The activation energy of solid-state phase transformation for the steel has been evaluated by the isoconversional method. It is demonstrated that the linear fitting is a mathematically invalid procedure that generally invalidates the isoconversional method. As an alternative, we apply the advanced isoconversional method that can be used to determine the activation energy of solid-state phase transformation of 1035 steel. The activation energy determined by this method varies with the transformed phase fraction. The variation of the activation energy was interpreted by the nucleation and growth model. It is shown that the advanced isoconversional method can be recommended as a trustworthy way of determining the activation energy of solid-state phase transformation of 1035 steel

C. J. Xu

D. Tang

D. Wang

G. L. Tan

T. Mu

X. T. Yin

English

HRČAK - Portal of Croatian Scientific and Professional Journals

337METALURGIJA 59 (2020) 3, 337-339G. L. TAN, D. TANG, X. T. YIN, T. MU, D. WANG, C. J. XU  THE ACTIVATION ENERGY DETERMINATION IN NON-ISOTHERMAL CONDITIONS FOR THE SOLID-STATE PHASE TRANSFORMATION OF 1035 STEELReceived – Primljeno: 2019-12-16Accepted – Prihvaćeno: 2020-03-20Preliminary Note – Prethodno priopćenjeG. L. Tan, D.Tang, T. Mu. Department of materials science and engi-neering, Yingkou Institute of Technology, Liaoning, China, G.Tan (E-mail: guangleitan1979@sina.com)X. T. Yin, D. Wang, C.J. Xu, School of materials and metallurgy, Uni-versity, Liaoning, ChinaThe activation energy of solid-state phase transformation for the steel has been evaluated by the isoconversional method. It is demonstrated that the linear fitting is a mathematically invalid procedure that generally invalidates the isoconversional method. As an alternative, we apply the advanced isoconversional method that can be used to de-termine the activation energy of solid-state phase transformation of 1035 steel. The activation energy determined by this method varies with the transformed phase fraction. The variation of the activation energy was interpreted by the nucleation and growth model. It is shown that the advanced isoconversional method can be recommended as a trustworthy way of determining the activation energy of solid-state phase transformation of 1035 steel.Keywords: steel, the activation energy, solid-state, non-isothermal, phase transformationINTRODUCTIONThe solid-state p hase transformation kinetics of the steel have been researched by some authors [1-4]. For the solid-state phase transformation kinetics, the model of KJMA (Kolmogorov-Johnson-Mehl-Avrami) which is deduced based on the assumption of random distribu-tion and isotropic growth of crystal nucleus, was used extensive [5]. It is often impossible to accurately de-scribe the actual kinetic behavior of solid-state phase transformation, because of assumption that the kinetic parameters are constant throughout the phase transfor-mation. In order to improve the applicability of the model in dealing with the actual solid-state phase trans-formation kinetics, some researchers have been revising the model [6].The Kissinger [7] method and the isoconversional method [8] are commonly used in determining the acti-vation energy of solid-state phase transformation. The Kissinger method determined the activation energy by using the “peak temperature” of the differential scan-ning calorimetry (DSC) curve [9]. For the past few years, Vyazovkin [10] has pointed out that this method appears to be generally inapplicable for evaluating the activation energy of the processes that occur on cooling. The use of this method with positive values of the cool-ing rate may result in erroneous values of the activation energy[11]. For the isoconversional method, some ap-plications of isoconversional methods have been de-ISSN 0543-5846METABK 59(3) 337-339 (2020)UDC – UDK 669.14:536.777.772:536.712:536.425-536.421/.422:536.425 = 111rived to deal with the processes of the solid-state phase transformation during continuous cooling [12]. How-ever, the application of isoconversional method which introduced the temperature integral approximation, has created a new misconception about kinetic analysis of cooling data [13].From the above, the application of these approaches has been debated because of their limitations. In fact, the solid-state phase transformation generally demon-strate a tangled interplay of various processes such as diffusion, nucleation, growth and impingement of the growing new phase particles [14]. These steps have their own activation energies, which are likely to be different [11]. Therefore, it is very important to find an effective method for handling kinetics data measured on cooling. In this paper, we consider the advanced isoconversional method. This method has been very helpful in kinetics analyses calorimetric data on crystallization of liquid metals [15]. The application of the advanced isoconver-sional method is illustrated for non-isothermal solid-state phase transformation of 1035 steel.The method of kinetic analysisThe experimental results of the nonisothermal dif-ferential scanning calorimetry(DSC) can be used to cal-culate the activation energy. The kinetics equation is expressed in the following  (1 ) where α is the transformed phase fraction,, T is the temperature, dH/dt is the heat flow, ΔrHm is the total heat released in the process 338G. L. TAN et al.: THE ACTIVATION ENERGY DETERMINATION IN NON-ISOTHERMAL CONDITIONS... METALURGIJA 59 (2020) 3, 337-339and α into the software of MATLAB. Dependence of Eα on α determined by the software is shown in Figure 2. As seen from figure 2, the activation energy for the solid-state phase transformation of 1035 steel can be di-vided into three distinct stages. In the initial stage, the activation energy decreases from about -70 kJ/mol at the low transformed phase fraction to nearly -163 kJ/mol at the 30 % transformed phase fraction. In the sec-ond stage, the activation energy exhibits a single overall value at the transformed phase fraction range of 0,3 - 0,8. In the last stage, the activation energy rises from -160 kJ/mol to about -67 kJ/mol near the completion of the reaction. From these phenomena, we can conclud that the investigated solid-state phase transformation kinetics cannot be described as a simple process by a unique set of kinetics parameters.DISCUSSIONFor the solid-state phase transformations process, the overall solid-state phase transformations rate is de-termined by the nucleation and growth [17]. At the ini-tial stage of reaction, the activation energy of solid-state phase transformations is high; because the necessary of phase transformation, A is the pre-exponential factor, β is the cooling rate. E is the activation energy of the solid state phase transformation, R is the gas constant and f (α) is a function that represents the reaction model. For the isoconversional method, there is a lot of iso-conversional method based on the logarithmic expres-sion of equation 1 and the approximations of the tem-perature integral. In my paper, the advanced isoconver-sional method has been developed which can be resolved the problem of the approximations of the temperature integral. This method can be represented as a condition of minimum value by the following equation [16]:  (2)Where J (Eα, Tα,i) is defined as [11]:   (3)The equation 2 can be used to determine the Eα for a given value of α based on the minimizing the function φ(Eα).Experimental As experimental examples, the 1035 steel grain was chosen, particle-size of samples were 3 mm in length, 2,5 mm in width and 2,5 mm in height, and the mass of sample is 105 ± 8mg. The experiments were carried out using a thermal Analyzer, SETSYS Evolution, which is made in Setaram of France. The temperature range is from ambient to 1 600 °C, with heating rate and cooling rate from 0,1 to 100 K/min. The isothermal temperature precision is 0,01 °C. The thermocouple is positioned immediately under the sample. The thermal history is determined by the analyzer controller after a standard calibration procedure under the proper conditions. The weighing capacity is 100 mg with a sensitivity of 0,1 μg. Sample was placed in corundum crucible and heat-ed in a flowing atmosphere of nitrogen (20 mL min-1). For experiments carried out under non-isothermal con-ditions, the sample was heated from room temperature to 1 550 °C at a constant heating rate (10 K/min). In order to melt completely the sample, the temperature was kept constant for 10 minutes under this tempera-ture. Subsequently, cool the sample to the room tem-perature at a constant cooling rate. Four cooling rate programs are studied: 10, 20, 30 and 50 K/min. The activation ene rgyFigure 1 shows the rate of the transformed phase, determined by the DSC curves at different cooling rates. As seen from figure.1, the temperature of the peak gets lower as the cooling rate increases.The values of Tα shown in Figure 1 were used for 40 values of α in the range 0.025-1 for four experiments per-formed at different cooling rates. By introducing the  Tα Figure 1  DSC curves for the solid-state phase transformation of 1035 steel at different cooling rates.Figure 2  Dependence of the Eα on the α determined by the nonlinear isoconversional method at different cooling rates.339G. L. TAN et al.: THE ACTIVATION ENERGY DETERMINATION IN NON-ISOTHERMAL CONDITIONS...METALURGIJA 59 (2020) 3, 337-339China (Grant No. 20180550632); also the authors like to express their sincere thanks to the editors and anony-mous reviewers for their helpful comments and sugges-tions on the quality improvement of our present paper.REFERENCES[1] J. W.Cahn, Transformation kinetics during continuous co-oling, Acta Metall. 4 (1956) 572-575[2] J. W. Cahn, The kinetics of grain boundary nucleated reac-tions, Acta Metall. 4 (1956) 449-459[3] H. I. Aaronson, C. Laird, K. R. Kinsman,  Application of a theory of precipitate morphology to the massive transfor-mation, Scripta Metall. 2 (1968) 259-264[4] M. Hillert,The kinetics of the first stage of tempering, Acta Metall. 7 (1959) , 653-658[5] G. Ghosh, M. Chandrasekaran, L. Delaey, Isothermal Crystallization Kinetics of Ni24Zr76 and Ni24 (Zr-X )76 Amorphous Alloys, Acta Metallurgica Sinica, 39 (1991) 925-936[6] J. Farjas, P. Roura, Modification of the Kolmogorov-John-son-Mehl-Avrami rate equation for non-isothermal experi-ments and its analytical solution, Acta Mater. 54 (2006) 5573-5579[7] H. E. Kissinger, Reaction kinetics in differential thermal analysis, Anal. Chem. 29 (1957) 1702-1706[8] L. Friedman, Kinetics of thermal degradation of char-for-ming plastics from thermogravimetry. Application to a phenolic plastic, J. Polym. Sci. Part C. 6 (1964) 183-195 [9] T. X. Liu, Z. S. Mo, S. G. Wang, Nonisothermal melt and cold crystallization kinetics of poly(aryl ether ether ketone ketone), Polym. Eng. Sci. 37 (1997) 568-575[10] S. Vyazovkin, Is the Kissinger Equation Applicable to the Processes that Occur on Cooling? Macromol. Rapid Com-mun. 23 (2002) 771-775[11] S. Vyazovkin, N. Sbirrazzuoli, Isoconversional analysis of calorimetric data on non-isothermal crystallization of a polymer melt, J. Phys. Chem. B. 107 (2003) 882-888[12]  S. Vyazovkin, N. Sbirrazzuoli, Isoconversional analysis of nonisothermal crystallization of a polymer melt, Rapid Commun. 23 (2002) 766–770[13] S. Vyazovkin. N. Sbirrazzuoli, Isoconversional approach to evaluating the Hoffman-Lauritzen parameters (Uand kg) from the overall rates of nonisothermal crystallization, Macromol. Rapid Commun. 25 (2004) 733–738. [14] F. Liu, Sommer, C. Bos, E. J. Mittemeijer, Analysis of so-lid state phase transformation kinetics: models and recipes Int. Mater. Rev. 52(2007) 193-212[15] J. H.Perepezko, P. G. Höckel, J. S. Paik, Initial crystalliza-tion kinetics in undercooled droplets, Thermochimica Acta, 388 (2002) 1, 129-141.[16] S. Vyazovkin, Advanced isoconversional method, J. Therm. Anal. 49 (1997) 1493-1499.[17] J. Y. MacDonald, The formation and growth of silver nu-clei in decomposition of silver oxalate, C. N. J. Chem. Soc (1925) 2764-2771. [18] E. J. Mittemeijer, F. Sommer, Solid state phase transforma-tion kinetics: evaluation of the modular transformation model, Int. J. Mater. Res., 102 (2011) 785-795.Note:  The responsible translator for language English is associate pro-fessor W. H. Ma - Yingkou Institute of Technology, Liaoning, Chinacondition for new phase nuclei growth is that the radius of the new phase nuclei is larger than the critical radius. With the temperature of reaction decreasing, the rate of nucleation increases, and the energy barrier of solid-state phase transformations decreases as the trans-formed phase fraction rises. Once the nucleation pro-cess arrives to the end, the new phase nuclei begin to growth. The activation energy basically doesn’t vary with the transformed phase fraction. Because the alloy element is conducive to the growth of new phase nuclei, once the temperature drops a certain value, the reaction rate becomes controlled by the diffusion process. At this moment, the activation energy increases with the trans-formed phase fraction rises because the atomic transi-tion capacity decreases with temperature decrease.In fact, the process of phase transformation of steel is a tangled interplay of various process such as nuclea-tion of the new phase particles, growth of the new phase particles, atomic diffusion, impingement of the new phase particles, etc [18]. Therefore, the activation ener-gy of phase transformation, which is determined by the activation energies of various processes as well as by the relative contributions of these processes to the total phase transformation rate, is generally a synthetical value, because these processes have their own activa-tion energies, which are likely to be different. In addi-tion, some authors [11] have demonstrated that the sol-id-state phase transformation kinetics of processes oc-curring on cooling can be analyzed accurately by the advanced isoconversional method.CONCLUSIONSThe widely used isoconversional method appears to be generally inapplicable for determining the activation energy of the solid state transformation that occurs on continuous cooling. The activation energy can be evalu-ated by using the advanced isoconversional method. The application of the advanced isoconversional meth-od to solid state transformation of 1035 steel has ob-tained the negative values of the activation energy that varies with the transformed phase fraction. The varia-tion of the activation energy can be explained by the nucleation and growth mechanism. In generally, the ap-plication of the advanced isoconversional method, which determined the activation energy from the DSC data of the process for the solid state transformation that occur on continuous cooling, can be recommended as a meaningful method.AcknowledgmentsWe gratefully acknowledge the National Natural Science Foundation of China (Grant No. 51504130) and Liaoning Province Natural Science Foundation of 

The activation energy determination in non-isothermal conditions for the solid-state phase transformation of 1035 steel

Abstract

Similar works

Full text

Available Versions

HRČAK - Portal of Croatian Scientific and Professional Journals