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Abstract
We report the results of a thorough investigation into the initial stages of the photo-thermo-induced (PTI) crystallization process in photo-thermo-refractive glass. The spectral location of the absorption peak characteristic of the surface plasmon resonance in the silver nanoparticles is known to be highly sensitive to the dielectric parameters of the nanoparticle surrounding. We have studied the evolution of the peak location in the course of the PTI crystallization process and shown that the red shift of the peak in the glass is caused by the occurrence, around the silver nanoparticles, of highly-refractive shell of a mixed nature. The blue shift of the peak that can be observed under the reduced speed of the process was shown to be inflicted by the precipitation of sodium fluoride crystals.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
At present, photo-thermo-refractive (PTR) glass is a well-known holographic material with practically no absorption in a wide spectral range (400–2500 nm), which allows one to prepare the highly homogeneous samples with significant aperture. A mechanism for recording holograms in this glass is based on the photo-thermo-induced (PTI) precipitation of nano-crystals in the glass bulk. A brief description of the PTI mechanism is following. First step is irradiation of the glass with UV light into the absorption band of cerium ions (∼ 305 nm). This irradiation lead to the photoionization of cerium ions. The subsequent heat treatment of UV-irradiated PTR glass near the glass transition temperature (Tg) leads to the silver molecular cluster formation which is followed by silver nanoparticle formation. The thermal treatment of these glasses at temperatures above Tg leads to the growth of silver bromide shell on a silver nanoparticle and then to precipitation of sodium fluoride crystals. [1]. The purely phase nature of the gratings and outstanding diffraction efficiency of the elements thus obtained [2–5] provides the extreme usefulness of PTR glass for applications that require the high selectivity and long-term stability of diffractive optical elements. PTR glass is applied mostly as a holographic medium in which the local changes in the refractive index are generated by the precipitation of NaF nanocrystals. Therefore, the current studies into the photo-thermo-induced crystallization process are mostly aimed at clearing the precipitation dynamics of sodium fluoride [6, 7]. However, the overall mechanism of PTI crystallization still has some blind spots. For instance, it is evident that (i) in the course of PTI process, the silver nanoparticles (NP) are formed and (ii) a phase responsible for the refractive index changes is sodium fluoride. However, the nature of processes that occur in a period between the silver NP precipitation and NaF nanocrystal formation remains to be unclear yet.
It is known that spectral location of the surface plasmon resonance (SPR) for silver NPs can be influenced by several reasons. In present case most relevant are: (i) variation (increase) of the silver nanoparticle size during thermal processing of the glass without modification of its shape; (ii) modification of the geometric shape of nanoparticle during thermal processing of the glass and (iii) modification of the refractive index of matrix, surrounding the silver nanoparticle. All these factors can influence significantly onto the dielectric permeability of silver NPs and thus affect the spectral position of the SPR [8, 9]. Thus, as soon as the silver NPs are formed, one acquires an opportunity to estimate the parameter magnitudes for a medium around the NP that correspond to the SPR peak shift observed and, thus, to make conclusions on what occurs at the initial stages of the process. Recent studies [10] of the SPR in PTR glass showed that position of the resonance is highly sensitive to the bromine concentration in the glass composition. moreover it was shown that increasing KBr concentration leads to red shift of the resonance thus proving the pretense of bromine shell. Conducted modeling was considering particles of 15 nm size and above with various shell thickness. However the real size of a particle can be much smaller.
In the given paper, we present the results of investigating the SPR behavior in the course of PTI crystallization process. Present study was conducted at lower temperatures than those implied by conventional heat treatment regimes. In the vicinity of glass transition temperature, the diffusion processes slow down, so we can observe changes in an appropriate time scale. Because our study relied on the analysis of the SPR absorption peak behavior, the resultant conclusions are only applicable to the short range around the particle. Therefore, we can neglect possible diffusion barriers on larger scales that might affect the crystal sizes.
2. Experimental
For a research described in the given paper, we used PTR glass based on sodium alumina silicate system, Na2O-ZnO-Al2O3-SiO2-KBr-NaF, doped with CeO2, Sb2O3, and Ag2O. The glass was synthesized in platinum crucibles at 1500°C in the air atmosphere. A platinum stirrer was used to homogenize the glass melt. After melting, the glass samples were cooled down to 500°C, then annealed at glass transition temperature (Tg = 494°C) for 1 h, and then cooled down to room temperature with a rate of 0.15 K/min. A sample was prepared as a polished 10×10 mm plate 1.5 mm thick. Then glass was exposed to the UV radiation of He-Cd laser with 325 nm wavelength, the exposure being equal to that used for preparing the conventional gratings (1 J/cm2).
Structural studies of the PTR glass were performed by means of transmission electron microscopy (TEM) using Jeol JEM-2100F microscope (accelerating voltage 200 kV, point-to-point resolution 0.19 nm). Specimens for TEM were prepared by conventional thinning technique involving mechanical grinding with subsequent Ar+ ion milling.
Our standard heat treatment regime for developing a grating in a sample includes no prenucleation stage and usually consists of (i) heating the sample for 90 minutes to a temperature slightly above Tg (e.g. 505°C) of the glass and then (ii) exposing at this temperature for 10 hours. Such thermal treatment leads to the refractive index modulation in the first harmonic by 1×10−3, which is far more than enough for the diffraction elements manufacturing. At the same time, this treatment ensures the absence of spontaneous precipitation of crystals in the unexposed areas.
In the given research, we divided this heat treatment schedule into a series of small steps. The first (heating) stage was divided into the 15 min intervals to observe the kinetics of the silver NPs formation. After every 15 min, the sample was extracted from an oven for conducting the spectral measures, whereas temperature in the oven was maintained at the same level. After measuring, the sample was returned into the oven and further heating was continued. The second (exposing) stage of heat treatment was divided into 30 min intervals to observe changes in the location of the SPR.
The spectral measurements were carried out by means of spectrophotometer Lambda 650 (Perkin-Elmer) in the range 200–800 nm with the step of 0.1 nm.
3. Results and discussion
In Fig. 1(a), one can see the evolution of the sample spectrum in the course of the heating process. Until 300°C, no significant changes appear in the visible absorption spectrum. Some processes occurring in this temperature range manifest themselves mostly in the UV. This provides certain variations in the complex exponential tails of the corresponding UV bands that can be observable in the visible. This behavior was already discussed a lot and was assigned to transitions involving the cerium ions together with accepting electrons by antimony. Under further heating the sample, the formation of silver clusters occurs, thus causing an increase in absorption throughout the visible. Finally, as soon as we reach temperature close to Tg, one can see that the silver NPs manifesting themselves in the SPR absorption peak around 400 nm are already formed.
Fig. 1 (a) Evolution of the absorption spectrum of the UV exposed sample of PTR glass for the heat treatment duration up to 90 min and (b) Dynamics of SPR peak location depending on the heat treatment duration for the parent PTR glass and glass with lowest possible concentration of fluorine.
To specify the exact location of the resonance peak, we performed the deconvolution of the spectrum using the parameters of the absorption bands discussed earlier for this type of glass [11]. As mentioned before, we can distinguish three bands at 304, 376, and around 415 nm that are assumed to be related to (i) the cerium absorption, (ii) the intrinsic hole centers created under the UV exposure, and (iii) the silver nanoparticles, respectively. When processing the spectra of samples under study recorded in the course of heat treatment, the same parameter magnitudes for all bands except the central wavelength of the silver-related band were used successfully. The accurate deconvolutions of all the spectra were obtained, thus confirming the reliability of the band parameter magnitudes fitted. Example of the spectrum deconvolution is presented on the Fig. 2. As to the silver plasmon resonance band, slow variations in the band area were assumed to be due to small inhomogeneities in the silver distribution throughout the glass bulk. It was noticed also that different regions of the glass can be characterized by slightly different SPR peak locations due to variations in the content of components responsible for the bromide shell growth and NaF crystal precipitation. However, a total error in the peak location across the glass sample bulk did not exceed 2 nm.
When starting the procedure of heat treating the sample, one can observe significant red shift of the SPR peak location. The SPR absorption band parameters remain intact in the course of entire heat treatment process, which is why we can conclude that the size of the particles is not changed. Therefore, this red shift can be explained only by the occurrence of highly refractive shell on the silver NP.
According to the modern idea of PTI crystallization process, the silver NP formation is followed by the growth of silver bromide shell with relatively high refractive index (∼ 2.25) compared to the glass matrix (1.498). Right after a moment when the peak location reaches 460 nm, it starts to shift backward to the shorter wavelengths. This blue shift continues to be observed till a moment when the SPR peak location reaches 450 nm and further increase in the treatment duration ceases affecting it anymore. It is worth noting that the final location of the peak is similar to that for the conventional PTR glass after the standard heat treatment procedure. We assume that the blue shift indicates the precipitation of NaF crystals that reduce the refractive index of the core-shell system surrounding. Stabilization of the peak location can be explained with an assumption that, at this stage of the process, NaF crystals already act as hosts for the core-shell structures. To confirm this assumption, we synthesized glass with the lowest possible concentration of fluorine (fluorine free glass Fig. 1(b)) and subjected it to the same heat treatment procedure. As seen, this glass demonstrates the red shift of the SPR resonance peak only with no subsequent blue shift, thus confirming our idea concerning the NaF precipitation. Hence, we can be sure that the blue shift is indeed inflicted by a decrease in the refractive index of the core-shell surrounding.
4. Computational
Relying on Lorenz-Mie scattering theory [12] we calculated the extinction of light by small spherical nanoparticles in a non-absorbing medium with the refractive index of nm = 1.498 equal to that of the PTR glass. The extinction of a multilayered sphere was computed by means of implementing Yang’s recursive algorithm implementation [13,14] (the algorithm is reduced to the standard Lorenz-Mie theory if a particle with no shell is considered). In the calculations, the dielectric constants of bulk silver as obtained by Johnson and Christy [15] were used. It is well known that if the particle sizes are comparable with or smaller than the mean free path l of electrons in the macroscopic material (2R ≤ l), the bulk dielectric constant ε(ω) = ε1 + iε2 should be modified by additional contribution coming from the electron scattering off the particle surface. In accordance with Sommerfeld’s theory, the bulk mean-free path value in silver equals l = vFγ−1 = vFτ ∼ 50 nm at room temperature, where vF = 1.39 × 106 ms−1 is the Fermi velocity and τ(ω = 0) = 37 fs is the relaxation time [16] of conduction electrons. Within the classical approach, the correction can be accounted by reducing the bulk damping constant γ with the extra electron-surface scattering term (so-called free path effect [17,18]) that, in terms of Matthiessen’s rule for spherical particles, is given by expression as follows:
Here R is the particle radius and A is the phenomenological constant of the order of unity that accounts for the details of the electron scattering process [19]. Thus, the size correction of the literature ε(ω) values was performed, in the framework of Drude model, by separating them into two terms, ε = εbound + εfree, where the first term is responsible for the interband electron transition (bound-electron term) and the second one represents the intraband electron transitions (free-electron term). Then, the bulk damping constant γbulk was replaced with the corrected one, γ(R). In this case, the contribution of free electrons takes a form as follows: where ωp is the plasma frequency, ħωp = 8.9 eV [20]. And the bound-electron term εbound is independent of the particle diameter and therefore remains unchanged. Previously, the experimental results have shown that the absorption halfwidth follows 1/R rule [21–23], which allows for estimating approximately the mean particle radius as R = vF/Γ [24], where Γ is the halfwidth in the angular frequency units (rad s−1). The observed halfwidth of the plasmon band at 415 nm equal to 100 nm corresponds to the calculated average particle size 2R of about 2.5 nm. According to our simulations, the SPR location should experience a slight red shift from 400 to 407 nm for nano-spheres with sizes in the 2 < 2R < 20 nm range. Taking into account that the next stage in our model of PTI crystallization is the formation of bromide shell on the nanoparticle and that the calculated peak resonance is far from 407 nm, one can assume that some shell should already be formed in glass heated to Tg (see Fig. 1(a)).Our simulation assuming the silver bromide shell on the NPs of 2.5 nm in size shows that several initial steps in the red shift cannot be achieved with this kind of crystal. A contrast in the refractive index between the silver bromide and the glass matrix is too high: to simulate the observable SPR location, we would be forced to apply a shell 0.05 nm thick. This is obviously impossible because the unit cell size of AgBr crystal is as great as 0.57 nm. Thus, we should assume that the refractive index of the shell is not equal to (namely, less than) that of AgBr crystal. It was already mentioned in literature on PTR glass [26] that the precipitation of other bromide crystal is also possible. The refractive index of NaBr is much closer to the glass host; thus, the required shell thickness for the observable red shift turns out to be similar to the realistic magnitude. According to our analysis, the SPR peak location at 415 nm can correspond to the sodium bromide shell of 2.42 nm thickness. On the other hand, when assuming the pure NaBr shell, it is impossible to reproduce the shift of SPR to 460 nm. The maximum shift of the SPR peak location obtainable with this type of shell is that to 417 nm, which is due to the too low contrast between the refractive indices of NaBr (1.65) and glass matrix. Considering these two facts, we assume that the shell on the silver NP in the PTR glass can consist of the NaBr-AgBr solid solution. Another possibility: the shell can be not continuous, i. e., can consist of a mixture of glass host and a bromide crystal. For both cases, the refractive index of the mixed shell should be in the 1.68–2.25 range, which will provide the reasonable magnitudes of the shell thickness.
Several possible mechanisms responsible for the observable resonance peak shifts can be assumed. However, if we consider the TEM image of the grating sample (Fig. 3(a)) we can see that the system of NaF crystal – bromide shell and silver NP fits in a sphere of approximately 10 nm diameter. In addition, it should be noted that the NaF crystal already became, by this moment, a host for the core-shell system. This fact allows us to assume that the NaF layer thickness in the system should be sufficient to provide the blue shift that is insensitive to further thickness increase. According to our simulation for the 3-layer system of silver NP core with the shell of bromides and outer shell of NaF, the above condition can be fulfilled only if the thickness of NaF is at least 3.17 nm (Fig. 3(b)). Thus, the bromide shell thickness cannot exceed 0.57 nm, which is in a good correlation with the lattice constants of crystals mentioned (0.597 nm for AgBr and 0.578 nm for NaBr) [26]. Therefore, we will consider only two situations, the first one being the shell of mixed NaBr and AgBr crystal. The second situation (which, in our opinion, is the more relevant) corresponds to a case in which the layer of 0.57 nm thick is formed by a mixed system of AgBr and glass matrix. In other words, the second situation assumes that the highly refractive shell of AgBr grows slowly rather than instantly filling a space around a NP only gradually and, thus, developing a thin layer of a complex nature. In both cases, we assume the constant layer thickness and growing refractive index of the layer due to an increase in the AgBr concentration either in the solid solution or in the crystal-glass mixture.
Fig. 3 a) TEM image of a grating recorded on a conventional PTR glass and (b) Model for the 3-layer system NP – highly refractive shell – NaF according to simulations taking into account the system size according to the TEM image photograph. Estimated thickness of the structures is denoted in nm.
According to the above first approach, we consider three-layer system of mixed AgBr-NaBr crystal with the AgBr concentration increasing in the course of heat treatment. Following Varotsos [27], the refractive index nx of the compound of two isomorphic crystals can be calculated based on the Lorentz-Lorenz equation given by the sum of the electronic and ionic polarizability terms:
Knowing the refractive index dispersion n(λ) of the pure AgBr [28] and pure NaBr [29] and also the corresponding lattice parameters [28] we estimated the nx values for the molar compositions x given by AgxNa1−xBr. For the given frequency range, the ionic polarizability was neglected. According to Vegard’s law, the lattice parameter of the mixed crystal can be expressed, assuming that both pure and mixed crystals have the face-centered cubic NaCl-like structure, as ax = xaAgBr +(1− x)aNaBr. As seen from the dashed line in Fig. 4(a), the composition dependence of the refractive index nx obtained with Eq. 3 slightly deviates from linear. As seen, the mole fraction interval of interest for the observable red shift lies in the 0.018–0.887 range. Thus, if we accept this model, we should admit that, in the very beginning of the process, the pure NaBr shell is formed.
Fig. 4 (a) Calculated refractive index of a layer depending on the AgBr mole fraction for the mixed crystal AgxNa1−xBr and (b) for the mixed layer of AgBr crystal and glass matrix. The solid and dashed lines represent the n values for 416 and 460 nm wavelengths, respectively. The ranges of n values for wavelengths in between 416 and 460 nm are represented by the shaded areas. The corresponding SPR peak locations (in nm) are shown by circles.
The second above approach implies that a thin layer of the glass host 0.57 nm thick is successively filled up, in the course of the heat treatment process, with AgBr inclusions, thus increasing the effective refractive index of such layer. In this case, Bruggeman’s two-component effective model [30] was used to calculate this effective refractive index. In this case, the concentration of AgBr is assumed to start from 25% and grow up to 89% of the layer volume (Fig. 4(b)). Thus, even after the heat treatment duration of 120 min, filling the shell with AgBr seems to be not total. Accepting this model leads to conclusions that (i) the precipitation of AgBr is the most rapid in the beginning of PTI crystallization process and (ii) there is a probability that, in the course of the NP formation, the silver bromide can already be present nearby
If we plot the concentration of AgBr in the shell as a function of the heat treatment duration for both above cases, the plots behave monotonically (Fig. 5) and can be approximated with sigmoidal Weibull function with zero error.
Fig. 5 Evolution of Ag mole fraction and AgBr filling factor in the course of the heat treatment process. The corresponding SPR peak positions are denoted in nm.
5. Summary
A thorough heat treatment of the UV-exposed sample of PTR glass was performed. This provided an opportunity to observe the effects of consistent red and blue shifts of the SPR absorption peak location, which, in turn, allowed for revealing some unique details of behavior of the NP surrounding in the course of PTI crystallization process. We conducted the complex numerical analysis of SPR peak location in the 3-layer system consisting of silver NP, the bromide shell, and sodium fluoride shell. As follows from our estimates that took into account the actual (finite) dimensions of the system illustrated by the TEM image, the thickness of high refractive index shell should not exceed 0.5–0.6 nm, which is in a good correlation with the unit cell size of the bromide crystals. Just such thickness allows us to reproduce, with numerical modeling, the SPR peak locations of 460 nm before the NaF precipitation and 450 nm after its precipitation including the fact that, under a further increase in the heat treatment duration, the latter peak location remains intact in spite of a further increase in the volume fraction of NaF. Further investigations revealed that, under the fixed shell size, the only way to reproduce shifting the SPR peak is to change the refractive index of such shell. In terms of this assumption, we considered two possible ways explaining this shell behavior. The first way is to assume that the shell has a mixed nature, i. e., is the solid solution of NaBr and AgBr with gradually increasing fraction of AgBr. The second way is to assume that the shell grows gradually at the expense of filling a thin layer of glass around NP by isolated cells of AgBr. So, strictly speaking, such a shell having practically a fixed thickness is assumed to be a mixture of nano-size fragments of glass and AgBr crystal (rather than a homogeneous material) whose effective refractive index grows gradually with an increase in the volume fraction of AgBr. In addition, it was shown that the initial location of SPR peak cannot be explained by the formation of pure AgBr shell or by particular NP size as well as the final peak location cannot be explained by the formation of NaBr shell alone. It was shown also that the observed blue shift of the SPR peak at the later stage of PTI crystallization is due to the NaF precipitation.
Funding
Ministry of Education and Science of Russian Federation (Project 16.1651.2017/4.6)
Acknowledgments
The authors are grateful to Pichugin I.S. for the glass synthesis. TEM characterizations were performed using equipment of the Federal Joint Research Center “Material science and characterization in advanced technology” supported by the Ministry of Education and Science of the Russian Federation (id RFMEFI62117X0018).
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