Advertisement

Journal of Thermal Analysis and Calorimetry

, Volume 133, Issue 1, pp 227–236 | Cite as

Crystallization kinetics of yttrium aluminate glasses

  • Anna Prnová
  • Alfonz Plško
  • Jana Valúchová
  • Peter Švančárek
  • Róbert Klement
  • Monika Michálková
  • Dušan Galusek
Article
  • 153 Downloads

Abstract

Yttrium aluminate glasses with eutectic AY-E and near-eutectic composition AY-NE were prepared in the form of glass microspheres. Their basic characterization was carried out by XRD, optical microscopy and SEM. In DSC records of both samples, two exothermic peaks in temperature interval 940–1027 °C were observed. In both samples, YAG phase crystallized in two steps, as determined by HT XRD. DSC experiments conducted in the temperature interval 35–1200 °C at heating rates 2, 4, 6, 8 and 10 °C min−1 were performed, and the kinetic parameters of crystallization were determined with the use of the JMAK model. Crystallization in both samples was controlled by diffusion flow with linear nucleation rate time dependence. One-dimensional growth and formation of needle-like (dendritic) YAG crystals was observed in AY-E glass crystallized at 932 °C corresponding to the first exothermic maximum at the DSC curve. Two-dimensional growth and the presence of plate-like YAG crystals were observed in AY-NE glass crystallized at 996 °C. For the second exothermic effect, plate-like crystals crystallized at higher temperatures (996 and 1020 °C) in both compositions. The results of SEM analysis are in agreement with the results of kinetic calculations in the prepared systems.

Keywords

Crystallization kinetics HT XRD DSC Yttrium aluminate glasses 

Introduction

Recently, the rare earth aluminate-based materials with eutectic microstructures prepared by direct solidification of eutectic melts have attracted significant attention for their excellent fracture strength/toughness, thermal stability and creep resistance at elevated temperatures. These properties are attributed to strong eutectic interfaces between present phases and designate these materials for high-temperature applications such as fibre materials for reinforcement or as bulk materials for machine parts (jet aircraft engines and high-efficiency power-generation gas turbines components) [1]. Normally a faster solidification rate leads to a finer microstructure, resulting in improved mechanical properties [2]. Therefore, directional solidification techniques facilitating higher cooling rates (Bridgman method [3], laser floating zone technique [4], laser zone re-melting [5], micro pulling down [6] and other) are frequently used for preparation of eutectic oxide ceramics materials. However, these methods are time and energy consuming and difficult to fabricate large and complex parts [7]. In order to mitigate these problems, preparations of a eutectic ceramic by indirect methods, using conventional sintering, and hot-pressing or spark plasma sintering (high temperatures and high pressures are required) were described [8, 9, 10, 11]. An alternative route is represented by controlled crystallization of glasses with eutectic composition. Harada et al. describe preparation of very fine-grained glass–ceramics and polycrystalline ceramics with eutectic microstructures through sintering of flakes prepared by rapid cooling of eutectic melts on rollers [12]. Raj et al. [13] in their work described a flash sintering method (assisted by electric field), which exhibits many advantages, such as low sintering temperature and short time, very high density and good mechanical properties of prepared materials. Dianguang et al. [7] used flash sintering method for preparation of Al2O3–Y3Al5O12–ZrO2 ternary eutectic ceramics, with very high density at low temperature and short time. The Vickers hardness (HV = 13.91 ± 1.43 GPa) and fracture toughness (6.2 ± 0.34 MPa m½) of the composite indicate that the mechanical properties of the (indirectly) prepared eutectic ceramics approach those of the composited prepared by direct methods. Tarafder et al. [14] described preparation of nano-glass ceramic materials in K2O–SiO2–Y2O3–Al2O3 system by isothermal controlled crystallization of precursor glasses. The result was a glass–ceramic material containing nanocrystalline YAG phase (25–40 nm) in KSYA glass matrix. Combination of sol–gel method and flame synthesis for preparation of glass microspheres with eutectic composition (76.8 mol% Al2O3) in the system Al2O3–Y2O3 followed by hot pressing at different temperatures and different holding times was successfully applied for preparation of YAG–Al2O3 composites in our previous work [15]. IR transparent ceramic and glass ceramic materials with fine two phase microstructure with α-Al2O3 and YAG (yttrium–aluminium garnet) phases percolating at submicrometre level and with hardness exceeding 15 GPa resulted from the experiments. Such controlled crystallization under the simultaneous hot-press sintering of flame synthesis prepared glass microspheres has its merits in terms of both the economical and technological advantages of the process. However, detailed knowledge of thermal behaviour and crystallization kinetics of the used glass systems is necessary for successful preparation of bulk eutectic ceramic materials with controlled microstructure and phase composition.

Theory

The experimental data on crystallization of glasses [16], obtained by DSC/DTA, are mostly interpreted in terms of the nucleation growth model formulated by Avrami [17, 18, 19]. This model describes the time dependence of fractional extent of crystallization, α (Eq. 1)
$$ \alpha = 1 - { \exp }\left( { - kt^{\rm m} } \right) $$
(1)
where k and m are constants with respect to time, t. The Eq. (1) has physical meaning only for the values of m constants strictly equal to 0.5, 1, 1.5, 2, 2.5, 3 or 4. After differentiation with respect to time, the Johnson–Mehl–Avrami–Kolmogorov (JMAK) rate equation is obtained (Eq. 2) [16, 20, 21]:
$$ \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = k \cdot m \cdot \left( {1 - \alpha } \right) \cdot \left[ { - { \ln }\left( {1 - \alpha } \right)} \right]^{{\left( {1 - \frac{1}{\rm m}} \right)}} . $$
(2)
The validity of the Eq. (2) is based on the assumptions that the crystallization is carried out under isothermal conditions and the following topokinetic features [22, 23]:
  • The existence of a potential site for nucleation,

  • The nucleation rate is constant or linearly temperature dependent,

  • The nuclei grow isotopically,

  • The rate of advancement of reaction interface is controlled by either chemical reaction, i.e. (linear function of time) or by diffusion (i.e. parabolic time dependence),

  • The reaction interface is a simple reactant–product contact and the rate equation of interface advancement does not change in the course of reaction.

The assignment of coefficient m to the above mentioned topokinetic features of crystallization is summarized in Table 1 [22, 23, 24].
Table 1

Assignment of the coefficient m values to individual processes of crystallization

Nucleation rate

The movement of the growth front controlled by

Growth dimension

Avrami coefficient m

Constant

Chemical boundary or chemical reaction (linear time dependence)

1-D

1

2-D

2

3-D

3

Diffusion (parabolic time dependence)

1-D

0.5

2-D

1

3-D

1.5

Linear

Chemical boundary or chemical reaction (linear time dependence)

1-D

2

2-D

3

3-D

4

Diffusion (parabolic time dependence)

1-D

1.5

2-D

2

3-D

2.5

In non-isothermal case, with constant heating rate, the Arrhenius equation (Eq. 3) has been widely applied to express the temperature dependence of rate constant k [22, 23, 25].

$$ k = A \cdot { \exp }\left[ { - \frac{{E_{\text{a}} }}{RT}} \right] $$
(3)
where A represents the pre-exponential constant, Ea is the activation energy, T is the thermodynamic temperature, R is the molar gas constant. Then the JMAK rate equation can be rearranged as follows (Eq. 4).
$$ \beta \cdot \frac{{{\text{d}}\alpha }}{{{\text{d}}T}} = A \cdot { \exp }\left[ { - \frac{{E_{\text{app}} }}{RT}} \right] \cdot m \cdot \left( {1 - \alpha } \right) \cdot \left[ { - { \ln }\left( {1 - \alpha } \right)} \right]^{{\left( {1 - \frac{1}{\rm m}} \right)}} $$
(4)
where β is the constant heating rate, α is the fractional extent of crystallization, A is pre-exponential constant of crystallization, and Eapp is the apparent activation energy of crystallization.

The coefficient m in the Eq. (4) can be determined in two ways. (1) First, during the analysis of measured data the value of empirical coefficient (assigned as M) is determined. This coefficient can gain any value, not just those with specific physical–chemical meaning of the coefficient m. The difference between the empiric coefficient M and the coefficient m is explained by the influence of experimental errors [22]. The second approach is based on selection of a suitable model of the crystallization process [26, 27]. From the set of models (one model for each of the seven possible m values the coefficient can assume), the most probable one is selected depending on statistical parameters of quality of fit assessment. In order to assess the quality of the fit a value of adjusted correlation coefficient is used (Eq. 5).

$$ R_{\text{adj}}^{2} = 1 - \frac{{{\raise0.7ex\hbox{${\text{RSS}}$} \!\mathord{\left/ {\vphantom {{\text{RSS}} {\left( {n - p - 1} \right)}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\left( {n - p - 1} \right)}$}}}}{{\left( {\sum \left( {y_{\rm i} - \bar{y}} \right)^{2} } \right)/\left( {n - 1} \right)}} $$
(5)
where \( y_{\text{i }} \), i = 1….n, are data values, \( \bar{y} \) is a mean of data values, RSS is residual sum of squares for a model, and p is the number of free parameters. Maximizing \( R_{\text{adj}}^{2} \), with no consideration of model complexity, always favours fuller (i.e. more parameter rich) models. However, it neglects the principle of parsimony and, consequently, can result in imprecise parameter estimates and predictions, making it a poor technique for model selection.
The criteria that account for both the fit and complexity are therefore better suited for model selection. The Akaike information criterion (AIC), as shown in Eq. 6, estimates the Kullback–Leibler information lost by approximating full reality with the fitted model (Eq. 6) [28, 29, 30]:
$$ {\text{AIC}} = n\ln \left( {{\raise0.7ex\hbox{${\text{RSS}}$} \!\mathord{\left/ {\vphantom {{\text{RSS}} n}}\right.\kern-0pt} \!\lower0.7ex\hbox{$n$}}} \right) + 2p. $$
(6)
The Akaike criterion determines not only which model is more likely to fit better the considered data but also quantifies how much more likely. The Akaike weight (wAIC) (Eq. 7) considers the difference between the AIC values of each model and determines the AIC value of the “best” model (i.e. the model with the lowest AIC value). It also yields a relative weight of how much a given model is the best one among the set of model examined [26, 31].
$$ {\text{wAIC}}_{\text{i}} = \frac{{{ \exp }\left( {{\raise0.7ex\hbox{${ - \Delta_{\text{i}} }$} \!\mathord{\left/ {\vphantom {{ - \Delta_{\text{i}} } 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}} \right)}}{{\mathop \sum \nolimits_{i = 1}^{U} { \exp }\left( {{\raise0.7ex\hbox{${ - \Delta_{\text{i}} }$} \!\mathord{\left/ {\vphantom {{ - \Delta_{\text{i}} } 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}} \right)}}\quad {\text{with}}\;0 \le w_{\text{i}} \le 1 $$
(7)
where \( \Delta_{\text{i}} = {\text{AIC}}_{\text{i}} - {\text{AIC}}_{ \hbox{min} } \), \( {\text{AIC}}_{\text{i}} \) and \( {\text{AIC}}_{ \hbox{min} } \) are the values for the model i, and the model giving the lowest AIC value. The parameter U is the total number of models under investigation.

The aim of this study was preparation of two different compositions in the system Al2O3–Y2O3 (eutectic and near-eutectic), their basic characterization by SEM and XRD, and the study of phase changes with temperature by HT XRD. DSC studies of the two systems were also carried out to obtain data for crystallization kinetics calculation. The best kinetics model was determined for both studied systems. The results of calculations were confronted with the data obtained by SEM examination of glasses crystallized under isothermal conditions.

Experimental

Preparation of glass microspheres

The precursor powders with eutectic composition AY-E (76.8 mol% Al2O3) and near-eutectic composition AY-NE (81.8 mol% Al2O3) were prepared by modified Pechini sol–gel method [32] as described in our previous work [33]. High-purity chemicals (Y2O3; 99.9%; Treibacher Industry, Austria, and Al(NO3)3·9·H2O; 99.9%; Sigma-Aldrich, Germany) were used for the synthesis. A narrow fraction of the precursor powder from 25 to 40 μm was fed into methane–oxygen flame to melt the powder particles. The molten droplets were quenched in distilled water and separated by microfiltration. Finally, the glass microspheres were dried and calcined at 650 °C for 1 h to remove any organic residua.

Crystallization experiments

The isothermal crystallization experiments were performed at temperatures 932, 996 and 1020 °C in air, using the vertical tube furnace (Classic, Czech Republic) and Pt crucibles. The temperatures of isothermal treatment were selected on the basis of DSC results, as shown below. The samples were heated at 10 °C min−1 to the required temperature, kept at this temperature for 40 min and then removed from the furnace and quickly cooled down in air to room temperature.

Characterization

The prepared glass particles were examined by optical microscopy (Nicon Eclipse, ME 600) in transmitted light, at 100–500× magnification, to verify the correct setting of the flame synthesis apparatus resulting in complete melting of precursor powders yielding spherical optically transparent particles.

Both the as-prepared and crystallized glass microspheres were embedded into a polymeric resin (Simplimet 1000, Buehler) and polished (Ecomet 300, Buehler) to obtain defined cross section. The samples were then carbon sputtered to prevent charging and examined by SEM (JEOL 7600F) at the accelerating voltage 20 kV. X-ray powder diffraction analysis (Panalytical Empyrean, 45 kV accelerating voltage, CuKα radiation with λ = 1.5405 Å, measured in the 2Θ range 10°–80°) was used to obtain qualitative information on the phase composition of prepared and heat treated glass microspheres. The Rietveld refinement with internal standard was used for estimation of residual glass amount in prepared glass microspheres, using the High Score Plus (v.3.0.4, PAN Analytical, The Netherlands) software equipped with the PDF4 database. Si powder (≈5 wt%) was used as the internal standard. The high-temperature X-ray diffraction experiments were performed in the temperature interval 25–1450 °C, using the powder diffractometer equipped with the high-temperature cell Anton Paar HTK 16. The powder dispersed in isopropyl alcohol was spread evenly on a Pt/Rh heating strip to form a thin uniformly distributed powder layer. The temperature control was provided by a Pt/PtRh10 thermocouple (type S) welded on the bottom surface of the strip. Two long scans at 25 and 750 °C (in the 2θ range 10°–80°; step 0.05° s−1; data accumulation time 194 s per step) were measured at the beginning of the experiment. Then, the sample was heated at 5 °C min−1 in ambient atmosphere, and diffraction patterns (in the 2θ range 30°–50°; step 0.05° s−1; data accumulation time 14 s per step) were recorded every 5 °C in the temperature interval 750–1450 °C. Finally, the sample was cooled down to 25 °C, and one long scan was recorded at the end of the measurement. The diffraction data were evaluated using the software High Score Plus (v.3.0.4, PAN Analytical, The Netherlands) with the use of the Crystallographic Open Database (COD_2013).

The DSC measurements were performed in the temperature range between 35 and 1200 °C at the heating rates β = 2, 4, 6, 8 and 10 °C min−1 in nitrogen atmosphere using the Netzsch STA 449 F1 Jupiter simultaneous thermal analyser. Approximately ≈ 15 mg of glass microspheres were weighed into Pt crucibles and used for the DSC experiments. The individual records (Fig. 1a, b) were evaluated by Netzsch Proteus (version 6.0.0.) software.
Fig. 1

DSC records of AY-E (a) sample and AY-NE (b) sample recorded at different heating rates (2, 4, 6, 8 and 10 °C min−1)

Calculations

From DSC curves (for both samples and for both peaks) recorded at constant heating rate regimes with β = 2, 4, 6, 8 and 10 °C min−1, the α(T) and dα(T)/dT values were obtained as proportional to the area under the DSC curve (in temperature interval TxTe,Tx—onset of crystallization peak temperature; Te—end of crystallization peak temperature) after subtracting the baseline. The values of kinetic parameters (A and Eapp) for JMAK equation with the coefficients m = 1, 1.5, 2, 2.5, 3 and 4 were calculated by two-step regression analysis. At first, Eq. 4 was linearized, and the linear least squares problem was solved. The next step was connected with solving the non-linear least squares problem using the equation (Eq. 4) in the form of the equation (Eq. 8).
$$ \beta \cdot \frac{{{\text{d}}\alpha }}{{{\text{d}}T}} = { \exp }\left[ {AA - \frac{B}{T}} \right] \cdot m \cdot \left( {1 - \alpha } \right) \cdot \left[ { - { \ln }\left( {1 - \alpha } \right)} \right]^{{\left( {1 - \frac{1}{\rm m}} \right)}} $$
(8)
where AA = lnA and B = Eapp/R. The results of linear regression were used as the starting values of optimized parameters. Together with calculation of kinetic parameters for individual models with different m the RSS, \( R_{\text{adj}}^{2} \) (Eq. 5) and AIC (Eq. 6) criterions were calculated. Subsequently, the wAIC values (Eq. 7) were calculated for the individual models.

Results and discussion

Results of DSC analysis

The prepared microspheres were studied by DSC in temperature interval 25–1200 °C with 10 °C min−1 heating rate in nitrogen atmosphere. DSC records (Fig. 1a, b) of both prepared samples show two exothermic effects, with the maxima at 942 and 1006 °C for the eutectic glass AY-E and 940 and 1027 °C for the near-eutectic glass AY-NE. It can be assumed that these exothermic effects are the results of crystallization processes. In the next steps, these effects were examined as two individual processes. The other DSC parameters (glass transition temperature, onset of crystallization peak temperature Tx, end of crystallization peak temperature Te and inflection point temperatures Tf1, Tf2) are shown in Table 2.
Table 2

The results of DSC analysis

Sample name

Peak position

Tg/°C

Tx/°C

Tf1/°C

Tp/°C

Tf2/°C

Te/°C

Difference Tp2 − Tp1

H/J g−1

AY-E

First

897

932

938

942

946

953

64

56.3

Second

996

1004

1006

1010

1013

44.0

AY-NE

First

898

932

937

940

943

950

87

59.4

Second

1020

1025

1027

1030

1032

50.0

Tg, glass transition temperature; Tx, onset of crystallization peak temperature; Tf1, Tf2, inflection points; Tp, maximum of crystallization peak temperature; Te, endset of crystallization peak temperature

Results of XRD analysis and SEM examination

X-ray powder diffraction patterns (Fig. 2) indicate that the eutectic sample AY-E was X-ray amorphous, while the presence of YAG and α-Al2O3 crystalline phases was detected in the as-prepared AY-NE sample. The Rietveld refinement of the AY-NE X-ray diffraction data showed the presence of 5.3 wt% of YAG phase (JCPDS 88-2048) and 2.2 wt% of corundum (α-Al2O3, JCPDS 46-1212) (Table 3). Examination of the AY-NE sample by SEM confirmed the results of XRD, showing the presence of a small portion of fully or partially crystallized microspheres (Fig. 3). However, every glass particle is an individual system, and fully or partially crystallized glass microspheres do not influence crystallization of other beads.
Fig. 2

XRD patterns of prepared AY-E (a) and AY-NE glass microbeads (b)

Table 3

The chemical and phase compositions of prepared samples

Sample name

Al2O3/mol%

Y2O3/mol%

Phase composition

Phases

wt%

AY-E

76.8

23.2

 

a

Amorphous

100

AY-NE

81.8

18.2

YAG

5.3

α-Al2O3

2.2

Amorphous

92.5

aContent of crystalline phases bellow detection limit of XRD

Fig. 3

SEM micrograph of polished cross section AY-NE microspheres. Crystallized microbead is marked by arrow

HT XRD

To study phase changes in studied systems, the HT XRD experiments in the temperature interval 25–1450 °C were also performed. The presence of two crystalline phases—YAG (yttrium–aluminium garnet) and α-Al2O3 (aluminium oxide) was observed in the last long RTG record, after completion of the whole heating cycle in both tested compositions. Crystallization of YAG phase was observed to start from the temperatures ≈ 900 °C, corresponding to the first exothermic maximum on DSC curves. Crystallization of α-Al2O3 followed at higher temperatures (≈ 1300 °C). Due to thermal expansion of the YAG and α-Al2O3 crystal lattice, a systematic shift of diffraction maxima with increasing temperature to lower 2θ values was observed.

By the comparison of HT XRD results (only the crystallization of YAG was observed in temperature interval 900–1200 °C) with the DSC analysis results (presence of two exothermic effects in measured records at a given temperature interval), it was concluded that crystallization of YAG phase in eutectic glass proceeds in two steps. This result was in more detail discussed in our previous work [34].

The kinetics calculations

The results of kinetics calculation for the first and the second peak for each model in the eutectic AY-E sample are shown in Tables 4 and 5. Similarly, results of kinetic calculation for the near-eutectic composition (AY-NE) are shown in Tables 6 and 7. Also, the resulting parameters of kinetics triplets (a pre-exponential constant, Eapp—apparent activation energy and f(α), in this case characterized by Avrami coefficient value-m) are summarized in Table 8.
Table 4

The values of RSS, \( R_{\text{adj}}^{2} \), AIC and wAIC criterions calculated for individual models with m = 1, 1.5, 2, 2.5, 3, and 4 for sample AY-E (first peak)

m

RSS

\( R_{\text{adj}}^{2} \)

AIC

wAIC

1

21.0

0.823

− 9010

0

1.5

2.5

0.979

− 13,244

1

2

6.5

0.945

− 11,332

0

2.5

12.5

0.895

− 10,033

0

3

17.7

0.851

− 9343

0

4

25.3

0.787

− 8636

0

Table 5

The values of RSS, \( R_{adj}^{2} \), AIC and wAIC criterions calculated for individual models with m = 1, 1.5, 2, 2.5, 3, and 4 for sample AY-E (second peak)

m

RSS

\( R_{adj}^{2} \)

AIC

wAIC

1

28.6

0.844

− 8391

0

1.5

3.2

0.982

− 12,707

0

2

1.2

0.993

− 14,624

1

2.5

4.0

0.978

− 12,298

0

3

7.4

0.960

− 11,065

0

4

13.4

0.927

− 9893

0

Table 6

The values of RSS, \( R_{\text{adj}}^{2} \), AIC and wAIC criterions calculated for individual models with m = 1, 1.5, 2, 2.5, 3, and 4 for sample AY-NE (first peak)

m

RSS

\( R_{\text{adj}}^{2} \)

AIC

wAIC

1

48.9

0.748

− 7335

0

1.5

3.3

0.983

− 12,680

3.1 × 10−36

2

3.0

0.984

− 12,844

1

2.5

9.6

0.951

− 10,574

0

3

16.2

0.916

− 9525

0

4

26.7

0.862

− 8534

0

Table 7

The values of RSS, \( R_{\text{adj}}^{2} \), AIC and wAIC criterions calculated for individual models with m = 1, 1.5, 2, 2.5, 3, and 4 for sample AY-NE (second peak)

m

RSS

\( R_{\text{adj}}^{2} \)

AIC

wAIC

1

96.3

0.741

− 5992

0

1.5

17.9

0.952

− 9325

0

2

3.0

0.992

− 12,898

1

2.5

3.7

0.990

− 12,456

1.1 × 10−96

3

8.1

0.978

− 10,892

0

4

17.8

0.952

− 9340

0

Table 8

The kinetic parameters (kinetic triplets) which describe the process of AY-E (first peak), AY-E (second peak), AY-NE (first peak) and AY-NE (second peak) crystallization

Sample

Peak

m

A ± SD/min−1

Eapp ± SD/kJ mol−1

AY-E

First

1.5

(5.1 ± 3.5) × 1052

1222.9 ± 5.4

Second

2

(4.7 ± 2.5) × 1071

1751.7 ± 4.5

AY-NE

First

2

(1.7 ± 0.9) × 1051

1184.5 ± 5.3

Second

2

(1.1 ± 0.9) × 1087

2159.0 ± 6.5

The choice of the models which describe best the experimental data was realized according to the RSS, \( R_{\text{adj}}^{2} \), AIC and wAIC values. The best model, according to RSS or AIC criteria, is considered the one which gains the minimal value. According to \( R_{\text{adj}}^{2} \) the best model should assume the maximal value of this criterion. The main selection criterion is wAIC, which allows, on the basis of comparison, the best model selection from a set of models. The wAIC value expresses to what extent the concrete model describes the experimental data. The value equal to 1 means that the model is the best to describe the experimental data. The comparison of measured and calculated data for the selected model is shown in Fig. 4.
Fig. 4

The comparison of measured and calculated data for the individual choice models; for the first peak AY-E sample (a), for the second peak AY-E sample (b), for the first peak AY-NE sample (c) and for the second peak AY-NE sample (d)

On the basis of comparison of m values for studied samples and for individual exothermic effects with Table 1, it can be concluded that prevailing crystallization process in case of the first exothermic effect in the eutectic AY-E glass is controlled by diffusion, with linear nucleation rate time dependence and 1-D growth dimension, with expected formation of dendrites (needle-like) crystals in the system. In the case of the second exothermic effect, the diffusion-controlled crystallization process with 2-D growth and linear nucleation rate time dependence prevails, characterized by formation of plate-like crystals. For the near-eutectic AY-NE system diffusion-controlled crystallization process with 2-D growth and linear nucleation rate time dependence prevails in both exothermic processes.

Crystallization experiments

On the basis of DSC analysis results and for verification of kinetic calculations and better understanding of the process of crystallization, isothermal crystallization experiments were performed in ambient atmosphere, at the temperatures 932, 996 and 1020 °C with 40 min holding time. The first two temperatures, respectively, correspond to the maxima of the first and the second exothermic effect on the DSC curve of the AY-E glass; the last temperature corresponds to the second exothermic maximum on the DSC curve of AY-NE system. The presence of needle-like crystals (dendrites) was observed by SEM analysis in eutectic sample AY-E, which crystallized at 927 °C for 40 min (Fig. 5a). At this temperature, the YAG phase crystallization was confirmed by HT XRD, confirming the results of kinetic analysis, which suggested diffusion-controlled crystallization of YAG by with prevailing 1-D growth of YAG crystals. On the other hand, the SEM micrographs of the AY-NE (near-eutectic) sample crystallized at the same temperature show the presence of plate-like crystals and prevalence of 2-D growth in the system (Fig. 5b). Both in the eutectic and near-eutectic systems crystallized at higher temperatures (996 and 1020 °C, respectively), the presence of plate-like crystals was detected by SEM (Fig. 5c, d), implying, with accord to the kinetic analysis data, that YAG phase crystallization at higher temperatures (≈ 1000 °C) is controlled by diffusion and 2-D growth prevails in studied systems. The SEM analysis also revealed numerous cases where heterogeneous crystallization took place, starting at defects (cavities, holes), or from the surface of microspheres.
Fig. 5

SEM micrographs of AY-E sample heat treated at 932 °C for 40 min (a), AY-NE sample heat treated at 932 °C for 40 min (b), AY-E sample heat treated at 996 °C for 40 min (c), AY-NE sample heat treated at 1020 °C for 40 min (d)

Conclusions

The presence of two exothermic effects in DSC records of prepared yttrium aluminate glass microspheres with the eutectic (AY-E) and near-eutectic (AY-NE) compositions was observed. The crystallization of YAG phase in two steps was determined by HT XRD experiments in both studied samples. In case of the eutectic composition, the diffusion-controlled crystallization process with linear nucleation rate time dependence and 1-D growth prevails in crystallization of the YAG phase. In case of the AY-NE composition, the diffusion-controlled crystallization process with 2-D growth and linear nucleation rate time dependence prevails. In case of second exothermic effect, the diffusion-controlled process with 2-D growth and linear nucleation rate prevails in both studied samples. The SEM analysis confirmed the conclusions of the kinetic analysis, showing the presence of needle-like crystals in the AY-E sample heat treated at the temperature corresponding to the first exothermic effect, while the presence of plate-like crystals in the AY-NE sample heat treated at 932 °C was observed. Similarly, the formation of plate-like crystals was detected both in the AY-NE and AY-E crystallized at temperature 1020 and 996 °C, respectively, corresponding to the maxima of the second exothermic effect observed at DSC curves of both studied systems.

Notes

Acknowledgements

The financial support of this work by the project SAS-MOST JRP 2015/6, VEGA 1/0631/14, VEGA 2/0026/17 and APVV 0014-15 is gratefully acknowledged. This publication was created in the frame of the project “Centre of excellence for ceramics, glass, and silicate materials” ITMS code 262 201 20056, based on the Operational Program Research and Development funded from the European Regional Development Fund.

References

  1. 1.
    Ochiai S, Ikeda S, Iwamoto S, Sha JJ, Okuda H, Waku Y, Nakagawa N, Mitani A, Sato M, Ishikawa T. Residual stresses in YAG phase of melt growth Al2O3/YAG eutectic composite estimated by indentation fracture test and finite element analysis. J Eur Ceram Soc. 2008;28:2309–17.CrossRefGoogle Scholar
  2. 2.
    Song K, Zhang J, Liu L. An Al2O3/Y3Al5O12 eutectic nanocomposite rapidly solidified by a new method: liquid–metal quenching. Scr Mater. 2014;92:39–42.CrossRefGoogle Scholar
  3. 3.
    Buyuk U, Engin S, Marasli N. Directional solidification of Zn–Al–Cu eutectic alloy by the vertical Bridgman method. J Min Metall B. 2015;51:67–72.CrossRefGoogle Scholar
  4. 4.
    Mesa MC, Oliete PB, Pastor YJ. Mechanical properties up to 1900 K of Al2O3/Er3Al5O12/ZrO2 eutectic ceramics grown by laser floating zone method. J Eur Ceram Soc. 2014;34:2081–7.CrossRefGoogle Scholar
  5. 5.
    Yu JZ, Zhang J, Su H-J. Fabrication and characterization of Al2O3/Y3Al5O12 eutectic in situ composite ceramics by double side laser zone remelting method. J Inorg Mater. 2012;27:843–8.CrossRefGoogle Scholar
  6. 6.
    Kurosawa S, Suzuki A, Yamaji A. Luminiscent properties of Cr-doped gallium garnet crystals grown by the micro-pulling- down method. J Cryst Growth. 2016;452:95–100.CrossRefGoogle Scholar
  7. 7.
    Dianguang L, Yan G, Jinling L, Fangzhoung L, Kai L, Haijun S, Yiguang W, Linan A. Preparation of Al2O3–Y3Al5O12–ZrO2 eutectic ceramic by flash sintering. Scr Mater. 2016;14:108–11.Google Scholar
  8. 8.
    Harada Y, Ayabe K, Uekawa N. Formation of GdAlO3–Al2O3 composite having fine pseudo-eutectic microstructure. J Eur Ceram Soc. 2008;28:2941–6.CrossRefGoogle Scholar
  9. 9.
    Harada Y, Uekawa N, Kojima T, Kokegawa K. Fabrication of Y3Al5O12–Al2O3 eutectic materials having ultra fine microstructure. J Eur Ceram Soc. 2008;28:235–40.CrossRefGoogle Scholar
  10. 10.
    Harada Y, Uekawa N, Kojima T, Kakegawa K. Formation of Y3Al5O12–Al2O3 eutectic microstructure with off-eutectic composition. J Eur Ceram Soc. 2008;28:1973–8.CrossRefGoogle Scholar
  11. 11.
    Yao B, Su H, Zhang J, Ren Q, Ma W, Liu L, Henghzhi F. Sintering densification and microstructure formation of bulk Al2O3/YAG autectic ceramics by hot pressing based on fine eutectic microstructure. Mater Des. 2016;92:213–22.CrossRefGoogle Scholar
  12. 12.
    Harada Y, Uekawa N, Kojima T, Kakegawa K. Development of formation method for homogenous and fine eutectic like microstructures with off eutectic composition in various rare-earth oxide—Al2O3 systems. Adv Appl Ceram. 2009;108:78–83.CrossRefGoogle Scholar
  13. 13.
    Raj R, Cologna M, Francis JS. Influence of externally imposed and internally generated electrical fields on grain growth, diffusional creep, sintering and related phenomena in ceramics. J Am Ceram Soc. 2011;94:1941–65.CrossRefGoogle Scholar
  14. 14.
    Tarafder A, Molla AR, Karmakar B. Effects of nano-YAG (Y3Al5O12) crystallization on the structure and photoluminiscence properties of Nd3+-doped K2O–SiO2–Y2O3–Al2O3 glasses. Sol Sci. 2010;12:1756–63.CrossRefGoogle Scholar
  15. 15.
    Prnová A, Galusek D, Hnatko M, Kozánková J, Vávra I. Composites with eutectic microstructure by hot pressing of Al2O3–Y2O3 glass microspheres. Ceram Silik. 2011;55:208–13.Google Scholar
  16. 16.
    Šesták J, Šimon P, editors. Thermal analysis of micro, nano- and non-crystalline materials: transformation, crystallization, kinetics and thermodynamics. New York: Springer; 2013. p. 225–46.Google Scholar
  17. 17.
    Avrami M. Kinetics of phase change. III. Granulation, phase change, and microstructure kinetics of phase change. J Chem Phys. 1941;9:177–84.CrossRefGoogle Scholar
  18. 18.
    Avrami M. Kinetics of phase change. I. General theory. J Chem Phys. 1939;7:1103–12.CrossRefGoogle Scholar
  19. 19.
    Avrami M. Kinetics of phase change. II. Transformation-time relations for random distribution of nuclei. J Chem Phys. 1940;8:212–24.CrossRefGoogle Scholar
  20. 20.
    Kolmogorov AE. On the statistic theory of metal crystallization. Izv Akad Nauk SSSR Ser Mat. 1937;1:355–9 (in Russian).Google Scholar
  21. 21.
    Johnson WA, Mehl RF. Reaction kinetics in processes of nucleation and growth. Trans Am Inst Min Metall Pet Eng. 1939;135:416–58.Google Scholar
  22. 22.
    Tanaka H. Thermal analysis and kinetics of solid state reactions. Thermochim Acta. 1995;267:29–44.CrossRefGoogle Scholar
  23. 23.
    Šesták J, Šatava V, Wendlandt WW. The study of heterogeneous processes by thermal analysis. Thermochim Acta. 1973;7:333–556.CrossRefGoogle Scholar
  24. 24.
    Málek J. The applicability of Johnson–Mehl–Avrami model in thermal analysis of crystallization kinetics of glasses. Thermochim Acta. 1995;267:61–73.CrossRefGoogle Scholar
  25. 25.
    Vyazovkin S, Burnham AK, Criado JM, Perez-Maqueda LA, Popescu C, Sbirrazzuoli N. ICTAC kinetic committee recommendation for performing kinetic computations on thermal analysis data. Thermochim Acta. 2011;520:1–19.CrossRefGoogle Scholar
  26. 26.
    Johnson JB, Omland KS. Model selection in ecology and evolution. Trends Ecol Evol. 2004;19:101–8.CrossRefPubMedGoogle Scholar
  27. 27.
    Cavanaugh JE. Criteria for linear model selection based on Kullback’s symmetric divergence. Aust N Y Stat. 2004;46:257–74.CrossRefGoogle Scholar
  28. 28.
    Akaike H. Information theory and an extension of maximum likehood principle. In: Petrov BN, Csáki F, editors. 2nd international symposium on information theory. Budapest: Akadémia Kiadó; 1973. p. 267–81.Google Scholar
  29. 29.
    Akaike H. A new look at the statistical model identification. IEEE Trans Autom Control. 1974;19:716–23.CrossRefGoogle Scholar
  30. 30.
    Kim HJ, Cavanaugh JE. Model selection criteria based on Kullback information measures for nonlinear regression. J Stat Plan Inference. 2005;134:332–49.CrossRefGoogle Scholar
  31. 31.
    Roduit B, Hartmann M, Folly P, Sarbach A, Baltensperger R. Prediction of thermal stability of materials by modified kinetic and model selection approaches based on limited amount of experimental points. Thermochim Acta. 2014;579:31–9.CrossRefGoogle Scholar
  32. 32.
    Pechini MP. Method of preparing lead and alkaline-earth titanates and niobates and coating method using the same to form a capacitor. US Patent No. 3 330 697, 1967.Google Scholar
  33. 33.
    Prnová A, Bodišová K, Klement R, Migát M, Veteška P, Škrátek M, Bruneel E, Driessche IV, Galusek D. Preparation and characterization of Yb2O3–Al2O3 glasses by the Pechini sol–gel method combined with flame synthesis. Ceram Int. 2013;40:6179–84.CrossRefGoogle Scholar
  34. 34.
    Prnová A, Klement R, Bodišová K, Valúchová J, Galusek D, Bruneel E, Driessche IV. Thermal behaviour of ytrium aluminate glasses studied by DSC, high temperature X-ray diffraction, SEM and SEM-EDS. J Therm Anal Calorim. 2017;128:1407–15.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Anna Prnová
    • 1
  • Alfonz Plško
    • 1
  • Jana Valúchová
    • 1
  • Peter Švančárek
    • 1
  • Róbert Klement
    • 1
  • Monika Michálková
    • 1
  • Dušan Galusek
    • 1
  1. 1.Vitrum Laugaricio – Joint Glass Center of the IIC SAS, TnU AD and FCHTP STUTrenčínSlovak Republic

Personalised recommendations