scholarly journals The 3-D Image of The Temperature Integral And Its Self-Similarity

Author(s):  
Wei Zhang ◽  
kui li ◽  
Juhua Zhang ◽  
Chengzhi Li ◽  
Zhangliang Xue ◽  
...  

Abstract How to derive the accurate value of temperature integral is a vital problem for the non-isothermal kinetic analysis. In the past six decades, researchers provided various methods to solve above problem, but the error usually becomes divergent when the value of x (x=Ea/RT) is too small or too large, no matter whether it is a numerical method or an approximation method. In this paper, we present a new series method and elaborately design a computer program to calculate the value of temperature integral. Finally, we reveal the mysterious relationship between the integral, the temperature and the activation energy, and we find an extremely interesting phenomenon that the 3-D image of the temperature integral is of self-similarity according to the fractal theory.

2001 ◽  
Vol 688 ◽  
Author(s):  
Gopinathan M. A. Kumar ◽  
Woo-Chul Kwak ◽  
Se-Yon Jung ◽  
Seung-Joon Hwang ◽  
Yun-Mo Sung

AbstractStrontium bismuth tantalate (SBT) having composition of Sr0.7Bi2.4Ta2O9 has been prepared through sol-gel method using their corresponding metal alkoxides as precursors. Seeded SBT powder was prepared by the addition of 5 wt.% of nanometer sized SBT particles to the sol followed by pyrolysis. By applying non-isothermal kinetic analysis to the DTA results, activation energy values for the unseeded and seeded samples were determined. Enhanced crystallization kinetics was observed for the seeded one and the activation energy for the aurivillius phase formation was found to be 318 kJ/mol, while 375 kJ/mol for the unseeded. The Avrami exponent values for the seeded and unseeded were found to be 2.80 and 0.96 respectively.


2002 ◽  
Vol 17 (6) ◽  
pp. 1463-1468 ◽  
Author(s):  
Woo-Chul Kwak ◽  
Yun-Mo Sung

The crystallization kinetics of Sr0.7Bi2.3Ta2O9 (SBT) and 0.7SrBi2Ta2O9–0.3Bi3TiTaO9 (SBT-BTT) thin films formed by the sol-gel and spin coating techniques were studied. Phase formation and crystal growth are greatly affected by the film composition and crystallization temperature. Isothermal kinetic analysis was performed on the x-ray diffraction results of the thin films heated in the range of 730 to 760 °C at 10 °C intervals. Activation energy and Avrami exponent values were determined for the fluorite-to-Aurivillus phase transformation. A reduction of approximately 51 kJ/mol in activation energy was observed for the SBT-BTT thin films, and an Avrami exponent value of approximately 1.0 was obtained for both the SBT and SBT-BTT. A comparison is made, and the possible crystallization mechanism is discussed.


2017 ◽  
Vol 20 (2) ◽  
pp. 52-56 ◽  
Author(s):  
Tomáš Ondro ◽  
Tomáš Húlan ◽  
Ivan Vitázek

Abstract A non-isothermal kinetic analysis of kaolinite dehydroxylation was carried out using thermogravimetric analysis on powder samples with heating rates from 1 to 30 °C・min-1 in a dynamic air atmosphere. The mechanism of the reaction, values of overall activation energy and pre-exponential factor were determined from a series of thermogravimetric experiments by the Coats- Redfern method. The results show that the dehydroxylation of kaolinite is controlled by the rate of the third-order reaction (F3) with the mean values of overall activation energy (EA) 255 kJ・mol-1 and pre-exponential factor (A) 25.56 × 1014 s-1.


2018 ◽  
Vol 64 (No. 1) ◽  
pp. 41-46 ◽  
Author(s):  
Ondro Tomáš ◽  
Vitázek Ivan ◽  
Húlan Tomáš ◽  
Lawson Michael K

Thermal decomposition of spruce wood (Picea abies) was studied using the thermogravimetric (TG) analysis in air atmosphere from 30°C to 600°C with the heating rates of 5, 10, 15, 20, 25 and 30°C.min<sup>–1</sup>. The TG results show that the main decomposition region is in the temperature range of 250–360°C, where a total disintegration of hemicellulose and cellulose with partial lignin decomposition can be observed. The values of apparent activation energy for this process are between 168.6–196.5 kJ·mol<sup>–1</sup>, 179.8–188.1 kJ·mol<sup>–1</sup> and 170.1–178.7 kJ·mol<sup>–1</sup> determined by the Friedman, Flynn-Wall-Ozawa and Kissinger-Akahira-Sunose methods, respectively. 


Materials ◽  
2011 ◽  
Vol 4 (12) ◽  
pp. 2231-2243 ◽  
Author(s):  
Joan Torrens-Serra ◽  
Shankar Venkataraman ◽  
Mihai Stoica ◽  
Uta Kuehn ◽  
Stefan Roth ◽  
...  

2012 ◽  
Vol 550-553 ◽  
pp. 2537-2540
Author(s):  
Hai Yan Gu ◽  
Yong Wang ◽  
Lei Yu

The wavelet analysis and fractal theory into the analysis of hydrological time series, fluctuations in hydrological runoff sequence given the complexity of the measurement methods--- fractal dimension. The real monthly runoffs of 28 years from Songhua River basin in Harbin station are selected as research target. Wavelet transform combined with spectrum method is used to calculate the fractal dimension of runoff. Moreover, the result demonstrates that the runoff in Songhua River basin has the characteristic of self-similarity, and the complexity of runoff in the Songhua River basin in Harbin station is described quantificationally.


2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Xinlei Jia ◽  
Jingyu Wang ◽  
Conghua Hou ◽  
Yingxin Tan

Herein, a green process for preparing nano-HMX, mechanical demulsification shearing (MDS) technology, was developed. Nano-HMX was successfully fabricated via MDS technology without using any chemical reagents, and the fabrication mechanism was proposed. Based on the “fractal theory,” the optimal shearing time for mechanical emulsification was deduced by calculating the fractal dimension of the particle size distribution. The as-prepared nano-HMX was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and differential scanning calorimetry (DSC). And the impact sensitivities of HMX particles were contrastively investigated. The raw HMX had a lower fractal dimension of 1.9273. The ideal shearing time was 7 h. The resultant nano-HMX possessed a particle size distribution ranging from 203.3 nm to 509.1 nm as compared to raw HMX. Nano-HMX particles were dense spherical, maintaining β-HMX crystal form. In addition, they had much lower impact sensitivity. However, the apparent activation energy as well as thermal decomposition temperature of nano-HMX particles was decreased, attributing to the reduced probability for hotspot generation. Especially when the shearing time was 7 h, the activation energy was markedly decreased.


Kavkaz-forum ◽  
2020 ◽  
Author(s):  
Э.Б. САТЦАЕВ

Время – грамматическая категория глагола, служит временной состояния, либо события. В различных языках наличествует соответствующее количество временных форм. Индоевропейский глагол в историческом плане имел три временные системы – презенс, аорист и перфект. В Авесте засвидетельствованы формы всех индоевропейских времен, наклонений и залогов. В ней в изъявительном наклонении раз­личаются следующие времена: настоящее время, имперфект, перфект и плюсквамперфект. В презенсе авестийского глагола выделяются два типа основ. Эти основы делятся на классы, количество которых доходит до двадцати двух. Глагольная система, которая наличествует в среднеиранских языках, значительно изменилась по сравнению с древнеиранскими языками. Однако древнеиранская временная система практически во всех иранских языках данного периода сохранилась. В новоперсидском языке насчитывается восемь времен. Идентичное количество временных форм можно наблюдать также в афганском языке, представленном в восточноиранской языковой подгруппе. Среди иранских языков осетинский характеризуется скудостью временных форм. В осетинском языке можно выделить три глагольные основы, от которых образуются формы соответствующих времен. В осетинских глаголах обнаруживаются следы древнеарийских классов настоящего времени. В современных иранских языках основное противоположение лежит между прошлым и не прошлыми временами. В изъявительном наклонении осетинский язык знает три времени: настоящее, прошедшее и будущее. Наиболее интересным явлением в осетинском языке является образование будущего времени, аналогичная с осетинским языком модель образования будущего времени наблюдаются в согдийском и хорезмийском языках, ко­торые считаются наиболее близкими к осетинскому языку. Tense is a grammatical category of a verb that serves as a temporary localization of an event or state. Different languages have a different number of temporary forms. Historically, the Indo-European verb had three temporal systems – present, aorist and perfect. In the Avesta, forms of all Indo-European times, moods and pledges are attested. The following tenses are distinguished in it in the indicative mood: present, imperfect, perfect and pluperfect. There are two types of stems in the presence of the Avestan verb. These basics are divided into classes, the number of which reaches twenty-two. The verb system in the Middle Iranian languages has changed significantly compared to the ancient Iranian, however, the ancient Iranian temporal system in almost all Iranian languages of this period has been preserved. There are eight tenses in the New Persian language. Almost the same number of temporal forms is observed in Afghan, which is part of the Eastern Iranian subgroup. Among the Iranian languages, Ossetian is a scarcity of temporary forms. In the Ossetian language, three verbal stems can be distinguished, from which the forms of the corresponding tenses are formed. In Ossetian verbs, traces of the ancient Aryan classes of the present tense are found. In modern Iranian languages, the main opposition lies between the past and non-past times. In the indicative mood, the Ossetian language knows three tenses: present, past and future. The most interesting phenomenon in the Ossetian language is the formation of the future tense, a model of the formation of the future tense similar to the Ossetian language is observed in the Sogdian and Khorezm languages, which are considered the closest to the Ossetian language.


2001 ◽  
Vol 666 ◽  
Author(s):  
Yun-Mo Sung ◽  
Woo-Chul Kwack

ABSTRACTPhase formation characteristics of Sr0.7Bi2.4Ta2O9 (SBT) powder, synthesized via sol-gel and pyrolysis process, was investigated by using thermal analysis. Each of the two exotherms, appearing in differential thermal analysis (DTA) scan curves, was identified as crystallization of fluorite phase and transformation of fluorite to aurivillius phase, respectively by using x-ray diffraction (XRD). By applying non-isothermal kinetic analyses to the DTA results, activation energy values for the formation of fluorite and aurivillius phases were determined as 192 and 375 kJ/mol, respectively and Avrami exponent values for each reaction were determined as 0.91 and 0.96, respectively. These activation energy and Avrami exponent values were discussed in detail to understand phase formation mechanism in SBT system.


Energies ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 4060
Author(s):  
Ziad Abu El-Rub ◽  
Joanna Kujawa ◽  
Samer Al-Gharabli

Oil shale is one of the alternative energies and fuel solutions in Jordan because of the scarcity of conventional sources, such as petroleum, coal, and gas. Oil from oil shale reservoirs can be produced commercially by pyrolysis technology. To optimize the process, mechanisms and rates of reactions need to be investigated. Omari oil shale formation in Jordan was selected as a case study, for which no kinetic models are available in the literature. Oil shale was analyzed using the Fischer assay method, proximate analysis (moisture, volatile, and ash), gross calorific value, elemental analysis (CHNS), and X-ray fluorescence (XRF) measurements. Non-isothermal thermogravimetric analysis was applied to study the kinetic parameters (activation energy and frequency factor) at four selected heating rates (5, 10, 15, and 20 °C/min). When oil shale was heated from room temperature to 1100 °C, the weight loss profile exhibited three different zones: drying (devolatilization), pyrolysis, and mineral decomposition. For each zone, the kinetic parameters were calculated using three selected methods: integral, temperature integral approximation, and direct Arrhenius plot. Furthermore, the activation energy in the pyrolysis zone was 112–116 kJ/mol, while the frequency factor was 2.0 × 107 − 1.5 × 109 min−1. Moreover, the heating rate has a directly proportional relationship with the rate constant at each zone. The three different methods gave comparable results for the kinetic parameters with a higher coefficient of determination (R2) for the integral and temperature integral approximation compared with the direct Arrhenius plot. The determined kinetic parameters for Omari formation can be employed in developing pyrolysis reactor models.


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