Kinetics of Isothermal Crystallization of Amorphous ...

March 29, 2004

23:12

GFER

TJ977-15

Ferroelectrics, 298: 107–112, 2004 C Taylor & Francis Inc. Copyright ISSN: 0015-0193 print / 1563-5112 online DOI: 10.1080/00150190490423309

Kinetics of Isothermal Crystallization of Amorphous PbTiO3 S. A. GRIDNEV N. I. REPNIKOV Voronezh State Technical University Voronezh 394026, Russia A crystallization process of amorphous samples of PbTiO3 has been studied during 8 hours isothermal annealing at various temperatures in a vicinity of crystallization temperature Tcr = 600◦ C. It was revealed, that transition of amorphous material to a crystalline state is accompanied by a growth in value of its conductivity during the all time of isothermal annealing. It was established, that kinetics of isothermal crystallization may be described within the framework of the thermodynamic formalism of Kolmogorov– Johnson–Mehl–Avrami. Keywords Amorphous material; crystallization; conductivity; lead titanate

Introduction In recent years ultrarapid quenching of melts is frequently used for production of different materials in the nonequilibrium disordered state [1]. Already more than 40 years this method is used for manufacturing metal alloys with amorphous structure [2, 3], oversaturated solid solutions, amorphous semiconductors [4]. Much later (in 80th years) some papers which concern producing and research of amorphous ferroelectrics have appeared [5, 6]. The dielectric properties and structure of amorphous LiNbO3 [6, 7], phase transitions in amorphous PZT and BaTiO3 [8, 9], and also in amorphous KH2 PO4 were investigated in detail [10]. However, the great number of publications devoted to amorphous ferroelectrics, was related to studies of PbTiO3 as in amorphous, and partially crystallized states [5, 11–17]. In parallel with studying of structural peculiarities and the basic properties of amorphous PbTiO3 the significant attention was paid to one of the most interesting and important questions of physics of an amorphous state, i.e. a study of transition process from an amorphous state to a crystalline state. In work [18] this process was studied by the differential thermal analysis method which has allowed to determine an activation energy of crystallization process, and also a temperature of crystallization of the given material. Here a glass composition PbO-TiO2 -B2 O3 -BaO was taken as an object of a study. A process of crystallization was studied also in thin films of amorphous PbTiO3 using Raman scattering spectra [19] as well as dielectric response at sequential cyclic temperature change from room temperature up to the temperatures close to crystallization temperature [17]. It was established, that crystallization of amorphous PbTiO3 occurs in rather wide temperature range, and, apparently, in some stages. The evolution of the dielectric constant peak arising at the Curie temperature as a result of heating runs, when repeated many times, speaks in favor of many stage process of the crystallization. To study kinetics and mechanism of crystallization would be very Received May 29, 2003; In final form June 25, 2003.

107

March 29, 2004

23:12

GFER

TJ977-15

108

S. A. Gridnev and N. I. Repnikov

interesting and useful to carry out measurements of crystallization process in isothermal conditions at various temperatures. Therefore, the purpose of the present work was the study of kinetics of isothermal crystallization process in amorphous PbTiO3 samples with thickness of 0.1 mm.

Experimental The samples of amorphous PbTiO3 in the form of plates 3 × 3 × 0.1 mm3 in sizes have been prepared by ultrarapid quenching of melts. For this purpose the PbTiO3 powder which was prepared by mixing of oxide PbO and TiO2 powders first of all was melted in a quartz ampoule at a temperature near 1300◦ C, then the jet of melt moved on rapidly rotated copper disk which provided super fast melt quenching. A lot of small size thin plates of amorphous PbTiO3 are produced for one procedure of samples preparation. For the measurements 7 samples approximately of the identical sizes were taken. A chemical composition of the prepared samples was identified using X-ray spectrum microanalyser JXA-840. X-ray structural analysis (MoKα -radiation; graphite monochromator) confirmed an amorphous state of the obtained samples. The temperature of crystallization Tcr ≈ 600◦ C was determined by means of the differential thermal analysis. For a measurement of conductivity platinum electrodes were evaporated on the greatest surfaces of samples. The samples were placed in a thermostat, where the temperature was changed from 20 up to 670◦ C and was measured with an error less then ±1◦ C. During experiments a sample was heated up to some definite temperature (Tan ), at which during isothermal annealing (∼8 hours) measurements of time dependences of electric conductivity σ were carried out. We used the capacitance bridge E7–12 at a frequency of 1 MHz and at the amplitude of a measuring field 10 V/cm. For each subsequent procedure of measurements, which was carried out at other temperature Tan , a “fresh” sample was used, not exposed to preliminary thermal treatment. Fluctuations of temperature in a thermostat during the isothermal measurements did not exceed ±2◦ C.

Results and Discussion To study kinetics of crystallization of amorphous PbTiO3 the measurements of time dependences of conductivity were carried out at various temperatures of isothermal annealing in a vicinity of Tcr . It was revealed, that process of conversion of amorphous material to a crystalline state is accompanied by a growth of its electric conductivity during the all time of isothermal annealing (Fig. 1). As one can see in Fig. 1, the obtained kinetic curves have characteristic “σ -like” form i.e. firstly a conductivity grows slowly, then it changes faster, and then again slowly. At a study of crystallization process, using the measurements of a conductivity, a relative volume of a crystalline phase for any moment of time was determined from the following equation:

Vcr =

σf · [σ (t) − σi ] , σ (t) · [σf − σi ]

(1)

where σi and σf is the initial and final electric conductivity (i.e. for the amorphous and crystallized sample) accordingly, σ (t) is the conductivity for any time t. As it follows from the expression (1), the relative volume of crystalline phase Vcr during the crystallization process changes from 0 at σ (t) = σi up to 1 in a case as σ (t) = σf . The time dependence of Vcr at the annealing temperature 600◦ C is plotted in Fig. 2. At other temperature annealing such as 575◦ C and 625◦ C curves Vcr (t) have a similar form.

March 29, 2004

23:12

GFER

TJ977-15

Isothermal Crystallization of Amorphous PbTiO3

109

FIGURE 1 The dependence of a conductivity on a time of isothermal annealing at various temperatures. Thus, there exists a possibility, to study kinetics of isothermal transformation of a disordered material from amorphous to a crystalline state using data of Vcr (t) measurements. The time dependences of a nucleition and a growth of a crystalline phase in the amorphous matrix obtained in the experiment were approximated by the equation of Kolmogorov– Johnson–Mehl–Avrami [20]:

1 − Vcr = exp(−Ktn ),

(2)

where Vcr is the volume fraction of material crystallized for time t; n is the Avrami exponent describing a nature of a nucleition and growth of a crystal; K is the kinetic factor dependent on temperature according to the Arrhenius equation. The Eq. (2) was derived for a condition, that nuclei of a new phase are randomly distributed in a bulk of a sample and that a growth rate of a new phase depends on temperature [20].

FIGURE 2 The time dependence of relative volume of a crystallized phase during the isothermal annealing at 600◦ C.

March 29, 2004

23:12

110

GFER

TJ977-15


FIGURE 3 The dependence of ln [−ln(1 − Vcr )] on lnt for isothermal annealing at the temperature 600◦ C. It is convenient to present the Eq. (2) as follows:

Vcr = 1 − exp[−(t/τ )n ].

(3)

Here the time of a relaxation τ is defined by the formula

τ = τ0 exp(Ecr /kT),

(4)

where Ecr is the activation energy of the crystallization process, k is the Boltzmann constant. To find the Avrami exponent from the experimental data, one can take the logarithm of the Eq. (3). As a result one has

ln[− ln(1 − Vcr )] = n ln t − n ln τ.

(5)

It is not difficult to see, that the Eq. (5) is the equation of the straight line in coordinates ln [−ln (1 − Vcr )] against lnt. It allowed us to find parameters n and τ at various temperatures of isothermal annealing and then to estimate the crystallization energy Ecr from the Eq. (4). For illustration the dependence of ln [−ln(1 − Vcr )] versus lnt is shown in Fig. 3 for T = 600◦ C with values of the Avrami exponent n estimated in different parts of a curve. In this case the value n is appeared to be equal 0.23 and 0.5 for two linear parts, where the experimental points fall approximately on the straight lines. The fractional value of a parameter n, apparently, speaks about a fractal nature of nuclei [21]. It should be noted that at other temperatures the dependences of ln [−ln(1 − Vcr )] versus lnt have a form, qualitatively similar to the curve obtained at T = 600◦ C, therefore values of a parameter n were estimated for them similarly: n = 0.6 at T = 575◦ C and n = 0.37 and 0.65 at T = 625◦ C, accordingly. Fractional values of the parameter n describing growth of a new phase, were observed also at the experimental study of time dependences in KNO3 [22] and PZT-19 [23, 24]. In these papers as a possible reason of fractional values of n the dependence of the velocity of interphase wall movement on a wall curvature (bends on it) during a process of nuclei growth was considered. From the experimental data it was revealed, that the more the time of samples annealing is, the higher a parameter n in each part of curve is observed. In Fig. 3 it is clearly seen, that

March 29, 2004

23:12

GFER

TJ977-15

Isothermal Crystallization of Amorphous PbTiO3

111

FIGURE 4 The dependence of lnσ on the annealing time at T = 600◦ C. parameter n tends to 1 as the annealing time becomes more than 7 hours. According to Ref. [20], the value n = 1 corresponds to the needle-like form of crystalline phase nuclei. Such nuclei are called one-dimensional ones and they, as a rule, characterize only an onset of the crystallization process. Therefore evidently, that 8 hour annealing of amorphous PbTiO3 is not sufficient for full crystallization of a sample. Assuming, that time dependence of conductivity during a process of isothermal crystallization obeys the conventional exponential law

σ = σ0 exp(t/τ ),

(6)

where σ0 is the temperature independent factor and τ is the relaxation time, we plotted the dependence of lnτ on t using obtained experimental data. In Fig. 4 such dependence is displayed for the temperature T = 600◦ C from which a value of relaxation time τ was estimated to be equal of 2253 minutes. In a case of other temperature, particularly at T = 575◦ C the value τ = 4032 minutes, and at T = 625◦ C the value τ = 1440 minutes. One can see, that τ decreases with an increase of isothermal annealing temperature, testifying that a process of crystallization is thermally activated. Using the Eq. (4) and values of relaxation times at various temperatures, we evaluated an activation energy of crystallization process Ecr which appeared to be equal about 2 eV. This value well agrees with the value Ecr = 2 ÷ 3 eV obtained in Refs. [11, 12].

Summary Amorphous materials prepared from melted ferroelectric compounds are very promising materials and they are of great interest, first of all, from the viewpoint of fundamental research since up to now there is no answer a question, whether or not the ferroelectric properties of a crystal still remain when the material is converted to the amorphous state. According to the Lines theory [25], considering the local fields in ferroelectrics in the amorphous state, ferroelectricity can occur in the amorphous samples of some ferroelectrics. Particularly, if a ferroelectric crystal has a highly-directional structure, than its amorphous state has not have the ferroelectric property. However, if it has a highly-symmetrical prototypic structure, like as PbTiO3 , the ferroelectricity can be in the amorphous state. However, from our dielectric and polarization measurements [16, 21] the ferroelectricity does not occur in the bulk amorphous PbTiO3 .

March 29, 2004

23:12

GFER

TJ977-15

112


Besides, almost no investigations of crystallization mechanisms i.e. the transition mechanisms from the amorphous state of ferroelectrics to the crystalline phase. Such investigations could be essential not only for pure fundamental study but also for the discovery of possible applications of the new amorphous materials. In the present study, amorphous samples of PbTiO3 were prepared by the ultrarapid quenching technique and their structure and physical properties were investigated during isothermal annealing at various temperatures close to a crystallization temperature. It was revealed that kinetics of the crystallization process from the amorphous state at isothermal conditions are obeyed the kinetic theory of Kolmogorov–Johnson–Mehl–Avrami in the assumption that nuclei growth of fractional dimensions occurs in the initial stage of the crystallization process. Estimations have shown that the process of the isothermal crystallization is controlled by activation energy of about 2 eV.

Acknowledgements The authors would like to thank Dr. L. N. Korotkov and Dr. S. A. Konstantinov for useful discussions and for kind advices. This work was supported by the Ministry of Education of the Russian Federation under the grant No 202.03.02.038 and the program “Universities of Russia” (the grant No. UR. 01. 01. 016).

References 1. H. Herman, Ultrarapid Quenching of Liquid Alloys (Academic Press, New York, 1981). 2. K. Sudzuki, H. Fudzimori, and K. Hasimoto, Amorphous Metals (Metallurgiya, Moscow, 1987). 3. I. V. Zolotukhin, Physic Properties of Amorphous Metals (Metallurgiya, Moscow, 1986). (in Russian) 4. Amorphous Semiconductors. Technologies and Devices. Editor Y. Hamakawa (OHM Publ., Tokyo, 1983). 5. M. Takashige and T. Nakamura, J. Phys. Soc. Jap. 49, 143 (1980). 6. M. Kitabatake, T. Mitsuyu, and K. Wasa, J. Appl. Phys. 56, 1780 (1984). 7. S. H. Kim, M. S. Jang, and Y. S. Yang, J. Korean. Phys. Soc. 32, 5807 (1998). 8. M. R. Srinivasan, P. Ayyub, and M. S. Multani, Phys. Letters 101 A8, 435 (1984). 9. Yu. Xu, C. H. Cheng, and J. D. Mackenzie, J. Non-Cryst. Solids 176, 1 (1994). 10. Yu. Kobayashi, Sh. Endo, and K. Koto, Phys. Rev. B 51, 9302 (1995). 11. T. Nakamura, M. Takashige, and H. Terauchi, Jap. J. Appl. Phys. 23, 1265 (1984). 12. S. W. Lee, K. B. Shim, and K. H. Auh, Material Letters 38, 356 (1999). 13. Yu. Miura, J. Phys. Soc. Jap. 52, 1127 (1983). 14. R. Orcowa and H. Uno, J. Phys. Soc. Jap. B 49, 144 (1980). 15. L. N. Korotkov, S. A. Gridnev, and A. A. Khodorov, JETF Letters 27, 13 (2001). (in Russian) 16. L. N. Korotkov, S. A. Gridnev, and S. A. Konstantinov, Izv. RAN., Ser. Fiz. 65, 1138 (2001). (in Russian) 17. L. N. Korotkov, S. A. Gridnev, and A. A. Khodorov, Izv. RAN., Ser. Fiz. 66, 833 (2002). (in Russian) 18. W. L. Seon, K. B. Shim, and K. H. Auh, J. Non-Cryst. Solids 248, 127 (1999). 19. T. Nakamura and M. Takashige, J. Phys. Soc. Jap. 49, 38 (1980). 20. Physical Metallurgy. Edited by R. W. Cahn (North-Holland Publ. Comp., Amsterdam, 1965). 21. L. N. Korotkov, S. A. Gridnev, S. A. Konstantinov, I. V. Babkina, and U. V. Barmin, Izv. RAN., Ser. Fiz. 65, 1138 (2001). (in Russian) 22. B. Dimmler, M. Parris, and D. Butler, J. Appl. Phys. 61, 5467 (1995). 23. J. F. Scott, L. Kammerdiner, and M. Parris, J. Appl. Phys. 64, 787 (1998). 24. V. Ya. Shur, S. A. Megashev, and A. L. Subbotin, Fiz. Tverd. Tela (St. Petersburg) 41, No. 2, 306 (1999). (in Russian) 25. M. E. Lines, Phys. Rev. 15, 388 (1977).