dielectric matrix is chemically bonded to the NP surface through O and Zn atoms. Therefore, the evaluation of the first- and second-nearest neighbor coordination needs to be sophistically carried out, since both volume and surface states of Cd are present. This is important, because smaller NPs are dominated by such surface states and effects. We have carried out the evaluation of surface contribution in the filling of the first and second coordination spheres of Cd atoms. NPs with a diameter D between 1 and 20 nm were modelled as perfect crystals. Then, the radial distribution function was calculated for Cd-Cd
3.3. Measuring NPs size using SAXS Optical absorption can be used for the estimation of the NPs size [28] since the bandgap of NPs depends on a mean size. This approach is based on the quantum confinement effect [29]. Optical absorption data allows for the maximum size to be estimated, because larger nanoparticles have higher extinction coefficients [30]. The size of smaller particles cannot be determined with this method since large NPs determine the location of optical absorption edge. The influence of temperature and exposure time of heat treatment on optical properties was already studied [19]. In this work, the same set of samples (see Table 1) was studied combining SAXS and WAXS. Here, sample A was the pure glass matrix. Samples B1-B4 were heat-treated at 580 °C for 3–24 h to study the influence of exposure time. Samples B1, C and D were heattreated for 3 h at 580 °C, 595 °C and 610 °C, respectively. Additionally, sample E was the extreme case with a maximum heat treatment temperature of 700 °C and time (23 h). The SAXS experimental results 3
Journal of Non-Crystalline Solids 529 (2020) 119781
I.D. Popov, et al.
Fig. 2. Evolution of the scattering intensity and number distribution of NPs depends on treatment temperature (a, b) and time (c, d). Sample details are given in Table 1. Inset: relative volume change with increasing heat treatment temperature (error bars are less than symbols). A line in the inset is drawn as guide to the eyes.
3.4. Nucleation and growth of NPs in glass matrix
demonstrate that the heat treatment heavily influences the growth rate of the NPs leading to an increasing mean diameter, broader size distribution and/or a larger number of NPs (Fig. 2). The absence of NPs in the reference sample (sample A) is confirmed due to a lack of X-ray scattering in the investigated q-vector range. Only heat treatment temperatures above 580 °C lead to a different scattering contrast compared to the glass reference (sample A) and a visible luminescence, which determined during preliminary experiments [19]. Increasing the heat treatment temperature to 610 °C is accompanied by a doubling of the mean diameter from 2.1 ± 0.1 up to 4.0 ± 0.1 nm (Table 1). The full width at half maximum (FWHM) of the size distribution doubles as well (Fig. 2b). Not only the heat treatment temperature changes the NPs size, but also the treatment time. By increasing it from 3 to 24 h, the NPs mean diameter grows from 2.1 ± 0.1 to 3.0 ± 0.1 nm, while the FWHM of their size distribution changes only slightly. Thus, the heat treatment time is a more precise instrument to control the mean size of NPs.
According to the experimental data, we assume the following growth process of CdS NPs in the glass matrix (Fig. 3). Before the heat treatment, each sample is a supersaturated solution of Cd and S ions in glass, which act as solvents. This supersaturated solution exists below glass melting (1300–1400 °C) down to room temperature. Until Tg is reached, the viscosity of glass is extremely high and a sufficient diffusion of ions to form NPs does not take place. At the same time, few and extremely small nuclei can grow at T < Tg. If the viscosity of glass decreases below 1011 Pa∙s (T > Tg), the growth of NPs become possible. The number of NPs remains relatively constant during isothermal heat treatment at 580 °C. The NP is growing due to ion diffusion. Local inhomogeneity in glass may cause minor deviations of the number of NPs. The temperature variation affects the nucleation rate. We suggest the following observations. First, the mean NP size (Dnp) is 2.1 ± 0.1 up to 4.0 ± 0.1 nm for heat treatment temperatures between 580 °C and 610 °C. Second, while the total NPs number is reduced by a factor of three, the CdS relative volume fraction (i.e. phase concentration) raises (inset Fig. 2b) with varying heat treatment temperatures. 4
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Fig. 3. Scheme of nanocomposite synthesis. At room temperature, glass is represented as a dielectric matrix with uniformly distributed ions of Cd and S. Extremely small nuclei can be formed during a first heat treatment around Tg. The CdS NPs are formed during the initial moments of heat treatment using temperatures higher Tg. This temperature leads to NPs growth with mean size from 1 to 10 nm. Further increasing of heat treatment temperature leads to the formation of crystalline NPs with D > 15 nm. The NPs formed in the initial moment then growth linearly in size.
several reasons. First, the amorphous structure of glass appears as an intense diffuse halo in X-ray diffraction patterns and overlaps the diffraction from the NPs. Second, standard laboratory XRD equipment is inefficient for crystalline structure analysis of minor phases at low concentrations due to a very low contrast. However, the low concentration of a semiconductor phase is the essential feature of nanocomposites based on glass. The concentration of the CdS phase is still below 1 wt.% when Cd and S ions, which are distributed in the glass matrix, form CdS. Along with that, we suppose that the NPs possess an amorphous or strongly disordered crystalline structure compared to bulk CdS due to their small size and inevitable interaction with the glass matrix. Thus, the mentioned factors hinder the determination of the crystalline structure of CdS NPs distributed in a glass matrix using conventional XRD laboratory equipment.
The nucleation and growth of NPs is similar to precipitation in a liquid solution [31]. This theory proposed that the particle size (Dnp) is proportional to the diffusion coefficient (D). Further, D is inversely proportional to the viscosity of the medium (η). The viscosity of amorphous materials η is a function of temperature 1/T. Therefore, particle size should be proportional to temperature Dnp ~ T, which was observed in the experiments. The nucleus size and the ratio of nucleation and growth are limited by two factors: the initial ion concentrations and the heat treatment temperature. Below Tg, the growth of NPs due to the diffusion of nuclei or particles is unlikely considering the large glass viscosity. Further investigations in terms of liquid solutions theory will improve the directed synthesis of semiconductor NPs for potential application in optics. Previously we proved that the CdS NPs are uniformly distributed in a glass matrix using FIB-SEM [19]. Within this experiment it was possible to evaluate the diameter of the largest particles, while smaller particles and their size distribution remained unspecified. The same sample (E) was measured using SAXS and WAXS in this work and the bimodal size distribution. Fig. 4 was determined with correlation coefficient χ2 = 231 (Table 1). This fact stresses that the rate of nucleation increases for higher heat treatment temperatures. The heat treatment at 700 °C (sample E) dramatically increases a mean size up to 19.4 ± 0.1 nm for the dominant population, while the total number of NPs is two orders of magnitude smaller compared to other samples. At the same time, the critical size increased up to 3 nm. Thus, the normal growth dominates the nucleation rate for higher heat treatment temperatures. Additionally, the heating rate of the glass matrix may change the equilibrium between nucleation and growth processes. The deviations of the optical properties can be caused by several reasons: quantum mechanical effects, the size distribution and the atomic and crystalline structure of NPs. The crystalline structure of CdS NPs in a glass matrix remains unspecified to our knowledge. This is due to the fact that laboratory XRD methods cannot provide results for
3.5. Crystalline structure of CdS NPs in glass matrix Bulk cadmium sulfide exists in two phases, sphalerite (cubic structure) and wurtzite (hexagonal structure). Disordered crystalline structures of CdS were discovered and attributed to the small (3–9 nm) NPs [32] due to random alternation of close packed hexagonal atomic planes. We have determined the crystalline structure of CdS NPs in glass combining SAXS and WAXS within the same device (Fig. 5). Diffraction peaks (110) and (013) appeared for smaller NPs (D = 4.0 ± 0.1 nm, sample D), but they were too weak in intensity for a proper baseline subtraction. Sample E (700 °C for 23 h) shows outstanding intensity in the diffraction pattern (Fig. 5a). The phase of CdS crystals can be clearly identified for this sample with an exclusive hexagonal crystalline structure (ICSD # 41490, space group P63mc) [33] with cell parameters a = 4.150(2), c = 6.732(3) Å. We assume a tiny number of incorporated Zn and O atoms in the NP crystalline structure due to the very small changes in the interatomic distances compared to bulk CdS. The diffraction pattern at Fig. 5a shows a significant redistribution of 5
Journal of Non-Crystalline Solids 529 (2020) 119781
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Fig. 4. Scattering intensity (gray dots) with models (χ2 = 231) (a) and number distribution (b) of both populations CdS NPs (sample E). Blue and pink color is attributed to the large and small CdS particles respectively. Error bars are less than symbol size.
CSR size was calculated to 13 ± 1 nm by the broadening of the diffraction peaks, which is in a good agreement with the SAXS data. The size of the CSR is smaller than the mean diameter of NPs since the smaller NPs produce a larger contribution to the broadening of the diffraction peaks. Deep peak profile analysis can not prove a significant difference in peak broadening alongside certain crystallography directions. Typically, this anisotropy is correlated with the size of CSR along the corresponding crystallography directions. Such differences in size can be observed from broadening along a certain family of planes. It has to be mentioned, that there were only few diffraction peaks for a distinct determination of the anisotropy broadening. The flat slope of the linear regression in the Williamson-Hall plot shows a moderate value of micro-strains in the NPs crystalline structure.
intensities, which fails to describe a preferred orientation of the NPs. However, such an orientation is not expected during their nucleation and growth. A temperature gradient and NP sedimentation during the heat treatment were assumed to be negligibly small. Here, a preferred direction of growth rather than a preferred orientation can be suggested. The preferred growth direction takes place along the z-axis of the hexagonal crystalline structure taking into account the large intensity of the (002)-diffraction peak.
3.6. Mismatch of coherent scattering region and actual NP size A preferred growth direction leads to the non-spherical shape of NPs. In case of non-spherical shapes, large and well-ordered nanoparticles should have a shape of extended spheroids or cylinders. The SAXS data does not suggest ellipsoidal or cylindrical shapes, but it must be clear, that the coherent scattering region (CSR) of NPs can differ from their overall shape and size. Highly intense diffraction peaks will only appear from large and well-ordered NPs. If atomic planes in the CdS crystals are practically close-packed along one axis (i.e. z-axis, see Fig. 6), the growth at the edges of the NP (i.e. along x- and y-axes in Fig. 6) may have a weaker ordered crystalline structure. The well-ordered and close-packed crystal direction yields into higher diffraction intensities and this results in a different shape of the CSR and NPs. Using Sherrer's formula [34] and the Williamson-Hall method [35] the
4. Conclusion The formation of the two-phase system (glass-NP) is similar to the process of precipitation from liquid solution. The applied heat treatment of glass with Cd and S ions leads to the nucleation and growth of semiconductor NPs. The correlation between the NP mean size and the heat treatment parameters (temperature, time) was shown here. Thus, the heat treatment time is the tool to control the NP size, while not changing the size distribution. However, the heat treatment temperature can be used effectively to adjust the size distribution. The obtained
Fig. 5. Diffraction pattern (baseline subtracted) (a) and Williamson-Hall plot (b) of CdS NPs (sample E). Red dashed line is 0.95 confidence interval of fit (adjusted R2 = - 0.136). Inset: WAXS patterns of sample E (blue line) before subtracting contribution by diffracted photons by sample A (black line) that is amorphous glass matrix. 6
Journal of Non-Crystalline Solids 529 (2020) 119781
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Fig. 6. Scheme of the difference between an actual particle size and CSR. Diffraction patterns are induced by large and well-ordered NPs. The Atomic planes in the CdS crystal (pale blue region) are close-packed along the z-axis. At the same time, a growth along the x- and y-axes forms the NP edges, which have a weak-ordered crystalline structures. This fact results in the observed difference between the shape of NP observed by WAXS and SAXS.
results were discussed using precipitation theory for liquid solutions. The oscillations and exciton absorption peak in the interband absorption spectra indicates quantization of the energy states of electrons and holes in NPs with < 10 nm. The CdS NPs with = 19.4 ± 0.1 nm shows properties of bulk CdS. Their crystalline structure was determined to be hexagonal. However, to study both the NPs crystalline structure with D < 10 nm and their distinct nucleation and growth processes, synchrotron radiation should be used during in situ experiments. The precise determination of defects remains a crucial challenge to study the effect of the atomic structure on optical properties. This knowledge will be the essential base for any future application of NP glasses in optical systems.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could influence the reported work. Acknowledgments This work was supported by Russian Foundation for Basic Research 17-03-01024. The authors are grateful to Balyakin I.A. (Ekaterinburg, Russia) for carrying calculation of coordination spheres of Cd in nanoparticles and Chufarov A.Yu. (Ekaterinburg, Russia) for valuable discussions of WAXS results. References [1] M. Alizadeh-Ghodsi, M. Pourhassan-Moghaddam, A. Zavari-Nematabad, B. Walker, N. Annabi, A. Akbarzadeh, State-of-the-Art and trends in synthesis, properties, and application of quantum dots-based nanomaterials, Part. Part. Syst. Charact. 36 (2019) 1800302, , https://doi.org/10.1002/ppsc.201800302. [2] V.P. Afanas'ev, V.N. Vasil'ev, A.I. Ignat'ev, E.V. Kolobkova, N.V. Nikonorov, A.I. Sidorov, V.A. Tsekhomskiĭ, New luminescent glasses and prospects of using them in solar energy, J. Opt. Technol. 80 (2013) 635, https://doi.org/10.1364/ JOT.80.000635. [3] L.M. Nikolenko, V.F. Razumov, Colloidal quantum dots in solar cells, Russ. Chem. Rev. 82 (2013) 429–448, https://doi.org/10.1070/RC2013v082n05ABEH004337. [4] M. Kazes, D.Y. Lewis, Y. Ebenstein, T. Mokari, U. Banin, Lasing from semiconductor quantum rods in a cylindrical microcavity, Adv. Mater. 14 (2002) 317–321, https:// doi.org/10.1002/1521-4095(20020219)14:4<317::AID-ADMA317>3.0.CO;2-U. [5] N.V. Hullavarad, S.S. Hullavarad, P.C. Karulkar, Cadmium sulphide (CdS) nanotechnology: synthesis and applications, J. Nanosci. Nanotechnol. 8 (2008)
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Metall. Mater. Trans. A. 41 (2010) 1151–1158, https://doi.org/10.1007/s11661009-9950-x. J. Ilavsky, P.R. Jemian, Irena: tool suite for modeling and analysis of small-angle scattering, J. Appl. Crystallogr. 42 (2009) 347–353, https://doi.org/10.1107/ S0021889809002222. B.R. Pauw, A.J. Smith, T. Snow, N.J. Terrill, A.F. Thünemann, The modular smallangle X-ray scattering data correction sequence, J. Appl. Crystallogr. 50 (2017) 1800–1811, https://doi.org/10.1107/S1600576717015096. T.M. Hayes, L.B. Lurio, P.D. Persans, Growth and dissolution of CdS nanoparticles in glass, J. Phys. Condens. Matter. 13 (2001) 425–431, https://doi.org/10.1088/ 0953-8984/13/3/305. T.M. Hayes, P.D. Persans, A. Filin, C. Peng, W. Huang, Cd and Se atomic environments during the growth of CdSe nanoparticles in glass, Phys. Scr. T115 (2005) 703–705, https://doi.org/10.1238/Physica.Topical.115a00703. T.M. Hayes, L.B. Lurio, J. Pant, P.D. Persans, Order in CdS nanoparticles in glass, Solid State Commun. 117 (2001) 627–630, https://doi.org/10.1016/S00381098(00)00511-1. V.G. Klyuev, D.V. Volykhin, M.S. Smirnov, N.S. Dubovitskaya, Influence of manganese doping on the luminescence characteristics of colloidal ZnxCd1−xS quantum dots in gelatin, J. Lumin. 192 (2017) 893–901, https://doi.org/10.1016/j.
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Baking nanoparticles: Linking the synthesis parameters of CdS nanoparticles in a glass matrix with their size and size distribution
T
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I.D. Popova, , B. Sochorb, B. Schummerb,c, Yu.V. Kuznetsovaa, S.V. Rempela,d, S. Gerthc, A.A. Rempela,e a
Institute of Solid State Chemistry, UB RAS, Pervomayskaya 91, 620990 Ekaterinburg, Russia Würzburg University, Chair for X-Ray Microscopy, Josef-Martin-Weg 63, 97074 Würzburg, Germany c Development Center X-Ray Technology EZRT, Flugplatzstraße 75, 90768 Fürth, Germany d Ural Federal University, NOC “Nanotech”, S.Kovalevskoy 7a, 620002, Ekaterinburg, Russia e Institute of Metallurgy of the Ural Branch of the Russian Academy of Sciences, Amundsena 101, 620016, Ekaterinburg, Russia b
A R T I C LE I N FO
A B S T R A C T
Keywords: Nanoparticle Semiconductor Cadmium sulfide Nanocomposite Glass SAXS
CdS nanoparticles in a glass matrix are attractive material for applications in numerous fields, especially optics. However, the growth kinetics of such nanoparticles and its effect on optical properties is still under investigation. Here, the influence of the heat treatment on the nanoparticles was investigated using SAXS and WAXS. The CdS nanoparticles are formed when heat treatment temperature is higher than the glass temperature of the matrix. Nanoparticles with a mean size from 1 to 10 nm are gradually formed followed by linear growth. Thus, the heat treatment time is the key tool to control the nanoparticle size, while the temperature may be used to adjust size distribution. Further heating of samples at 700 °C has led to the formation of nanoparticles with D < 15 nm with hexagonal crystalline structure. Different definitions for particle size and size of coherent scattering region were applied to explain shape and size differences.
1. Introduction Semiconductor nanoparticles (NPs) recently attracted interest in various fields of science. Such materials are successfully developed for applications in different areas: biology [1], solar cell industry [2,3] or laser engineering [4]. Numerous techniques were described [5,6] for the synthesis of NPs in liquids with desirable size using different types of stabilizers. The stabilization is typically based on matrices, micelles or shells around the NPs using organic molecules like proteins, polymers or surfactants. The type of stabilizer determines the particular field of potential application. Liquid colloidal solutions are subject to aging [7,8], while these disadvantages can be solved using nanocomposites based on dielectric matrices, such as glass. These materials show outstanding storage time and resistance to chemical and physical treatment [9]. The NPs synthesis in glass is based on the precipitation process during heat treatment [10]. The heat treatment time and temperature are the defining parameters for this directed synthesis [11]. However, it is still unclear how the synthesis conditions influence the exact size and size distribution of the NPs, which are essential for optical properties. Their unique optical properties provide the possibility of applications in
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optoelectronic devices [12]. The potential applications of such glasses are quantum dot lasers [13], solar concentrators [14], LEDs, optical switches [15] etc. The production process of such materials is well known since it is used for manufacturing of color cut-off filters [9]. However, the lack of knowledge still exits concerning the growth kinetic of NPs, its effect on optical properties and efficiency of the devices mentioned above. The mean size and size distribution of NPs are triggered by the kinetics of growth. Typically, the growth of particles is considered with several competitive processes: nucleation, linear growth and coarsening. The kinetics of semiconductor NPs in glass were described [16,17] by the domination of coarsening process, which means, that the particle growth occurs due to the dissolution of smaller ones. This theory was developed by Lifshitz and Slyozov for supersaturated solid solutions [18]. However, the nucleation kinetics and initial growth remains undescribed for NPs up to 10 nm in size, which show attractive luminescent properties. We considered that the kinetics of NP growth in glass is comparable to the kinetics of precipitation in liquid solution. The growth kinetics of NPs was studied using small-angle-x-ray-scattering (SAXS) and wide-angle-x-ray-scattering (WAXS).
Corresponding author. E-mail address: [email protected] (I.D. Popov).
https://doi.org/10.1016/j.jnoncrysol.2019.119781 Received 13 September 2019; Received in revised form 5 November 2019; Accepted 10 November 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
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Table 1 Heat treatment conditions of samples, size distribution, volume fraction and number of CdS nanoparticles obtained by SAXS. Sample
A B1 B2 B3 B4 C D E
Heat treatment temperature, °C
time, h
Mean Dnp, nm
FWHM, nm
Relative volume, cm4∙10−6/cm3
Total number of nanoparticles, 1015/cm3
Eg, eV
– 580 580 580 580 595 610 700
– 3 5 15 24 3 3 23
– 2.1 ± 0.1 2.2 ± 0.1 2.8 ± 0.1 3.0 ± 0.1 2.6 ± 0.1 4.0 ± 0.1 5.2 ± 0.1 19.4 ± 0.1
– 0.3 0.4 0.3 0.3 0.3 0.6 1.9 12.2
– 6.71 ± 0.12 7.57 ± 0.23 23.55 ± 0.07 24.95 ± 0.07 10.87 ± 0.06 19.19 ± 0.04 0.72 ± 0.04 25.44 ± 0.04
– 203 246 234 205 157 64 1.13 1.18
4.10 3.03 2.98 2.85 2.82 2.92 2.70 2.43
2. Experimental
3. Result and discussion 3.1. Optical absorption of nanocomposite The optical absorption of the samples is shown in Fig. 1 that demonstrates the effect of heat treatment. The spectra were normalized due to the different sample thicknesses, nanoparticle concentrations and attenuation coefficients caused by changing nanoparticle sizes. The normalization was done to the values at the first maximum to improve comparability of the data sets. The reference sample A has an optical absorption edge at 4.10 ± 0.02 eV, which indicates the absence of CdS NPs. The heat treatment leads to a shift of the absorption edge of all samples proving the formation and growth of CdS NPs in the glass. The oscillations in the inter-band absorption spectrum appear due to dimensional quantization of the energy states of electrons and holes. This quantization is caused by the restriction of their motion at the boundaries of the nanocrystal [24]. The formation of the first absorption peak is a result of the most probable exciton transition 1S3/2-1Se. The blueshift of the absorption indicates the small size of the obtained CdS NPs. In addition, the narrow peak shape and sharp optical absorption edge show the narrow size distribution of the NPs. By using a heat treatment at 580 °C,(samples B1-B4) the optical absorption edge shifts while the shape of first absorption peak remains unchanged. This is a clear sign for the gradual growth of NPs in the glass matrix. Heat treatment at 595 °C still leads to the absorption peaks formation and shifts optical absorption edge (sample C). After heat treating the samples at 610 °C, the first absorption maximum begins to disappear, which may be associated with a softer confinement and increasing particle size
Table 2 The first- and second-nearest coordination of Cd atoms in NPs. Number of atoms
Average coordination number Cd–S Cd–Cd
Occupancy fraction in coordination sphere First Second
1 2 4 6 8 10 20
22 160 1324 4498 10,658 20,848 16,669,038
2.46 3.24 3.63 3.75 3.81 3.85 3.91
0.62 0.81 0.91 0.94 0.95 0.96 0.98
4.91 8.35 10.14 10.76 11.07 11.26 11.59
0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
The data was modelled using particle populations represented by spheres with a log-normal size distribution [23]. Least squares method was used for fitting. Chi squared (χ2) was used as correlation coefficient. The value of χ2 significantly depends on number of data points. In current work values of χ2 for all data fits were in the range from 128 to 333 that was accepted to be appropriate.The error bars represent a combination of random (poison noise) and systematic (solid angle correction) errors. Both influences were treated in thoroughly and to the existing standards described in literature [24]. Log-normal size distribution was used since the effect of many factors (temperature, time, local chemical composition, diffusion, etc.) may be accumulated during the nucleation and growth of NPs. Additionally, such distribution law takes into account critical or minimal size of particles which must be considered during the particle nucleation process. WAXS patterns represent the intensities of the integrated detector images that were scaled taking the samples thickness, X-ray transmission, detector accuracy and setup geometry into account [24]. Bragg peaks on WAXS pattern were modelled using pseudo-Voight functions by means of Retvield refinement. The instrumental parameters of widening were determined using a Standard Reference Material (NIST 660c, LaB6), which is intended for the calibration of diffraction line positions and line shapes.
Glass synthesis by charge melting of raw oxides and sulfides was described in our previous report [19]. Glass temperature for the used type of glass Tg = 546 ± 1 °C. The NPs nucleation and growth was controlled by secondary heat treatment at distinct temperatures (see Table 1), which start the ion diffusion. Subsequently, the samples were polished and their thickness was reduced. The optical absorption of samples were measured using FS-5 Spectrofluorometer equipped arc Xe-lamp (450 W) and Si photodiode with a maximum absolute error of ± 0.01 absorbance units. The measurements were carried out with spectral resolution of 1 nm and 0.1 s of integration time per every point. Bandgap energy of samples was determined using method developed by Tauc [20]. SAXS and WAXS methods give information about the investigated samples on different scale. SAXS might be used for the evaluation of the size and shape of the nanoparticle, which is usually on the scale of 1 to 100 nm. WAXS on the other hand gives information about the crystalline structure in the atomic (Angstroms) scale. All SAXS/WAXS measurements were carried out at a setup build by Fraunhofer EZRT at the Chair of X-ray Microscopy (University Würzburg, Germany). It consists of a Rigaku MicroMax-007 HF as a source and a Dectris Eiger R 1 M as a detector. The sample-detector distance can be varied between 6 cm and 3.5 m, which corresponds to possible Q-values between 0.005 and 5 Å−1. The complete setup is operated in a vacuum below 0.1 mbar to reduce air scattering. The samples were positioned perpendicularly to the X-ray beam and had the thickness of around 100 µm. The presented experiments were done at sample-detector distances of 46.90 mm for WAXS measurements, 280.59 mm and 977.22 mm for SAXS measurements with an integration time of 2 h each. All distances were calibrated using Silver behenate as a standard. Additionally, all data was calibrated in terms of absolute intensities with Glassy Carbon using the secondary calibration standard method [21,22]. Finally, the scattering data was reduced taking the samples thickness, X-ray transmission, detector accuracy and setup geometry into account. To correct for the glass/reference scattering, glass without nanoparticles was used as a reference (sample A, see Table 2). For SAXS data analysis, the Igor Pro macros IRENA was used.
DNP, nm
± ± ± ± ± ± ± ±
0.41 0.69 0.85 0.89 0.92 0.94 0.97
2
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Fig. 1. Evolution of the optical absorption depending on heat treatment temperature (a) and time (b). Each spectrum was normalized to the value of the first absorption peak. All samples are described in Table 1. Sample A and E demonstrate the optical absorbtion properties of the pure glass matrix and NPs with properties of bulk CdS. The normalization was done due to the different thickness of samples, concentration of NPs and attenuation coefficients due to size changing.
and Cd-S pairs in NPs. The calculations were carried out using the following simplifications: the NPs are in vacuum, have spherical shape and a perfect wurzite (B4 type) crystalline structure. The Radial distribution function for a S-S pair is the same as for a Cd-Cd pair due to the wurzite structure symmetry. Furthermore, the first and second average coordination number of Cd was calculated. Using these coordination numbers we can evaluate the fraction of Zn and O atoms, which are bound to the NP surface. The average first coordination number changes from 2.46 to 3.91 with increasing NP diameter from 1 to 20 nm (Table 2). By increasing the NP size, the average coordination number approach 4 and 12, for the first and second coordination number, respectively. At the same time, the occupancy fraction for NP with D = 1 nm shows, that up to 38% of atoms in the first coordination sphere can be located onto the surface of the NP. Thus, up to 38% of first nearest neighbor of Cd might be O atoms taking into account chemical composition of glass. Hereby, the oxygen might be found as the nearest neighbor of Cd due to the presence of the presence of the glass-nanoparticle interface rather than due to impurities in nanoparticle volume. Additionally, O can be observed in first coordination sphere due to the presence of Cd outside the NPs, because it is dissolved in glass matrix and oxidized. With these results, we can neglect changes in the local density of the matrix and chemical composition of NPs, which is important for SAXS data handling. In other words, the scattering contrast between CdS NPs and glass is assumed to be constant. Consequently, the increasing scattering intensity is caused by the growth of NPs.
distribution (sample D). Comparing all the samples, E shows the strongest optical absorption and has a bandgap at Eg = 2.43 ± 0.02 eV. Thus, increasing the heat treatment temperature up to 700 °C during 23 h will lead to the formation of large particles with optical properties of bulk CdS. 3.2. Before SAXS data handling The nanocomposite samples show a significant difference in the scattering intensity compared to the pure glass matrix (sample A). This change in intensity points out the presence of CdS NPs in dielectric matrices. We have suggested two reasons for the increasing scattering intensity with rising of heat treatment temperature (Fig. 2a). First, an increased scattering intensity can be caused by a larger particle size and/or number or, second, by changing the scattering contrast between NPs and the dielectric matrix. During the growth of NPs, modifications of their chemical composition can arise due to impurities and defects of the crystalline structure during the heat treatment, where the presence of light atoms mainly leads to a lower contrast. Hence, dielectric matrices, which are based on oxides including ZnO, have a significant influence on the atomic structure of NPs. As a result, a solid substitution solution Cd(1-x)ZnxS can exist with a certain number of O ions. The presence of O and Zn was shown by EXAFS in other works [25–27]. Here, the increasing heat treatment temperature and time changed the occupancy ratio of the first-nearest coordination from 50:50 up to 75:25 for S and O, respectively. Consequently, the larger the NP size is, the less O are in the nearest coordination of Cd atoms since heat treatment leads to increasing NP mean size. A similar result was observed for Zn atoms in the second-nearest coordination of Cd [25]. However, EXAFS fails to determine the Cd bounds in the NPs or with the dielectric matrix. Moreover, when the particle size is less than 10 nm, the ratio of atoms at the surface and in the particle volume increases accordingly. Thus, the average coordination number of nearest neighbors for each Cd atom is significantly less than 4 due to dangling bonds. However, the dielectric matrix is chemically bonded to the NP surface through O and Zn atoms. Therefore, the evaluation of the first- and second-nearest neighbor coordination needs to be sophistically carried out, since both volume and surface states of Cd are present. This is important, because smaller NPs are dominated by such surface states and effects. We have carried out the evaluation of surface contribution in the filling of the first and second coordination spheres of Cd atoms. NPs with a diameter D between 1 and 20 nm were modelled as perfect crystals. Then, the radial distribution function was calculated for Cd-Cd
3.3. Measuring NPs size using SAXS Optical absorption can be used for the estimation of the NPs size [28] since the bandgap of NPs depends on a mean size. This approach is based on the quantum confinement effect [29]. Optical absorption data allows for the maximum size to be estimated, because larger nanoparticles have higher extinction coefficients [30]. The size of smaller particles cannot be determined with this method since large NPs determine the location of optical absorption edge. The influence of temperature and exposure time of heat treatment on optical properties was already studied [19]. In this work, the same set of samples (see Table 1) was studied combining SAXS and WAXS. Here, sample A was the pure glass matrix. Samples B1-B4 were heat-treated at 580 °C for 3–24 h to study the influence of exposure time. Samples B1, C and D were heattreated for 3 h at 580 °C, 595 °C and 610 °C, respectively. Additionally, sample E was the extreme case with a maximum heat treatment temperature of 700 °C and time (23 h). The SAXS experimental results 3
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Fig. 2. Evolution of the scattering intensity and number distribution of NPs depends on treatment temperature (a, b) and time (c, d). Sample details are given in Table 1. Inset: relative volume change with increasing heat treatment temperature (error bars are less than symbols). A line in the inset is drawn as guide to the eyes.
3.4. Nucleation and growth of NPs in glass matrix
demonstrate that the heat treatment heavily influences the growth rate of the NPs leading to an increasing mean diameter, broader size distribution and/or a larger number of NPs (Fig. 2). The absence of NPs in the reference sample (sample A) is confirmed due to a lack of X-ray scattering in the investigated q-vector range. Only heat treatment temperatures above 580 °C lead to a different scattering contrast compared to the glass reference (sample A) and a visible luminescence, which determined during preliminary experiments [19]. Increasing the heat treatment temperature to 610 °C is accompanied by a doubling of the mean diameter from 2.1 ± 0.1 up to 4.0 ± 0.1 nm (Table 1). The full width at half maximum (FWHM) of the size distribution doubles as well (Fig. 2b). Not only the heat treatment temperature changes the NPs size, but also the treatment time. By increasing it from 3 to 24 h, the NPs mean diameter grows from 2.1 ± 0.1 to 3.0 ± 0.1 nm, while the FWHM of their size distribution changes only slightly. Thus, the heat treatment time is a more precise instrument to control the mean size of NPs.
According to the experimental data, we assume the following growth process of CdS NPs in the glass matrix (Fig. 3). Before the heat treatment, each sample is a supersaturated solution of Cd and S ions in glass, which act as solvents. This supersaturated solution exists below glass melting (1300–1400 °C) down to room temperature. Until Tg is reached, the viscosity of glass is extremely high and a sufficient diffusion of ions to form NPs does not take place. At the same time, few and extremely small nuclei can grow at T < Tg. If the viscosity of glass decreases below 1011 Pa∙s (T > Tg), the growth of NPs become possible. The number of NPs remains relatively constant during isothermal heat treatment at 580 °C. The NP is growing due to ion diffusion. Local inhomogeneity in glass may cause minor deviations of the number of NPs. The temperature variation affects the nucleation rate. We suggest the following observations. First, the mean NP size (Dnp) is 2.1 ± 0.1 up to 4.0 ± 0.1 nm for heat treatment temperatures between 580 °C and 610 °C. Second, while the total NPs number is reduced by a factor of three, the CdS relative volume fraction (i.e. phase concentration) raises (inset Fig. 2b) with varying heat treatment temperatures. 4
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Fig. 3. Scheme of nanocomposite synthesis. At room temperature, glass is represented as a dielectric matrix with uniformly distributed ions of Cd and S. Extremely small nuclei can be formed during a first heat treatment around Tg. The CdS NPs are formed during the initial moments of heat treatment using temperatures higher Tg. This temperature leads to NPs growth with mean size from 1 to 10 nm. Further increasing of heat treatment temperature leads to the formation of crystalline NPs with D > 15 nm. The NPs formed in the initial moment then growth linearly in size.
several reasons. First, the amorphous structure of glass appears as an intense diffuse halo in X-ray diffraction patterns and overlaps the diffraction from the NPs. Second, standard laboratory XRD equipment is inefficient for crystalline structure analysis of minor phases at low concentrations due to a very low contrast. However, the low concentration of a semiconductor phase is the essential feature of nanocomposites based on glass. The concentration of the CdS phase is still below 1 wt.% when Cd and S ions, which are distributed in the glass matrix, form CdS. Along with that, we suppose that the NPs possess an amorphous or strongly disordered crystalline structure compared to bulk CdS due to their small size and inevitable interaction with the glass matrix. Thus, the mentioned factors hinder the determination of the crystalline structure of CdS NPs distributed in a glass matrix using conventional XRD laboratory equipment.
The nucleation and growth of NPs is similar to precipitation in a liquid solution [31]. This theory proposed that the particle size (Dnp) is proportional to the diffusion coefficient (D). Further, D is inversely proportional to the viscosity of the medium (η). The viscosity of amorphous materials η is a function of temperature 1/T. Therefore, particle size should be proportional to temperature Dnp ~ T, which was observed in the experiments. The nucleus size and the ratio of nucleation and growth are limited by two factors: the initial ion concentrations and the heat treatment temperature. Below Tg, the growth of NPs due to the diffusion of nuclei or particles is unlikely considering the large glass viscosity. Further investigations in terms of liquid solutions theory will improve the directed synthesis of semiconductor NPs for potential application in optics. Previously we proved that the CdS NPs are uniformly distributed in a glass matrix using FIB-SEM [19]. Within this experiment it was possible to evaluate the diameter of the largest particles, while smaller particles and their size distribution remained unspecified. The same sample (E) was measured using SAXS and WAXS in this work and the bimodal size distribution. Fig. 4 was determined with correlation coefficient χ2 = 231 (Table 1). This fact stresses that the rate of nucleation increases for higher heat treatment temperatures. The heat treatment at 700 °C (sample E) dramatically increases a mean size up to 19.4 ± 0.1 nm for the dominant population, while the total number of NPs is two orders of magnitude smaller compared to other samples. At the same time, the critical size increased up to 3 nm. Thus, the normal growth dominates the nucleation rate for higher heat treatment temperatures. Additionally, the heating rate of the glass matrix may change the equilibrium between nucleation and growth processes. The deviations of the optical properties can be caused by several reasons: quantum mechanical effects, the size distribution and the atomic and crystalline structure of NPs. The crystalline structure of CdS NPs in a glass matrix remains unspecified to our knowledge. This is due to the fact that laboratory XRD methods cannot provide results for
3.5. Crystalline structure of CdS NPs in glass matrix Bulk cadmium sulfide exists in two phases, sphalerite (cubic structure) and wurtzite (hexagonal structure). Disordered crystalline structures of CdS were discovered and attributed to the small (3–9 nm) NPs [32] due to random alternation of close packed hexagonal atomic planes. We have determined the crystalline structure of CdS NPs in glass combining SAXS and WAXS within the same device (Fig. 5). Diffraction peaks (110) and (013) appeared for smaller NPs (D = 4.0 ± 0.1 nm, sample D), but they were too weak in intensity for a proper baseline subtraction. Sample E (700 °C for 23 h) shows outstanding intensity in the diffraction pattern (Fig. 5a). The phase of CdS crystals can be clearly identified for this sample with an exclusive hexagonal crystalline structure (ICSD # 41490, space group P63mc) [33] with cell parameters a = 4.150(2), c = 6.732(3) Å. We assume a tiny number of incorporated Zn and O atoms in the NP crystalline structure due to the very small changes in the interatomic distances compared to bulk CdS. The diffraction pattern at Fig. 5a shows a significant redistribution of 5
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Fig. 4. Scattering intensity (gray dots) with models (χ2 = 231) (a) and number distribution (b) of both populations CdS NPs (sample E). Blue and pink color is attributed to the large and small CdS particles respectively. Error bars are less than symbol size.
CSR size was calculated to 13 ± 1 nm by the broadening of the diffraction peaks, which is in a good agreement with the SAXS data. The size of the CSR is smaller than the mean diameter of NPs since the smaller NPs produce a larger contribution to the broadening of the diffraction peaks. Deep peak profile analysis can not prove a significant difference in peak broadening alongside certain crystallography directions. Typically, this anisotropy is correlated with the size of CSR along the corresponding crystallography directions. Such differences in size can be observed from broadening along a certain family of planes. It has to be mentioned, that there were only few diffraction peaks for a distinct determination of the anisotropy broadening. The flat slope of the linear regression in the Williamson-Hall plot shows a moderate value of micro-strains in the NPs crystalline structure.
intensities, which fails to describe a preferred orientation of the NPs. However, such an orientation is not expected during their nucleation and growth. A temperature gradient and NP sedimentation during the heat treatment were assumed to be negligibly small. Here, a preferred direction of growth rather than a preferred orientation can be suggested. The preferred growth direction takes place along the z-axis of the hexagonal crystalline structure taking into account the large intensity of the (002)-diffraction peak.
3.6. Mismatch of coherent scattering region and actual NP size A preferred growth direction leads to the non-spherical shape of NPs. In case of non-spherical shapes, large and well-ordered nanoparticles should have a shape of extended spheroids or cylinders. The SAXS data does not suggest ellipsoidal or cylindrical shapes, but it must be clear, that the coherent scattering region (CSR) of NPs can differ from their overall shape and size. Highly intense diffraction peaks will only appear from large and well-ordered NPs. If atomic planes in the CdS crystals are practically close-packed along one axis (i.e. z-axis, see Fig. 6), the growth at the edges of the NP (i.e. along x- and y-axes in Fig. 6) may have a weaker ordered crystalline structure. The well-ordered and close-packed crystal direction yields into higher diffraction intensities and this results in a different shape of the CSR and NPs. Using Sherrer's formula [34] and the Williamson-Hall method [35] the
4. Conclusion The formation of the two-phase system (glass-NP) is similar to the process of precipitation from liquid solution. The applied heat treatment of glass with Cd and S ions leads to the nucleation and growth of semiconductor NPs. The correlation between the NP mean size and the heat treatment parameters (temperature, time) was shown here. Thus, the heat treatment time is the tool to control the NP size, while not changing the size distribution. However, the heat treatment temperature can be used effectively to adjust the size distribution. The obtained
Fig. 5. Diffraction pattern (baseline subtracted) (a) and Williamson-Hall plot (b) of CdS NPs (sample E). Red dashed line is 0.95 confidence interval of fit (adjusted R2 = - 0.136). Inset: WAXS patterns of sample E (blue line) before subtracting contribution by diffracted photons by sample A (black line) that is amorphous glass matrix. 6
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Fig. 6. Scheme of the difference between an actual particle size and CSR. Diffraction patterns are induced by large and well-ordered NPs. The Atomic planes in the CdS crystal (pale blue region) are close-packed along the z-axis. At the same time, a growth along the x- and y-axes forms the NP edges, which have a weak-ordered crystalline structures. This fact results in the observed difference between the shape of NP observed by WAXS and SAXS.
results were discussed using precipitation theory for liquid solutions. The oscillations and exciton absorption peak in the interband absorption spectra indicates quantization of the energy states of electrons and holes in NPs with
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