Crystallization kinetics and thermal stability in Ge–Sb–Se glasses

Abstract

The crystallization kinetics of Ge–Sb–Se chalcogenide glasses prepared by melt-quenching method was investigated using differential scanning calorimetry under non-isothermal conditions with several different heating rates. Kissinger's equation and Matusita model were employed to analyze kinetic crystallization behavior of the glasses. The crystallization parameters were calculated and the crystallization mechanism was studied. The results indicate that the crystallization activation energy increases rapidly at the glass with a mean coordination number (MCN) of 2.4, and reaches its maximum at MCN of 2.65. These two transition thresholds correspond to the structural phase transition in the glassy network. The evolution of the glass transition temperature (T_g), activation energy for crystallization (E_c), glass forming ability and thermal ability as functions of MCN and chemical composition might have substantial implication on screening the best glass for the application in photonics.

1 Introduction

Chalcogenide glasses are promising for the application in integrated non-linear optical components due to their high refractive index, large non-linearities, as well as low optical loss 1. However, structural instability in chalcogenide glasses, which is intrinsical in amorphous materials hampers further applications in optoelectronics 2. Therefore, for an application in photonics, one of the challenging issues is to find out the best chalcogenide compositions with relatively stable structure. For this purpose, crystallization kinetics in the glasses plays an important role in determining the stability of amorphous materials as well as understanding the crystallization mechanism 3, 4 and directing the subsequent annealing processing of chalcogenide glasses.

Among various chalcogenide glasses, Ge–Sb–Se systems have received attention because of their important optical applications since they are good transmitters in the infrared region (the range 2–16 µm) 5–8. Compared with Ge–As–Se systems that have been well used to create integrated optical waveguide devices 9–11, replacement of highly toxic element As with Sb makes the glass more environmentally-compatible, therefore searching Ge–Sb–Se glasses with stable structure and excellent optical properties is important for the application in photonics. Although there are few reports on the study of crystallization kinetics in Ge–Sb–Se glasses, systematical investigation on this issue over a wide compositional range is rare. This is particularly interesting in ternary glasses, since the physical properties of the glasses are arguably dominated by mean coordination number (MCN) which is defined as a sum of the respective elemental concentrations times their covalent coordination number, while they are naturally expected to be tuned by chemical compositions 11, 12.

The present paper concentrates on the study of the crystallization kinetics, thermal stability, glass forming ability, and the activation energy of crystallization for Ge–Sb–Se glasses over a wide compositional range using the non-isothermal technique. Take Ge_12.5Sb₂₅Se_62.5 for example, two different methods, Kissinger's equation and Matusita model have been employed to evaluate the crystallization activation energy in glasses in relation to MCN. The evolution of the glass transition temperature, activation energy for crystallization, glass forming ability and thermal ability, and their correlation with MCN and chemical compositions were further discussed.

2 Experiments

High purity (99.999%) germanium, antimony, and selenium metals were loaded in a cleaned and dried quartz ampule which was subsequently heated at 110 °C for 4 h to remove surface moisture from the raw materials. The ampule was then sealed under vacuum (10⁻⁶ Torr) using oxygen hydrogen torch and introduced into a rocking furnace for melting of the contents at 900 °C. Not <30 h continuous stirring of the melt was carried out to make good homogeneity. The melt was finally removed from the furnace and then rapidly quenched in air to form bulk glass. The resulting glass boule was subsequently annealed at a temperature of 30 °C below the glass transition temperature to reduce the internal stress that may be formed during the quenching.

Glass powders weighing about 20 mg were sealed in standard aluminium pans. A series of differential scanning calorimetry (DSC, Shimadzu DSC-50) curves were measured at different heating rates (α) of 7, 10, 14, 20, and 30 K min⁻¹, respectively, with nitrogen gas flux of 30 ml min⁻¹.

Results and discussion

A typical DSC curve for Ge_12.5Sb₂₅Se_62.5 glass obtained at a heating rate of 10 K min⁻¹ is plotted in Fig. 1 It is clear from this figure that two well-defined characteristic transitions, such as endothermic and exothermic peaks, were observed at glass transition temperature (T_g = 523.8 K) and crystallization peak temperature (T_p = 663.7 K), respectively. As defined in Ref. 13, the crystallization process is characterized by several temperatures, where T_c corresponds to the onset crystallization temperature (T_c = 638.8 K), T_s to that the crystallization just starts and T_e to that the crystallization completes. This behavior is typical for a glass-crystal transformation, and similar curves have been found for other glasses with different heating rates (not shown here). The characteristic temperatures at a heating rate of 10 K min⁻¹ in Ge–Sb–Se glasses are given in Table 1.

Figure 1. (online color at: www.pss-b.com) Typical DSC curves at a heating rate of 10 K min⁻¹ for Ge_12.5Sb₂₅Se_62.5. The inset shows ln (α/T) against 1000/T_p for Ge_12.5Sb₂₅Se_62.5.

Table 1. Several typical temperatures (K) at a heating rate of 10 K min⁻¹, the crystallization activation energy (kJ mol⁻¹) and kinetic exponent (n) for Ge–Sb–Se glasses.

sample composition			MCN	Tg	Tp	Tc	Kissinger's equation	Matusita model	n
Ge	Sb	Se
5	10	85	2.2	347.3	531.4	511.7	94.7	108.3	2.76
7.5	10	82.5	2.25	380.4	569.2	532.9	105.9	121.3	1.29
7.5	15	77.5	2.3	389.8	572.5	543.3	109.1	129.2	2.22
7.5	20	72.5	2.35	411.8	558.1	542.9	114	134.5	4.07
10	20	70	2.4	435.3	606.8	574.3	152.3	156.4	1.59
10	25	65	2.45	467.2	616.9	594.3	181	169.2	2.19
12.5	20	67.5	2.45	461.8	622.6	597.7	179.3	171.1	1.91
12.5	25	62.5	2.5	523.8	663.7	638.8	193	229.9	1.98
15	25	60	2.55	510	656	639.2	198.6	225.9	1.76
18	23	59	2.59	522.3	686.7	651.9	201.8	231.7	1.17
22.5	20	57.5	2.65	530.8	651.9	633.3	204.3	233.3	2.68
25	20	55	2.7	533.7	627.1	615.2	193.5	226.5	4.23
27.5	15	57.5	2.7	545	652.4	631.3	199.9	214.6	2.66
32.5	10	57.5	2.75	566.4	680.1	667	188.7	199.9	3.95

The activation energy can be estimated by the Kissinger's equation 14, where T_g is correlated with the heating rate α as

• ((1))

where E_a and R are the activation energy for glass transition and the universal gas constant, respectively. A modified Kissinger equation was also employed to calculate the activation energy for crystallization (E_c) 15, where the crystallization peak temperature of T_p has a similar relation with the heating rate:

• ((2))

The inset in Fig. 1 shows the relation of ln(α/T) versus 1000/T_p for Ge_12.5Sb₂₅Se_62.5 glass. The crystallization activation energy E_c estimating from the slope of plots is 193.0 ± 3.2 kJ mol⁻¹.

The Matusita model was another suitable model that was frequently used to quantitatively describe the crystallization process and dimensionality of the crystals under non-isothermal conditions 16. In this method, the crystallization fraction (χ) precipitated in the glass heated at a fixed rate, is related to the activation energy for crystallization (E_c), through the following expression,

• ((3))

where n and m are integers related to the crystallization mechanism and the dimensionality of the crystal growth. When the nuclei are formed during heat treatment prior to thermal analysis, n is equal to m 15, 17, 18. One-, two-, or three-dimensional growth occurs corresponding to m = 1, 2, or 3, respectively 16–20. The fraction χ crystallized at any temperature T is given by χ = A_T/A, where A is the total area of the exothermic peak between T_s and T_e, and A_T is the partial area of the exothermic peak between temperature T_s and T as shown by the hatched portion in Fig. 1.

Figure 2 shows the plots of ln[−ln(1−χ)] versus lnα at three different temperatures. The kinetic exponent n can be obtained from the slopes of these curves. The averaged n is 1.98 ± 0.07 for the chalcogenide glass Ge_12.5Sb₂₅Se_62.5. Therefore, the round-off number of n is 2 as well as m, which suggests that the crystallization mechanism is concluded to be two-dimensional growth. This result is in good agreement with those reported by Bordas et al. 21.

Figure 2. (online color at: www.pss-b.com) ln[−ln(1−χ)] versus lnα for the Ge_12.5Sb₂₅Se_62.5 chalcogenide glass at three different temperature.

The activation energy E_c for crystallization can also be obtained from Matusita's equation by plotting ln[−ln(1−χ)] against 1000/T as shown in Fig. 3. From the slopes of these curves, an average of mE_c values was calculated by considering all the heating rates. From the value of m and the slopes in Fig. 3, the average value of the crystallization activation energy for Ge_12.5Sb₂₅Se_62.5 is equal to 229.9 ± 2.6 kJ mol⁻¹, which is about 15% larger than the estimated value from Kissinger's equation. The difference in E_c should be attributed to the different approximations used in these models.

Figure 3. (online color at: www.pss-b.com) ln[−ln(1−χ)] against 1000/T for the Ge_12.5Sb₂₅Se_62.5 chalcogenide glass at different heating rates.

The total area of the exothermic peak is directly proportional to the amount of glass that has been crystallized. Following Ref. 22, 23, we define the corresponding crystallization rate as:

• ((4))

Figures 4 and 5 show the plot of crystallized fraction (χ) and the plot of crystallization rate (dχ/dt) as a function of temperature, respectively. The typical sigmoid curves as a function of temperature for different heating rates can be observed in Fig. 4 during the crystallization processes that are in agreement with the results in Ref. 24, 25. One can also infer from Figs. 4 and 5 that the saturation of crystallization shifts towards the higher temperature as the heating rate increases 26.

Figure 4. (online color at: www.pss-b.com) Crystallized fraction (χ) as a function of temperature at different heating rates.

Figure 5. (online color at: www.pss-b.com) Rate of crystallization (dχ/dt) versus temperature at different heating rates.

The crystallization activation energy for Ge–Sb–Se glasses estimated using different approaches were summarized in Table 1. Figure 6 shows the crystallization activation energy as a function of MCN. Basically, the estimated E_c from Masusita's method is slightly larger than that from Kissinger's equation. Nevertheless, the evolution tendency of E_c as a function of MCN is same as shown in Fig. 6, where E_c starts to increase rapidly at around MCN = 2.4 and has a maximum at MCN = 2.65. This is in excellent with the previous constraint argument in the network of chalcogenide glasses, where MCN = 2.4 corresponds to a transition from an under-constrained to an over-constrained network 27, 28, while MCN = 2.67 to a transition from 2- to 3-dimensional structure 29, 30. However, the kinetic exponent shows no clear trend against MCN. These results can be analyzed assuming that a kinetic compensation effect 31 occurs, which arises from the crystallization dynamic processes 32, 33.

Figure 6. (online color at: www.pss-b.com) Crystallization activation energy as a function of MCN.

Dietzel 34 investigated the difference between T_c and T_g, and used ΔT = T_c − T_g as a criterion to judge thermal stability in the glasses. The higher the value of this difference, the more the delay in nucleation, therefore more stable in the glass 35, 36. The glass forming ability is another indicator of the relative ability of the glass remaining in the amorphous state, which can be determined using Hruby number 37 based on the characteristic temperatures,

• ((5))

where T_m is the melting temperature that can be estimated by using an empirical “two-thirds rule” (T_g/T_m = 2/3) 38–40. Higher values of ΔT indicate a delayed nucleation process while smaller values of (T_m − T_c) defer growth after nucleation. Therefore higher values of ΔT and H_r reflect greater thermal stability of the glass. Figure 7 illustrates the glass transition temperature, thermal stability and glass forming ability as functions of MCN. Basically, the glass transition temperature increases monotonically, but the thermal stability and glass forming ability decreases with MCN. Consequently, the glasses with MCN of 2.4–2.5 should be suitable for the application in photonics since the material have a reasonably high glass transition temperature, strong glass forming ability, good thermal stability, and low crystallization activation energy.

Figure 7. (online color at: www.pss-b.com) Glass transition temperature, thermal stability and glass forming ability as functions of MCN.

To understand the role of the chemical composition and MCN, we plotted the evolution of the crystallization activation energy, glass transition temperature, thermal stability, and glass forming ability for five pieces of the glasses with the same concentration of Sb at 20 at% but different Ge contents from 7.5 to 25 as shown in Fig. 8. It is clear that T_g increases with increasing content of Ge, and the maximum of E_c appears at 22.5 at% of Ge. For the thermal stability and glass forming ability, both of them increase with increasing Ge concentration up to 10 at%, and then decrease with further addition of Ge. Nevertheless, the maximum values observed at the glasses with 10 and 22.5 at% Ge correspond to MCN of 2.4 and 2.65, respectively.

Figure 8. (online color at: www.pss-b.com) Crystallization activation energy, glass transition temperature, thermal stability and glass forming ability as functions of chemical compositions and MCN.

Our recent results have shown that, Ge–As–Se glasses with MCN of 2.4–2.5 generally have relatively low fragility index, and thus strong glass-forming ability and relatively stable glass network 41. The same behavior can be found in Fig. 8 for Ge–Sb–Se glasses. For Se-rich glasses with lower MCN, Se-chain and -ring structure can be expected. Addition of Ge into the glass will increase the degree of cross-linking, leading to increasing T_g 42. However, if Ge and Sb concentrations reach certain amounts where all Se can be consumed out, homopolar bonds such as Ge–Ge and Sb–Sb can be formed. In the case of Se-heavily-poor glass, phase separation can occur in the nano- or micrometer scale, destroying the connectivity of the glass network and reducing the thermal stability and glass forming ability 43.

4 Conclusions

The investigation on non-isothermal crystallization kinetics in Ge–Sb–Se glasses was performed using DSC with five different heating rates of 7, 10, 14, 20, 30 K min⁻¹, respectively. Two different approaches, Kissinger's equation and Matusita model were employed to analyze kinetic crystallization. E_c estimated from Matusita model is slightly larger. However, the evolution of E_c as a function of MCN follow an identical tendency, e.g. E_c starts to increase rapidly at around MCN = 2.4 and the maximum E_c appears at MCN = 2.65, corresponding to the structural transitions in the glassy network. Our results show that the appropriate glass for the application in photonics should have a composition with MCN of 2.4–2.5 where the glass exhibits a reasonably high glass transition temperature and low crystallization activation energy, as well as good thermal stability, and strong glass forming ability.

Acknowledgements

This research was supported by the Fundamental Research Funds for the Central Universities (Project No. CDJXS11100004), the Graduate Innovation Foundation (No. CDJXS11102210), the International Science and Technology Cooperation Program of China (Grant No. 2011DFA12040), the National Program on Key Basic Research Project (973 Program) (Grant No. 2012CB722703), the Natural Science Foundation of China (Grant Nos. 61008041 and 60978058), the Natural Science Foundation of Zhejiang Province, China (Grant No. Y1090996), the Natural Science Foundation of Ningbo City, China (Grant No. 2011A610092), the Program for Innovative Research Team of Ningbo city (Grant No. 2009B21007). WWH acknowledges the financial support from China Scholarship Council.