Introduction

The synthesis of glass ceramics is commonly performed by the crystallization of amorphous bulk samples [1,2,3]. In order to achieve the desired properties, the microstructure has to be tuned with different additives [4, 5]. These additives enable a drastic change in the crystallization behavior, so that the crystallization mechanism can be adjusted [6,7,8,9]. Well-known examples of such additives are ZrO2 and TiO2, which are used as nucleation agents, e.g., in Li2O–Al2O3–SiO2 [10,11,12,13,14,15] or MgO–Al2O3–SiO2 glasses [16,17,18]. This means that without ZrO2 and TiO2, the respective glasses tend to undergo surface crystallization, i.e., during annealing, the crystals grow from the glass surface into the volume. In order to achieve an almost transparent and crack-free material with good mechanical properties, a huge number of tiny crystals within the glass body is needed [5]. However, both mechanisms, surface and volume crystallization, may occur simultaneously [19, 20].

In order to study the crystallization behavior, in many cases, glass is heat-treated and the microstructure is studied by microscopic techniques [21]. If the temperatures during heat treatment are correctly chosen, then this way clearly shows the crystallization mechanism. However, the preparation of numerous samples for electron microscopy and the microscopic measurements themselves are time-consuming and expensive, especially if transmission electron microscopy is required. Recently, there have also been attempts to investigate the crystallization behavior in glasses, supercooled liquids, or glass ceramics by means of computational methods [22, 23]. Another way to predict the crystallization mechanism without microscopic techniques is the use of thermal analysis techniques, where different grain size fractions of the same glass are heated up in a differential scanning calorimeter (DSC) using various heating rates [24]. It is shown in the literature that these techniques are suitable tools to give information on the crystallization mechanism of different glasses [25, 26] as well as on crystallization kinetics, such as nucleation or crystal growth rate [27,28,29,30,31]. However, the methods based on thermal analyses are often used for model glass systems such as Li2O–SiO2 glasses, where the crystallization mechanism has been investigated in detail [32,33,34,35]. If glass ceramics show a significant extend of concurrent volume and surface crystallization, the results from DSC method are not distinct [36].

The DSC evaluation methods differ remarkably in their fundamental assumptions and it is often not clear how the respective method is used correctly, which then leads to contradictory or misleading results [37]. In principle, there is a controversy about the reliability of the statements deduced from the different evaluation methods. Several critical reviews deal with recommendations for a proper and reliable evaluation of kinetic parameters from DSC data (e.g., [37,38,39,40]). In the cases where more than one phase is crystallized or where glass systems show concurrent surface and volume crystallization, the probability is fairly high that these DSC methods will fail in predicting the prevailing crystallization mechanism. Therefore, the aim of this study is the search for a generally applicable method to determine the occurring crystallization mechanism. This is why this work describes such glasses, whose crystallization behavior differs strongly, which is why their effect on the DSC signal is not clarified. The glasses are all based on the system BaO–SrO–ZnO–SiO2 and have very similar compositions which are varied by small quantities of additives in order to control the crystallization mechanism. Therefore, four pairs were synthesized. Both glasses of each pair have a similar composition but one crystallizes solely from the surface and the other shows bulk crystallization. The four glasses, which show volume crystallization, also have a different nucleation behavior, where it is not clear what the DSC method is able to predict:

  1. (a)

    Volume crystallization with a very low nucleation rate,

  2. (b)

    Volume crystallization with a high nucleation rate but crystallization of more than one phase,

  3. (c)

    Precipitation of metallic nanoparticles in the volume followed by surface crystallization,

  4. (d)

    Precipitation of metallic nanoparticles in the volume followed by volume crystallization.

The crystallization mechanisms of those glasses have already been described in detail in Refs. [41,42,43,44,45]. The glass compositions are given in Table 1, and a summary showing the respective crystallization mechanisms related to the additives can be found in Table 2. Results from microscopic investigations are also compared with the DSC results. In the following, one method was detected that reliably identifies the crystallization mechanism. This method was applied to two more glasses which have not been studied so far.

Table 1 Chemical compositions of the glasses in units of (mol%)
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Table 2 Summary of the crystallization mechanisms within the different glasses
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Materials and methods

Synthesis and characterization of glasses

Glasses were melted in an induction furnace at temperatures between 1300 and 1450 °C. BaCO3, SrCO3, ZnO, SiO2, SnO2, AgNO3, Sb2O3, WO3, RuCl3, Au, and PtCl4 were used as raw materials for glass synthesis. After melting of the raw materials, the melts were homogenized using a Pt stirrer for 1.5 to 2.0 h. Afterward, the glasses were cast in a preheated steel mold and both, the glass and the mold, were transferred into a cooling furnace preheated to a temperature slightly above the glass transition temperature Tg of the respective glass. Then, the furnace was switched off in order to allow the glass to cool slowly to room temperature. In the case of the Au-containing glasses, the respective quantity of metallic gold was dissolved in warm aqua regia. This solution was dropwise added to the batch. Then the batch was again carefully homogenized, and the glass was melted as mentioned above.

It is known from previous studies that a glass, which contains only BaO, SrO, ZnO, and SiO2 shows solely surface crystallization. Such a glass was also melted for this study and is denoted as A-S (S for surface crystallization) [46]. If the composition A-S is slightly modified by the addition of SnO2, then volume crystallization starts [44]. The Sn-containing glass is hence denoted as A-V (V for volume crystallization). The same nomenclature was used for the other pairs, where WO3 (glasses B-S and B-V), Au (glasses C-S and C-V), and Ag (glasses D-S and D-V) were used to modify the crystallization mechanism.

The crystallization behavior was studied at first with electron microscopy. Therefore, bulk samples were heat-treated and afterward cross sections were mechanically polished. The polished samples were then carbon-coated, and the microstructure was analyzed with a Jeol JSM 6510 LV scanning electron microscope.

DSC measurements were performed with a Linseis DSC Pt1600 and Al2O3 crucibles. Powders with different grain size fractions (25–71, 71–100, 100–250, 250–315, 315–400, and 400–500 µm) were obtained by crushing bulk glass with a steel mortar and then sieving to the respective size. The powders with different grain sizes were all heated with 10 K/min. Furthermore, measurements with different heating rates α (8, 10, 12, and 14 K min−1) were performed using that powder with the largest grain size fraction of 400–500 µm. All measurements were performed with 60 ± 0.3 mg of glass.

Evaluation of the DSC measurements

The activation energy for crystallization may be determined using different equations. The most common equations are the Kissinger [47] (Eq. (1)) and the Ozawa [48] equations, which are used here. These equations are based on the shift of the crystallization peak temperature to higher values as well as on the increasing crystallization peak area with increasing heating rate. Both equations can only be applied if the glass predominantly crystallizes from the surface or if the condition n = m (n—number which represents the nucleation and crystal growth mechanism, m—dimensionality of crystal growth) is fulfilled, i.e., crystallization takes place from a fixed number of nuclei at different heating rates and hence the nucleation rate is insignificant.

$${ \ln }\left( {\frac{\alpha }{{T_{\text{p}}^{2} }}} \right) = \frac{{ - E_{\text{a}} }}{{RT_{\text{p}} }} + {\text{const,}}$$
(1)

Ea corresponds to the activation energy of the overall crystallization process, Tp is the maximum crystallization peak temperature in units of (K), α is the heating rate in units of (K min−1), and R is the gas constant.

The plot \({ \ln }\left( {\frac{\alpha }{{T_{\text{p}}^{2} }}} \right)\) versus \(\frac{1000}{{T_{\text{p}} }}\) [Eq. (1)] yields a straight line with a slope of \(\frac{{ - E_{\text{a}} }}{R}\).

When the number of nuclei changes during the DSC measurement, the modified Kissinger equation proposed by Matusita and Sakka [49] should be used to calculate the activation energy:

$${ \ln }\left( {\frac{{\alpha^{\text{n}} }}{{T_{\text{p}}^{2} }}} \right) = \frac{{ - mE_{\text{a}} }}{{RT_{\text{p}} }} + {\text{const}} .$$
(2)

The plot \({ \ln }\left( {\frac{{\alpha^{\text{n}} }}{{T_{\text{p}}^{2} }}} \right)\) versus \(\frac{1000}{{T_{\text{p}} }}\) [Eq. (2)] yield a straight line with a slope of \(\frac{{ - mE_{\text{a}} }}{R}\).

From DSC analyses with different heating rates, Avrami parameters were determined as schematically illustrated in Fig. 1. In Fig. 1a, the crystallization peaks of one and the same sample are shown as a function of the heating rate. From each peak, the crystallization degree x has to be determined. For this purpose, the total area under the peak A0 and the area AT have to be determined. AT is the area under the peak up to the temperature T (see Fig. 1b). The ratio AT/A0 is the crystallization degree x of the sample at the temperature T, which is plotted against the temperature in Fig. 1c. The Avrami parameter, which represents the nucleation and growth mechanism of the glass, can be calculated according to Eq. (3) proposed by Ozawa [50]:

$$- n = \left| {\left. {\frac{{{\text{d}}\left[ {\ln \left( { - \ln \left( {1 - x} \right)} \right)} \right]}}{{{\text{d}}\left( {{ \ln }\alpha } \right)}}} \right|_{\text{T}} } \right..$$
(3)
Fig. 1
figure 1

Determination of the Avrami parameter. a Baseline-corrected DSC measurements with different heating rates showing solely the crystallization peak. b Crystallization peak with its total area A0 and the area of the peak up to a certain temperature T denoted as AT. c The crystallization degree x = A0/AT as a function of temperature shown for different heating rates. d Logarithmic representation of the crystallization degree x and the heating rate α in a way that the Avrami parameter is the negative slope of the displayed linear regressions

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In order to determine the Avrami parameter n, a regression analysis of the plot ln(− ln(1 − x)) versus lnα is performed and the slope of the regression line corresponds to − n (see Fig. 1d). While a value close to 1 indicates surface crystallization, in the case of the preferred volume crystallization, a value of 4 is obtained. In Ref. [51], the values n and m are summarized for different crystallization mechanisms.

In the literature, the dimensionality of crystal growth m is often determined by a combination of the Marseglia, the Ozawa, and the modified Kissinger equation. The Marseglia equation [52] is also based on the shift of the crystallization peak with varying heating rate and is used to determine the ratio Ea/n:

$${ \ln }\left( {\frac{\alpha }{{T_{\text{p}} }}} \right) = - \left( {\frac{{E_{\text{a}} }}{nRT}} \right).$$
(4)

According to a DSC method proposed by Ray et al. [24], the favored crystallization mechanism in a glass can be determined by plotting the height of the crystallization peak as a function of the particle size. If surface crystallization is the dominant crystallization mechanism, the peak height decreases with increasing particle size. An increase in the peak height is observed in the case of volume crystallization. The height of the crystallization peak is proportional to the total number of nuclei, i.e., surface and volume nuclei, in the sample. Hence, if volume crystallization is favored while surface crystallization is negligible, the peak height should increase with higher particle size. In the opposite case, i.e., predominant surface crystallization, the effective surface area of the particles and hence the maximum possible number of surface nuclei decrease with higher particle size, for which reason the peak height should decrease [24]. Moreover, in the latter case, only small variations in the crystallization peak temperature as a function of the particle size should be obtained, whereas a strong dependency should occur if surface crystallization is predominant [51, 53].

The comparison of the crystallization peak temperatures of glass as well as pre-nucleated samples (powder with 400–500 µm grain size) was used as complementary approach to determine the predominant crystallization mechanism. This means that at first the glass powder was pre-nucleated in a muffle furnace at a certain temperature, where nucleation is expected (see below), and afterward, a DSC measurement was performed. Therefore, the following nucleation treatments were applied: 690 °C for 10 h (A-S, A-V), 670 °C for 20 h (B-S, B-V, and D-S), 685 °C for 100 h (C-S, C-V) as well as 715 °C for 20 h (D-V). DSC measurements were performed at a rate of 10 K min−1. The chosen temperatures are slightly above the glass transition temperatures and below the crystallization temperatures of the respective glasses and hence in a temperature range, where nucleation is expected.

Results

In order to obtain accurate statements about the real crystallization mechanism, the DSC results are correlated with the microstructure of heat-treated samples. In Fig. 2, SEM micrographs of the samples after different heat treatments are presented. In the first row, the microstructures of samples A-S and A-V are compared. While a heat treatment of sample A-S at 790 °C for 1.5 h leads to sole surface crystallization, in sample A-V also volume crystals are observed. In sample A-S, fine elongated Ba1−xSrxZn2Si2O7 crystals are found at the surface forming ray-like domains. However, in the case of sample A-V, some elongated Ba1−xSrxZn2Si2O7 crystals are detected in the volume after a nucleation step at 710 °C for 20 h followed by a crystal growth step at 770 °C for 5 h. A longer heat treatment at the nucleation temperature 770 °C for 100 h results in a higher number of crystals, but the portion of residual glassy matrix is still very high. In both samples, cracks running perpendicular to the longitudinal axis of the crystals are observed. These cracks are formed during cooling the samples and are caused by a strongly anisotropic thermal expansion behavior and a mismatch in the thermal expansion between the crystal phase and the glass.

Fig. 2
figure 2

SEM micrographs of different glass compositions after different heat treatments. The samples on the left show surface crystallization. The crystals grow from the bottom to the top of each micrograph. The middle and the right column show volume effects of the respective compositions. Except for the sample C-V heat-treated at 650 °C for 50 h, SEM micrographs of cross sections are presented. In the case of the as mentioned exception, a TEM micrograph is shown

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The microstructure of sample B-S (first micrograph in the second row in Fig. 2) is very similar to that of sample A-S. Here, also fine elongated Ba1−xSrxZn2Si2O7 crystals are grown from the surface. An increase of the WO3 concentration from 3 to 4 mol% (sample B-V) leads to the precipitation of a high number of small dendritic Ba1−xSrxWO4 crystals if a two-step heat treatment at 670 °C for 10 h and 750 °C for 5 h is performed. A longer nucleation time of 100 h results in a huge number of tiny Ba1−xSrxWO4 crystals. Moreover, a low number of Ba1−xSrxZn2Si2O7 crystals can be observed in the volume. In contrast to the other samples, the heat-treated B-V samples are crack-free.

A heat treatment of sample C-S (contains additionally 0.01 mol% Au) at 710 °C for 200 h leads to a surface crystallized layer with a smaller thickness and less microcracks compared with sample B-S. If 0.01 mol% Au and 0.5 mol% Sb2O3 are combined (sample C-V), a thermal treatment at 650 °C for 50 h induces the precipitation of Au particles in the volume. Despite this volume effect, after heat treatment at 675 °C for 10 h and 760 °C for 5 h, only a surface crystallized layer is detected, i.e., bulk crystallization of Ba1−xSrxZn2Si2O7 does not occur.

The microstructure of sample D-S shows strong similarities to that of sample B-S. In comparison to the gold-doped glasses (C-S and C-V), a nucleation treatment of sample D-V leads to the precipitation of numerous small Ag-particles in the volume. Moreover, 30–40-µm-large Ba1−xSrxZn2Si2O7 crystals are also observed in the sample volume. If the time for crystal growth is prolonged to 5 h, the volume is completely covered by Ba1−xSrxZn2Si2O7 crystals, which contain microcracks.

It should be mentioned that the results in Fig. 2 show only selected micrographs, which should illustrate the differences in the crystallization behavior. All those systems were studied in detail in Refs. [41, 42, 44,45,46]. In Fig. 3, the results of the Avrami analyses are illustrated. The left column of Fig. 3 shows the DSC profiles of the studied glasses measured using different heating rates. In all samples, an increasing heating rate leads to a shift of the crystallization peak to higher temperatures. Furthermore, the peak heights and areas also increase with increasing heating rates. The comparison of the samples A-S and A-V shows that the addition of SnO2 results in a shift of the crystallization peak to notably higher temperatures. In the case of the sample B-S, the crystallization peak is composed of a small shoulder and a strong peak which gets more pronounced with increasing heating rates. By contrast, in the case of sample B-V, i.e., the glass with 4 mol% WO3, the two main crystallization peaks are more separated. However, the first peak consists of three overlapping peaks if a DSC measurement using a heating rate of 8 K min−1 is performed. These three peaks overlap much more in the case of higher heating rates. While the second main peak is very broad for the lowest heating rate, it gets sharper with increasing heating rate. The comparison of the samples C-S and C-V shows that the crystallization starts at almost the same temperature and that the addition of Sb2O3 (sample C-V) leads to sharper crystallization peaks. Sharper DSC peaks are also observed in the case of the higher Ag concentration (sample D-V). When this concentration is increased, the crystallization starts at remarkably lower temperatures. The middle column of Fig. 3 presents the crystallization degree as a function of the temperature, whereas the respective temperature range used for the determination of the Avrami parameter is highlighted by a grayish rectangle. With the exception of sample B-V, the crystallization degree is described by the typical S-curve. However, in the case of the sample B-V, a double S-curve is obtained due to the two broad crystallization peaks. Here, the “first” S-curve, i.e., the part at lower temperature, is used for the analyses. While the temperature ranges in which the calculation of the Avrami parameter was performed are similar for the samples A-S, C-S, C-V, and D-S, in the case of the samples B-S and D-V, this range is shifted to lower temperatures. Only in the case of sample A-V, the temperature range is shifted to higher values. The right column of Fig. 3 shows the Avrami parameters calculated for those temperatures highlighted by the grayish rectangles. Generally, the Avrami parameters decrease with increasing temperature whereas the effect differs from sample to sample. The minimum, mean, and maximum Avrami parameters of the respective glasses are summarized in Table 3. Most glasses show Avrami parameters between 1 and 3. Only sample D-V has a mean Avrami parameter of 3.9. Moreover, it is visible that the Avrami parameter is not notably affected by slight changes in the chemical composition of the glasses, i.e., the addition of 2 mol% SnO2 (samples A-S and A-V) or 0.5 mol% Sb2O3 (samples C-S and C-V). In these cases, the determined values are the same within the limits of error. An increase of the WO3 concentration (sample B-V) leads only to slightly higher Avrami parameters in comparison with sample B-S. Here, it should be mentioned that the Avrami parameter is slightly affected by the grain size. The Avrami parameter of B-V powder with a grain size 25–71 µm is marginally higher than that of powder with a grain size between 400 and 500 µm. By contrast, a remarkable difference in the Avrami parameters is obtained for the samples D-S and D-V. While the first sample shows a mean value of 2.3, the latter one possesses a notably higher value of 3.9.

Fig. 3
figure 3

Determination of the Avrami parameter using the DSC method and powder with a grain size fraction of 400–500 µm (heating rates: 8, 10, 12, and 14 K min−1). The left column shows the exothermal crystallization peaks from DSC measurements of eight different glass compositions. The middle column displays the crystallization degree x as a function of the temperature. The gray rectangles mark the temperature range in which the Avrami parameters were determined. These parameters are shown in the right column, also as a function of the temperature

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Table 3 Avrami parameters of the glasses
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According to the method proposed by Ray et al. [24], DSC measurements with different grain size fractions and a heating rate of 10 K min−1 were performed. In the left panel of Fig. 4, the DSC profiles of the different samples are compared in the temperature range from 820 to 950 °C. It becomes apparent that the crystallization peak is shifted to higher temperatures with increasing grain size. Furthermore, the exothermic peaks become broader and less intense if larger grain sizes are used. In the case of sample B-V, some additional effects can be observed. In the DSC profile recorded from the grain size fraction 25–71 µm, a strong crystallization peak as well as a small shoulder at a slightly higher temperature are visible. With larger grain size, the shoulder becomes more intense. A further increase of the grain size to 100–250 µm leads to the occurrence of a third crystallization peak directly next to the already observed ones and a fourth peak at about 890 °C. These peaks become more pronounced with larger grain sizes. On closer inspection of the DSC profiles obtained from B-S samples with grain sizes larger than 100 µm, also a second crystallization peak occurs at higher temperature which becomes more intense with increasing grain size. The effect of the different additives on the crystallization onset has already been explained for the left column of Fig. 3. The upper right panel of Fig. 4 shows the shift of the crystallization peak temperature as a function of the particle size. Here, it is visible that the peak shift is differently pronounced in the respective glasses. While for example glass A-S shows a shift of about 33 K, the crystallization peak temperature of sample B-V differs by only 3 K. The peak shift increases in the following order: B-V, B-S, D-V, A-V, D-S, C-V, C-S, and A-S. The lower right panel of Fig. 4 illustrates the height of the crystallization peak as a function of the particle size. For a better comparison of the different glasses, the peaks are normalized to the peak height of the sample with a grain size of 25–71 µm. The normalized peak height decreases with increasing particle size with the exception of sample A-V. Here, at the beginning a slight increase in the peak height occurs followed by a remarkable decrease. The effect of the particle size on the peak height is most pronounced in the samples B-S and B-V.

Fig. 4
figure 4

DSC measurements with different grain size fractions applying a heating rate of 10 K min−1. The left panel shows the original DSC measurements in a temperature range from 820 to 950 °C. The upper right panel shows the shift of the peak temperature with increasing particle size. The lower right panel displays the heights of the crystallization peaks as a function of the grain size. The peaks are normalized to the height of the peak of the sample with a grain size of 25–71 µm. All samples were measured with the same fractions except for sample D-S, where two fractions 71–160 and 160–250 µm were used instead of 71–100 and 100–250 µm

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Table 4 shows the activation energies determined from the DSC measurements. With the exception of sample D-V, the activation energies were calculated using the Kissinger equation. In the case of sample D-V, the modified Kissinger equation with n = 3.92 and m = 3 was used. Table 4 shows that the activation energies are all in the same range except for sample C-V which possesses a remarkably higher value. However, the activation energies of the samples A-V and B-V are somewhat higher. A comparison between values obtained from the Kissinger and the modified Kissinger equation proves to be difficult.

Table 4 Activation energies Ea determined from the Kissinger or modified Kissinger equation
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In Fig. 5, the DSC profiles of the non-nucleated as well as previously nucleated samples are shown. It becomes apparent that the crystallization peak temperatures are still the same after nucleation treatments of the samples A-S, B-S, C-S, and D-S. On the contrary, in the case of the other glasses a remarkable shift of the crystallization peak temperatures is considered (e.g., sample D-V with a shift of 34 K). With exception of sample C-V, crystallization of nucleated samples starts at lower temperatures.

Fig. 5
figure 5

DSC measurements of non-nucleated samples as well as previously nucleated ones (grain size fraction 400–500 µm, 10 K min−1). The following nucleation treatments were applied: 690 °C for 10 h (A-S, A-V), 670 °C for 20 h (B-S, B-V, and D-S), 685 °C for 100 h (C-S, C-V) as well as 715 °C for 20 h (D-V)

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Discussion

Thermal analysis techniques may be useful and fast tools for the determination of the crystallization kinetics as well as for the indication of the predominant crystallization mechanism. Hence, besides heat treatments followed by subsequent sample preparation and microscopic analyses, the DSC method should provide a good opportunity to screen different additives regarding their applicability as nucleating agent. In the literature, the DSC technique was intensively applied in the case of model glass systems such as lithium silicate and soda–lime–silica glasses [24, 32,33,34]. Especially, in the case of lithium silicate glasses, this tool was sensitive enough to determine the preferred crystallization mechanism if the glass was doped with minor amounts of platinum or if the storage conditions of the glasses prior to the DSC measurement were changed [33]. In this study, the glass compositions are very similar and only minor quantities of the additives were used to control the crystallization mechanism. Hence, the question arose if the thermal analysis techniques are sensitive enough to detect the volume effects in BaO–SrO–ZnO–SiO2 glasses. By means of the SEM analyses, it becomes apparent that the addition of SnO2 (sample A-V) results in a precipitation of volume crystals, however, only with a low number density. Regarding the results of the DSC analyses, the Avrami parameters of the base glass without any additive (sample A-S) and the SnO2-doped sample A-V are almost identical and the activation energies are also in a similar range. Basically, a mean Avrami parameter of 2.1 is an indication for a combination of both, surface and volume crystallization, but surface crystallization is the predominant crystallization mechanism in both glasses A-S and A-V. In the case of sample A-S, this indication is valid, whereas in the case of sample A-V, the volume crystallization is more or less disregarded. Sample A-V needs nucleation times of more than 10 h in order to precipitate only a low number of volume crystals. Hence, it was expected that activation energies and Avrami parameters give no hint at the formation of volume crystals. The glass particles used for DSC analysis possess a size between 400 and 500 µm and crystallize immediately from the surface. If the crystallization fronts reach a thickness of 200–250 µm, they collide before volume crystals can precipitate. Hence, those volume crystals cannot lead to a detectable release of the heat of crystallization. The Avrami parameter of sample A-S is in agreement with results of a previous study where a value of 1.8 was determined [20]. The activation energy reported in Ref. [20] is slightly lower (356 kJ mol−1), but the analyses were performed with different measuring conditions (crucible material, heating rates, remelted glass) [20].

The comparison of the WO3-containing samples B-S and B-V shows that the Avrami parameters are in a similar range. However, the values are lower than that of the base glass and predominant surface and minor volume crystallization are indicated. While the result for sample B-S is in agreement with the SEM studies, in the case of sample B-V (higher WO3 concentration) preferred volume crystallization with a high nucleation rate was detected by means of SEM analyses. Hence, a remarkably higher Avrami parameter than 1.96 was expected for the latter. However, DSC studies on nanocrystallizing oxyfluoride glasses reported in the literature yielded n and m values of 1 which was correlated with a bulk crystallization mechanism with a constant number of nuclei and two-dimensional, diffusion-controlled crystal growth [54, 55]. Applying the procedure proposed by Pascual et al. [53], i.e., determination of E/n from the Marseglia equation followed by the calculation of n using the Ozawa equation, and finally using the modified Kissinger equation in order to obtain the dimensionality of crystal growth m, an m value of 1 was obtained for sample B-V. According to Refs. [51, 56], the combination of n = 2 and m = 1 is a sign of bulk nucleation with varying nuclei number and needle-like growth should be observed.

Besides the tiny Ba1−xSrxWO4 dendrites also large Ba1−xSrxZn2Si2O7 crystals precipitate which is in agreement with the occurrence of more than one crystallization peak in the DSC profiles. The broad crystallization peaks are slightly overlapped leading to a double S-curve in the graph in Fig. 3 where the crystallization degree is shown as a function of the temperature. Since a deconvolution of the peaks and hence a separate consideration proves to be difficult, the first S-curve was used for the evaluation. Since the DSC profile of the 25–71 µm powder shows only one crystallization peak including a smaller shoulder, an Avrami analysis of powder having this grain size fraction was additionally performed yielding the value 2.27. Although the effect of surface crystallization should be more pronounced and hence the Avrami parameter should possibly be smaller, this value is slightly higher than that of the powder with larger grain size. Based on the previous remarks, it is questionable if the DSC method is applicable for this glass.

While in the gold-doped glass solely surface crystallization is observed (sample C-S), the combination of gold and Sb2O3 (sample C-V) results in the formation of gold nanoparticles in the glass matrix. Those nanoparticles are not able to act as nuclei for the formation of volume crystals [42]. This is why glass C-V shows a strong surface crystallization tendency and volume crystallization is not observed. The mean Avrami parameters of C-S and C-V are 1.75 and 1.5, respectively, and hence match very well the results of the SEM analyses. Since the gold nanoparticles in sample C-V do not induce volume crystals or otherwise affect the crystallization behavior, the obtained Avrami parameters are not surprising. However, this sample shows a significant increase of the activation energy from 470 kJ mol−1 (sample C-S) to 760 kJ mol−1 (sample C-V). This might be due to different surface crystallization mechanisms of the two Au-containing glasses already reported in the literature [42].

In contrast to the gold-doped glasses, the addition of silver remarkably affects the crystallization behavior, but only if the silver and Sb2O3 concentrations are high enough. As seen in the lower row of Fig. 2, a heat treatment of sample D-V at 675 °C for 10 h followed by a short growth step leads to the precipitation of a huge number of Ag-particles. A longer growth treatment results in a completely crystallized volume with Ba1−xSrxZn2Si2O7 as crystal phase. This shift of the dominant crystallization mechanism from surface to bulk crystallization becomes also apparent by the increase of the Avrami parameter from 2.3 to 3.9. Due to the preferred volume crystallization, the activation energy was calculated using the modified Kissinger equation and hence a comparison with the value of sample D-S obtained from the Kissinger equation is difficult.

In addition, it should be kept in mind that non-stoichiometric glass compositions are studied and the continuous change in the composition of the residual glass matrix may lead to time-dependent crystal growth velocities and hence different crystallization mechanisms which might be overlain by some extent.

According to the method proposed by Ray et al. [24], the favored crystallization mechanism may be also determined by the dependency of the peak height from the particle size. Here, it should be mentioned that the peak intensity is proportional to the number of nuclei present in the glass if the nucleation process is completed prior to the crystal growth process. This means that crystallization takes place from a fixed number of nuclei, and moreover, a constant crystal growth rate is assumed [57,58,59]. In the case of non-stoichiometric glasses in which the glass composition changes during the crystallization process, the latter condition might not be fulfilled. According to Ref. [59], the crystallization peak area can be influenced by elastic stresses or by the occurrence of non-equilibrium phases. In Fig. 4 (lower right panel), it is visible that the peak height of all glasses decreases as a function of the particle size indicating preferred surface crystallization. In the case of sample B-V, the decrease is strongest whereas sample A-V shows the smallest reduction. Hence, there is no notable difference between surface and volume crystallizing glasses and this method is not suitable to predict the predominant crystallization mechanism in BaO–SrO–ZnO–SiO2 glasses. High nucleation times are necessary to produce a sufficient number of volume crystals. Hence, the number of nuclei in the volume of crystallizing samples is probably too low compared with the number of surface nuclei. The latter have a major contribution to the total number of nuclei of the sample. Although large particle sizes are studied, this effect is observed. Since for example in a study concerning lithium disilicate glass powders with different particle sizes also no correlation between the peak intensity and the particle size was reported [35], it can be concluded that the prediction failures are independent of the glass system chosen and hence this method cannot be universally applied. In the case of the aforementioned study, the failure of this method is explained by a change of the activation energy with glass particle size [35].

According to Ray et al. [24], the crystallization mechanism is strongly affected by the particle size and can switch from surface to volume crystallization if a critical particle size is exceeded. Barium disilicate glass, for example, shows a critical particle size of about 75 µm, while in the case of lithium disilicate glass the slope in the plot peak height versus particle size remained unaffected [21]. This is probably due to the fact that the critical particle size is larger than the largest particle size studied [24].

Finally, it can be concluded that the DSC techniques described in the literature, i.e., determination of the Avrami parameter as well as plotting the peak height as a function of the particle size, cannot be applied to predict reliably the crystallization mechanism in glasses from the system BaO–SrO–ZnO–SiO2. Even obvious and distinct changes in the crystallization mechanism (see, for example, the WO3-containing samples B-S and B-V) could not clearly be interpreted in terms of these DSC methods. Hence, in the studied system, microscopic techniques are necessary to complement the DSC results and to draw clear conclusions on the crystallization mechanism.

In Refs. [51, 53], a correlation between the shift of the crystallization peak temperature and the particle size is indicated as a sign of the prevailing crystallization mechanism. In the case of surface crystallizing glasses, the peak shift as a function of the particle size should be more pronounced in contrast to volume crystallizing ones. In fact, this relationship is also observed in Fig. 4 upper right panel. Only sample B-S is somewhat out of line as the low peak shift actually suggests volume instead of surface crystallization. However, this glass shows some small Ba1−xSrxWO4 crystals in between the large surface crystals (see Fig. 6), and hence, the low peak shift might be a hint that there are some volume crystals, but the overall crystallization mechanism cannot be determined via this “peak shift method.” Interestingly, sample C-V where the gold nanoparticles do not induce volume crystallization is correctly assigned as surface crystallizing. However, this type of prediction works only if several glasses are compared and information about the crystallization behavior is already known, e.g., by microstructural investigations. A more reliable method which can securely identify the preferred crystallization mechanism has been identified for the case that only one glass is considered. Here, the crystallization temperatures of a non-nucleated and a previously nucleated sample are compared (see Fig. 5). The shift of the crystallization temperature after foregoing nucleation treatment is directly correlated with the appearance of nuclei in the glass and hence indicates volume crystallization. This approach is based on a method proposed by Marotta [60] where a nucleation curve can qualitatively be determined. Ray and Day have also shown that the crystallization temperature notably decreases with increasing nucleation time due to a higher concentration of nuclei in the glass [61]. While the results obtained from methods already described in the literature (Figs. 3, 4) give unreliable results, this method provides the correct crystallization mechanism for all the glasses studied and could be applied to two more glasses with a so far unknown nucleation and crystallization behavior. In Fig. 7, the peak shift between as-cast and previously nucleated samples of glasses E and F are shown. Since the peak shift is smaller than around 5 K and hence within the limit of error, it is indicated that the nucleation treatments did not lead to the precipitation of additional nuclei. In the right part of Fig. 7 the microstructures of the crystallized glasses E and F are shown. There, an obvious difference between those two glasses is observed. Whereas sample E (Ru-doped, upper right panel of Fig. 7) shows solely surface crystallization, which is in agreement with the results from thermal analysis (left part of Fig. 7), in sample F (Pt-doped, lower right panel of Fig. 7) volume crystals can be found. At first glance, this is contradictory to the results from thermal analysis. However, in a slightly different glass composition with 0.01 mol% PtCl4 described in Ref. [62], Pt particles have been formed. However, it was not proven in which stage of the glass ceramic synthesis procedure, the Pt particles have been formed (during melting or during reheating). The Pt-concentration of glass E was chosen to be much higher than the solubility limit in silicate glasses (see Ref. [63]), and hence, the glass already contains the metallic particles directly after synthesis. The results from DSC (left part of Fig. 7) indicate that additional Pt particles, which are able to act as nuclei for crystal growth, have not been formed in the sample volume, even after a 70-h nucleation treatment. This means that all the Pt particles should have formed during synthesis.

Fig. 6
figure 6

SEM micrograph of a cross section of glass B-S after a two-step heat treatment. The nucleation was performed at 760 °C for 10 h followed by the crystallization at 800 °C for 5 h. The surface crystals grew from the bottom to the top. Two areas near the surface which contain small volume crystals are highlighted

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Fig. 7
figure 7

Comparison of DSC results with micrographs of heat-treated samples E and F. In the left panel, DSC profiles of non-nucleated and nucleated samples E and F (grain size fraction 400–500 µm, 10 K min−1) are shown. The nucleated samples E and F were heat-treated at 690 °C for 100 h and 660 °C for 70 h, respectively. While in the upper right panel the microstructure of sample E after a heat treatment at 690 °C for 20 h and 800 °C for 5 h is displayed, the lower right panel displays the microstructure of sample F provoked by a heat treatment at 770 °C for 1 h

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In Fig. 8, the differences between Tp,glass and Tp,nuc are compared for all glasses studied. In the case of sample B-V, the left column is related to the first crystallization peak. The right one describes the second peak. Since the glass sample shows three crystallization peaks that are close together and hence a deconvolution proves to be difficult, an average value was assumed for the calculation of the difference. Since the measurement error of the crystallization peak temperature is about ± 5 K, and it is assumed that the peak temperature of predominantly surface crystallizing glasses is almost unchanged, samples with a peak shift smaller than 5 K are classified as surface crystallizing samples (shaded area). In Fig. 8, it becomes clear that only the samples A-V, B-V, and D-V which show in fact pronounced volume crystallization have a peak difference much larger than 5 K. The peak differences correlate remarkably well with the ability to form volume crystals, except for the case of glasses, where all nuclei have already been formed during synthesis. If additional nuclei, which are able to trigger volume crystallization, form during a nucleation treatment, this can be identified via the combination of nucleation treatment followed by DSC analyses.

Fig. 8
figure 8

Comparison of the shift of peak temperatures between non-nucleated and nucleated samples. The shaded area indicates surface crystallization while a difference higher than around 5 K means that additional nuclei being able to trigger volume crystallization form during a nucleation treatment

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The proposed method offers the possibility to quickly and especially reliably determine the prevailing crystallization mechanism in glass systems which are difficult to access using other methods. Thus, multiphase systems as well as glass systems showing simultaneous surface and volume crystallization may be evaluated regarding their crystallization behavior with comparatively little effort. Using the example of glass A-V, it is shown that even very low nucleation rates do not constitute a hindrance. If the crystallization behavior is completely unknown, a heat treatment for several hours at a temperature slightly above Tg should be sufficient for an evaluation. If such a heat treatment is not adequate to cause a shift of the crystallization peak, then additional nuclei have not been formed within the sample volume. In the case of the Au-doped glasses C-S and C-V, it could also be shown that the precipitation of metallic particles leads to a shift of the crystallization peak to higher temperatures. This correlates very well with the high activation energy. This means that glass C-V shows even a lower crystallization tendency after a nucleation treatment.

Conclusions

In this study, glasses from the system BaO–SrO–ZnO–SiO2 and only slight compositional changes were prepared. These minor changes cause very different crystallization mechanisms. The DSC method in combination with electron microscopy was performed to study if the non-isothermal technique is sensitive enough to detect different volume effects. It becomes apparent that even the prediction of the dominant crystallization mechanism in glasses is ambiguous. This prediction may be hindered by pronounced induction times for nucleation, long nucleation times of the bulk crystals or the presence of multiple crystalline phases. Hence, a prediction of the predominant crystallization mechanism using non-isothermal DSC techniques is not appropriate without deeper knowledge of nucleation and growth processes obtained using traditional microscopic analyses. Otherwise, these methods may give misleading results. If a strong overlap of both, surface and volume crystallization, can be found, then the probability of an incorrect prediction is very high. Nevertheless, these methods may provide important information concerning the crystallization kinetics, but they are as time-consuming as the microscopic techniques. A first estimation if a glass is able to precipitate volume crystals, even in a very small quantity, is possible by comparing the crystallization temperatures of non-nucleated and nucleated glass via thermal analyses. This method seems to be universally applicable for many different crystallization mechanisms and also in the case of different crystallization mechanisms appearing in one and the same glass.