The phase structure, transitions, and non-isothermal crystallization kinetics of Zn2V2O7 glass

The Zn2V2O7 glass was prepared by solid-state reaction using the initial reactant ZnO and V2O5 powder. X-ray diffraction was employed to characterize the phase composition of the as-prepared Zn2V2O7 powder. The crystallization kinetics of Zn2V2O7 glass prepared by solid-state reaction was studied using differential thermal analysis under non-isothermal conditions. It was established that the crystallization process of Zn2V2O7 can be divided into two steps, which is controlled first by a Disc-like with kinetic equation G(α)=[-ln(1-α)]1/3 and then by a Fibril-type growth type with kinetic equation G(α)=[1-(1-α)1/3]1/2 . The apparent activation energy calculated by different methods (Kissinger method, Ozawa method, Tang method, and Starink method) under non-isothermal conditions were similar, varying between 335.6 kJ·mol−1 and 371.6 kJ·mol−1, and the average apparent activation energy was equal to 362.2 kJ·mol−1.


Introduction
Multicomponent transition metal oxides (TMOs) have attracted widespread attention as the most promising candidate materials for advanced technological applications in contrast with their counterbinary oxides [1][2][3][4].The enhancement in the performance is due to the presence of two metals in these double oxide species, which render additional redox reactions during the device operation.which depends on the relationship between heat flow and temperature was intensively applied in the crystallization process to understand the reaction mechanism [12][13][14][15].
In the present study, the Zn2V2O7 was prepared by solid-state reaction using ZnO and V2O5 powder as raw materials, and X-ray diffraction (XRD) was conducted to analyze and characterize the Zn2V2O7 compound.Above all, we investigated the temperature change of two kinds of phase transition of Zn2V2O7 using TG and DSC treatment.In addition, we aimed to present a detailed analysis of the nonisothermal crystallization kinetics based on the various DSC curves, mechanism analysis was deduced by using the Avrami method, and the apparent activation energy was calculated and compared by using various methods, such as Kissinger method, Ozawa Method, Tang method, and Starink method.

Non-isothermal crystallization mechanism analysis
2.1.1.Avrami model.Non-isothermal kinetic analysis based on the linear heating or cooling process is widely applied with the rapid development of thermal analysis technology [16,17], various methods were deduced to explore the reaction mechanism and calculate the apparent activation energy during the non-isothermal crystallization process.As the most common method, the Avrami model [18] and Ozawa model [19] have been extensively employed in previous studies, which was derived from the isothermal system and extended to the non-isothermal system by substituting reaction time with temperature.Ding et al [20] studied the non-isothermal kinetics of the 2CaO• Fe2O3 and CaO• Fe2O3 in the CaO-Fe2O3 system by employing the Avrami model, indicating this model is much more suitable for studying its crystallization.
The degree of conversion, α, is the volume fraction of the sample transformed into the crystalline phase at temperature T1 during crystallization and can be obtained from the DSC curves using the following Eq.( 1): where α(T) is the conversion ratio that corresponds to the temperature period in the temperature range T0 to T1. S T T0 is the area integrated under the heat flow peak and the baseline from the initial crystallization temperature T0 to a specific crystallization temperature T. S T1 T0 is the total area from the initial temperature T0 to the final temperature T1.
During the non-isothermal crystallization process for the various cooling rates β, the conversion ratio corresponding to temperature can be obtained directly, while the Avrami model was formulated using the conversion ratio as a function of time, the relationship between temperature and time can be defined as shown in Eq. ( 2): 0 In the present study, the relationship between conversion ratio and time can be determined by substituting the temperature with time, which can be further described as shown in Eq. ( 3): where α(t) is the conversion ratio at a given time t corresponding to a specific temperature, K is the rate constant of crystallization change, and n is the Avrami exponent, which is determined by using time t and the conversion ratio α by plotting ln[−ln (1−α)] against lnt, as shown in Eq. ( 4): where the Avrami model exponent n represents a type of nucleation and growth mechanism [21].Table 1 shows the crystallization growth type based on different n values.The Avrami model derived from the non-isothermal process should be modified to include the parameter K of the formula when extending to the non-isothermal process.Jeziorny [22] amended K as shown in Eq. ( 5):

Calculation of activation energy using various methods
Besides the mechanism analysis for the non-isothermal crystallization of Zn2V2O7, the apparent activation energy is another critical parameter, which indicates the additional energy for an atom to create an activated cluster.The apparent activation energy was determined and compared using various methods, such as the Kissinger method, Ozawa Method, Tang method, and Starink method in the present study.

Kissinger method.
The most frequently used method of apparent activation energy evaluationthe Kissinger method [23], is applicable only for non-isothermal experiments where the temperature corresponding to the maximum peak (Tp) shifts with the heating rate (β).The slope of the line, which plots the ln (β/T 2 P ) dependence on 1/Tp, is equal to the -E/R, as shown in Eq. ( 6).
Where Tp is the peak temperature of heat flow curves at a fixing heating rate, A is the pre-exponential coefficient, and E is the apparent activation energy of the non-isothermal crystallization.
The Kissinger method can be further converted to Eq. ( 7): Apparent activation energy can be calculated using the slope of the plot of ln (|β|/T 2 P ) against 1/T P .According to the Kissinger method [23], the peak temperature in the DSC curves at various heating rates must be obtained first.After fitting the plots of ln (|β|/T 2 P ) against 1/T P , Thus, the apparent activation energy was calculated from the slope of the fitted line.

Ozawa method.
Very similar to Kissinger's Method [23], Ozawa [19] simplified it by using Dolye's approximation [24] and proposed a new method to calculate the activation energy under the non-isothermal kinetic analysis of crystallization, as shown in Eq. ( 8) where Tp is the peak temperature at a specific heating or cooling rate, A is the pre-exponential coefficient, and E is the apparent activation energy of crystallization.Apparent activation energy E can be calculated using the slope of the plot of ln (β) against 1/T P .

Tang method.
The Flynn-Wall-Ozawa [25,26] and Kissinger-Akahira-Sunose [23] methods can be expressed in the general formula, as shown in Eq. ( 9) where Tp is the peak temperature, Donghua and Wanjun [27] presented a method in which the parameters s and A were treated as the constant values, namely s = 1.895 and A = 1.00145.Then, Eq. ( 10) is rearranged as Apparent activation energy E can be calculated using the slope of the plot of ln (|β|/T 1.895 ) against 1/T P .

Starink method.
Modifications were further done based on linear regression and mathematical analysis by Starink [28], and they deduced a new formula in which s = 1.92 and A = 1.0008,Then, Eq. ( 11) is rearranged as where Tp is the peak temperature, Apparent activation energy E can be obtained using the slope of the plot of ln (|β|/T 1.92 ) against 1/T P .

Experimental process
The raw materials ZnO (99.99%, purity) and V2O5 (99.99%, purity) were provided by Shanghai Jingjinle Industry Co., LTD.Before preparing the desired sample, the powder ZnO and V2O5 were first separate pre-roasting at 473 K for approximately 3 h under the constant flow of argon (50 ml• min -1 ) to remove any absorbed moisture.The Zn2V2O7 sample was then prepared by the repeated roasting and crushing method, for the first step, the starting materials ZnO and V2O5 were thoroughly mixed to obtain a homogenous mixture, according to the specific molar ratio (ZnO: V2O5 = 2:1).The mixture was compacted into some pellets with 12 mm diameter utilizing hydraulic press under 10 Mpa, and the pellets was subsequently heated from room temperature to target temperature of 873 K with a heat rate of 10 K/min and maintained for 10 h to complete solid-state reaction, the calcinated samples cooled down to room temperature within furnace and immediately pulverized in a vibration mill.Repeating the above procedure twice until the high-purity and homogenous Zn2V2O7 sample was finally obtained.
The phase composition was checked using X-ray diffraction (XRD, Model D/max2500/PC; Cu Kα) with an angular range of 10°-90° and a scan rate of 3°/min.Qualitative and quantitative analyses of XRD patterns compared with standard one (NO #70-1523) were performed to verify the prepared Zn2V2O7 sample after several roasting and cooling processes.Differential scanning calorimetry was carried out using a Netzsch thermal analyzer (Model STA 449C).The Zn2V2O7 sample (approximately 12 mg) was tiled in a Pt crucible, with an Al2O3 crucible as a reference.The samples were heated from room temperature to 900°C and then cooled to room temperature at the specific cooling rates of 10 °C/min, 15 °C /min, and 20 °C /min in an argon atmosphere with a gas flow rate of 50 ml/min.The various heat flow curves can be obtained to analyze the non-isothermal crystallization process and calculate the apparent activation energy.The heat flow curve was obtained to analyze the polycrystalline transition temperature and enthalpy change.

Phase structure and transitions of Zn2V2O7 glass
The Zn2V2O7 compound has two polymorphs forms, namely α-Zn2V2O7 at low temperature, and β-Zn2V2O7 at high temperature, Figure 1 shows the XRD patterns of the prepared sample at room temperature along with a standard PDF card, indicating typical reflections of Zn2V2O7 phase (PDF#70-1523).No additional reflection of other phases, e.g., initial reactants, were observed.Narrow and strong reflection confirmed the good crystallinity of the as-prepared sample.The refinement of the cell parameters shows that the Zn2V2O7 crystallizes in monoclinic system, belonging to space group C2/c, with the lattice parameters a=7.429Å, b=8.340Å, c=10.098Å, which was very close to the reference one (PDF#70-1523) and previous study by Gopal et al. [29] and Chen et al. [30].The results were presented and compared as shown in Table 2 Quantitative analysis by Jade 6.0 ® indicated that the Zn2V2O7 sample mainly comprises Zn2V2O7 with approximately 95%.TG and DSC investigation were both carried out in the present study to determine the temperature change of two kinds of phase transition with a heat rate of 10℃/min up to 900 ℃ as shown in Figure 2, no significant mass loss occurs in the temperature ranging from 150-950 ℃ in the TG curve.The DSC curve exists in two obvious endothermic peaks corresponding to polymorphic transition and melt fusion.The temperature of polymorphic transition and melt fusion is determined on the onset of heat flow peak, which was presented and compared with the previous studies as shown in Table 3, indicating that the values excellently agree with previous work Kurzawa M et al. [9]， Makarov VA et al. [10], and Clark GM et al. [11].

Non-isothermal crystallization kinetics of Zn2V2O7 glass
In this study, many curves corresponding to different cooling rates of 10 ℃/min, 15 ℃/min, and 20 ℃/min were obtained during the non-isothermal crystallization process using DSC investigations as shown in Figure 3 those curves can be applied to analyze the reaction mechanism and calculate apparent activation for non-isothermal crystallization process of Zn2V2O7.The positions and intensities of these heat flow peaks change with the cooling rate, the positions of the heat flow peaks are shifted to lower temperatures with increasing cooling rate, which indicates that cold crystallization was activated.The intensities, corresponding to the enthalpy changes during the non-isothermal crystallization process; increase with raising the cooling rates, indicating that increased cooling rates can reinforce the thermal hysteresis phenomenon during the non-isothermal crystallization process, this conforms to the basic physical-chemical rules.For the shape of each heat flow peak, the temperature of heat flow is obvious and can be explained by basic physical-chemical knowledge, the freezing point of a pure substance is constant and only changes with rising cooling rates.See other articles for more on the principles of analysis.[32,33] Fig. 3 Heat flow vs. temperature during non-isothermal crystallization at different cooling rates.

Crystal mechanism analysis.
According to the Avrami model, the conversion ratio corresponding to temperature and time for non-isothermal melt and cold crystallization is obtained using the original DSC curves as shown in Figure 4 and Figure 5, the sigmoid shape of the temperature dependence of the degree of conversion indicated bulk crystallization and excludes the possibility of surface crystallization.For all the cooling rates, these curves can be separated into two characteristic regions corresponding to the two physical stages of non-isothermal crystallization: a rapid initial period in which nucleation is dominant, followed by a process of slow growth of nuclei.The non-isothermal cold crystallization of Zn2V2O7 included two stages based on the Avrami model, which were discussed in this study.As shown in Table 4, Kc increased with increasing heating rates both in Stage 1 and Stage 2, indicating that increasing the heating rate increases the cold crystallization rate; this conclusion is consistent with the actual situation.In addition, the n values of modification change of Zn2V2O7 are approximately between 2 and 3 for Stage 1 and between 1 and 2 for Stage 2. This finding indicates that the cold crystallization process of Zn2V2O7 is controlled first by a Disc-like and then by a Fibril-type growth type, which was consistent with the DSC curves.

Calculation of apparent activation energy using various methods.
In the present study, the peak temperature, corresponding to the different cooling rates, as shown in Table 5, was frequently used to calculate the apparent activation energy during the non-isothermal cool crystallization process [34].To obtain reasonable and credible results, lots of different methods have been applied to explore the apparent activation energy were applied and compared with each other in this study.After drawing the plots of ln(β/T 2 α ) against 1000/Tα (based on Kissinger method), ln(β) against 1000/Tα (based on Ozawa method), ln(β/T 1.895 α ) against 1000/Tα (based on Tang method) and ln(β/T 1.92 α ) against 1000/Tα (based on Starink method) for the non-isothermal cool crystallization process with reasonable linear fits, the corresponding apparent activation energy can be obtained from the slopes of those fitted lines and the values are shown in Table 6 and Figure 7, respectively.The apparent activation energy was extremely consistent with each other using the Kissinger method, Tang method, and Starink method, while the value obtained by the Ozawa method is a little bit lower than other methods as shown in Table 6, which may be caused by the method itself and the difference is within the normal range.The average apparent activation energy is 362.2 kJ• mol -1 , indicating the obtained values were correct and reasonable.(1) Kissinger method (2) Ozawa method (3) Tang method (4) Starink method Fig. 7 The calculations of the apparent activation energy during the non-isothermal crystallization process using various methods: (1) Kissinger method, (2) Ozawa method, (3) Tang method, and (4) Starink method.

Conclusions
The Zn2V2O7 glass was synthesized by solid-state reaction and characterized using XRD, TG, and DSC.Thermal analysis was applied to the crystallization kinetics of the Zn2V2O7 glass under non-isothermal conditions.It was established that the crystallization process can be divided into two steps, cold crystallization process of Zn2V2O7 glass is controlled first by a Disc-like with kinetic equation G(α)=[ln(1-α)] 1/3 and then by a Fibril-type growth type with kinetic equation G(α)=[1-(1-α) 1/3 ] 1/2 .The values of apparent activation energy of Zn2V2O7 glass calculated by different methods (Kissinger method, Ozawa method, Tang method, and Starink method) under non-isothermal conditions were close to each other and varied between 335.6 kJ• mol -1 -371.6 kJ• mol -1 , the average apparent activation energy is equal to 362.2 kJ• mol -1 .

Fig. 1
Fig. 1 XRD patterns of Zn2V2O7 and standard PDF card.

Fig. 2
Fig. 2 TG and DSC curves at a heating rate of 10℃•min -1 in Ar atmosphere.
It indicates that raising the heating and cooling rate shortens crystallization time.In addition, by drawing the plots of ln[−ln(1−α)] vs. lnt for the prepared Zn2V2O7 compound, the slope of those plots can be divided obviously into two stages with reasonable linear fits, namely Stage 1 and Stage 2, the Avrami kinetics parameter Kc and n of melt and cold crystallization are determined as shown in Figure 6, respectively.

Fig. 4
Fig.4 Conversion ratio corresponding to temperature for non-isothermal crystallization.

Fig. 5
Fig. 5 Conversion ratio corresponding to time for non-isothermal crystallization.

Table . 1
Correspondence between growth types and n Kc is the modified rate constant based on the non-isothermal crystallization.According to the Avrami model, Kc and n can be determined by the intercept and slope of plotting ln[−ln(1−α)] against 4where

Table . 3
The phase transition temperature of Zn2V2O7 glass.

Table . 5
The peak temperature corresponds to different cooling rates during the non-isothermal crystallization process.

Table . 6
The calculations of the apparent activation energy during the non-isothermal crystallization process using the Kissinger method, Ozawa method, Tang method, and Starink method.