Avrami-Erofeev Equation Research Articles

Effect of Mg content on structure, hydrogen storage properties and thermal stability of melt-spun Mgx(LaNi3)100−x alloys

Amorphous Mgx(LaNi3)100−x (x = 40, 50, 60, 70) alloys with ribbon shape (5 mm wide, 0.2 mm thick) have been prepared by rapid solidification, using a melt-spinning technique. Their microstructure, hydrogen storage properties and thermal stability were studied by means of XRD, SEM, PCTPro2000 and DSC analysis, respectively. The results indicated that when Mgx(LaNi3)100−x alloys have been hydrogenated at 573 K under 2 MPa hydrogen pressure, LaH3 phase is formed in the case of x (x = 40, 50, 60, 70), Mg2NiH4 phase formed in the case of x (x = 40, 50, 60, 70), Mg2NiH0.3 phase formed in the case of x (x = 40, 50), and MgH2 phase formed in the case of x = 70. Experimental data of hydrogen desorption kinetics, tested at 523 K, 573 K and 623 K, are in good agreement with Avrami–Erofeev equation. The maximum hydrogen absorption capacity is 2.71 wt.% for Mg70(LaNi3)30 and 2.35 wt.% for Mg70(LaNi3)30, the increase of hydrogen desorption capacity is in the order of x = 70 > x = 60 > x = 50 > x = 40. Based on DSC analysis, the activation energies for dehydrogenation of these samples are calculated to be 122 ± 2 kJ/mol (x = 40) > 101 ± 3 kJ/mol (x = 50) > 84 ± 5 kJ/mol (x = 60) > 64 ± 3 kJ/mol (x = 70), which are in agreement with the results of hydrogen desorption kinetics.

Gasification of Graphite and Coke in Carbon–Carbon Dioxide–Sodium or Potassium Carbonate Systems

The thermodynamics of possible reactions, including gasification and reduction reactions, in carbon–carbon dioxide–sodium or potassium carbonate systems was analyzed first. And then, the gasification reactions of graphite and coke with CO2 in this system were studied kinetically by temperature programmed thermogravimetry. The results showed that the carbon conversion curve shifted to a lower temperature zone after Na2CO3 or K2CO3 was added, and graphite was more susceptible than coke to be catalyzed by Na2CO3 or K2CO3. Ten kinetic equations were adopted to simulate the reaction process using the method of Coats–Redfern. The Avrami–Erofeev equation was found to be the most probable kinetic equation, with which the values of activation energy and frequency factor were calculated. The kinetic simulation indicated that the activation energy of coke carbon had been activated to the lowest level by its inner factors, thus it was difficult to be reduced by adding Na2CO3 or K2CO3. The kinetic compensation effect was confirmed to exist in both graphite gasification and coke gasification. X-ray diffraction and Raman spectra were used to characterize the inner difference between graphite and coke, which showed that coke carbon structure was greatly different from graphite structure because of its highly disordered and heterogeneous carbon structure.

Leaching kinetics of scheelite in hydrochloric acid solution containing hydrogen peroxide as complexing agent

The reaction kinetics for the leaching of scheelite with hydrogen peroxide and hydrochloric acid have been studied to determine the effect of process parameters, such as temperature, concentrations of hydrogen peroxide and hydrochloric acid and particle sizes. The Avrami–Erofeev equation and the Mampel equation were proposed based on the experimental data. Comparing the curve obtained from the kinetic model equation and experimental data, it was determined that both equations were well-fitted to the experimental data. Comparison of the results also demonstrated that Avrami–Erofeev equation was the best kinetic model equation. The Avrami–Erofeev equation was as follows:−ln1−x=5.60×102⋅CH2O20.29⋅e−38930RT⋅t1.01.

Effect of Co substitution for La on hydrogen storage properties and thermal stabilities of amorphous Mg60Ni30La10−xCox (x = 0, 2 and 4) alloys prepared by melt spinning

A comparison of the hydrogen storage properties and thermal properties of amorphous Mg60Ni30La10−xCox hydrogen storage alloys prepared by melt spinning has been investigated. A, B and C were used to represent each alloy composition when x = 0, 2 and 4 respectively. Their microstructures, the hydrogen storage properties and the thermal stabilities were analysed by X-ray diffraction (XRD), PCTPro2000 and differential scanning calorimetry (DSC) respectively. After hydrogenation of Mg60Ni30La10−xCox (A, B and C) samples at 573 K under 2 MPa hydrogen pressure, XRD pattern results indicate the formation of new phases of MgH2 (A, B, C), Mg2NiH4 (A, B, C), La4H12·19 (A, B, C), Mg2Ni0·9Co0·1H4 (B), Mg2NiH0·26 (C) and Mg2CoH2 (C). It is observed that the experimental data of hydrogen desorption kinetics at 523, 573 and 623 K are well fitted through Avrami–Erofeev equation, and the hydrogen desorption kinetics is in the order of C>B>A. In addition, with increasing Co content, alloy C has the maximum hydrogen absorption capacity of 3·05 wt-% and the maximum hydrogen desorption capacity of 2·85 wt-%. Based on the results of DSC analysis, dehydrogenation activation energies of these alloys are determined to be 98·31±2·82 kJ mol−1 (A), 96·33±5·61 kJ mol−1 (B) and 78·99±2·98 kJ mol−1 (C), which are in accordance with the results of hydrogen desorption kinetics.

Powder X‐Ray Diffraction Investigation of Xylazine Hydrochloride Solid Phase Transformation Kinetics

ABSTRACTThe kinetics of the solid‐state phase transformation of xylazine hydrochloride form X to A has been investigated using powder X‐ray diffraction and differential thermal analysis. Three different kinetic models have been used to describe transition kinetics: the Avrami–Erofeev equation, the Cardew equation, and the methodology for simulation of solid‐state phase transition kinetics by the combination of nucleation and nuclei growth processes. The latter has been recently developed and has been tested in this paper for the case of a real solid‐state transition. The relative humidity, mechanical pressure, temperature, and sample‐preparation effect on phase‐transition kinetics have been investigated, and rate constant changes have been analyzed.

Non-isothermal decomposition kinetics of diosgenin

The thermal stability and kinetics of isothermal decomposition of diosgenin were studied by thermogravimetry (TG) and Differential Scanning Calorimeter (DSC). The activation energy of the thermal decomposition process was determined from the analysis of TG curves by the methods of Flynn-Wall-Ozawa, Doyle, Satava-Sestak and Kissinger, respectively. The mechanism of thermal decomposition was determined to be Avrami-Erofeev equation (n = 1/3, n is the reaction order) with integral form G(α) = [−ln(1 − α)]1/3 (α = 0.10–0.80). Ea and logA [s−1] were determined to be 44.10 kJ mol−1 and 3.12, respectively. Moreover, the thermodynamics properties of ΔH≠, ΔS≠, and ΔG≠ of this reaction were 38.18 kJ mol−1, −199.76 J mol−1 K−1, and 164.36 kJ mol−1 in the stage of thermal decomposition.

The Sintering Process and Reaction Kinetics of Fe–Se System after Ball Milling Treatment

The formation mechanism of superconducting phase β-FeSe during sintering process plays a vital role in determining superconductive properties and understanding the mechanism of superconductivity in the iron-based superconductor. In the present work, the sintering process and reaction kinetics of Fe–Se system after ball milling were investigated. It was found that most of the crystalline Se would transform into the amorphous state after long-time ball milling. Some Se can also enter the Fe crystal lattice forming solid solution and lead to the lattice distortion of Fe. According to thermal analysis, the reaction between Fe and Se during the subsequent sintering process orderly underwent the formation of FeSe2, Fe7Se8, and α-FeSe. Finally, α-FeSe would transform into the superconducting phase β-FeSe after sintering for a long time at elevated temperature. Additionally, the Flynn-Wall-Ozawa (FWO) multiple scanning method under non-isothermal conditions was employed to study the kinetic mechanism and it is found that random nucleation followed by a gradual growth of nuclei (Avrami–Erofeev equation, n=2) is the kinetics mechanism of solid–solid reaction between Fe and Se during sintering process. The value of the activation energy decreases from 70.19 kJ/mol to 63.16 kJ/mol as the reaction proceeds.

Kinetics of the transformation of Ln2O2SO4 into Ln2O2S (Ln = La, Pr, Nd, and Sm) in a hydrogen flow

The kinetic dependences of the yield of Ln2O2S (Ln = La, Pr, Nd, and Sm) upon the treatment of Ln2O2SO4 in a hydrogen flow at 950, 1120, and 1170 K are constructed. The plots are approximated by Avrami-Erofeev equations, equations of compressed volume and compressed surface, and Jander’s equation. The correctness of choosing these equations is evaluated using the numerical values of Fisher’s criterion. Images of the particles of Nd2O2SO4 → Nd2O2S transformation in the flow are obtained on an Ntegra Aura atomic force probe microscope. A mechanism of the crystal growth of the Nd2O2S phase from the nucleation site of the Nd2O2SO4 and Nd2O2S phase boundaries is proposed.

A study of non-isothermal kinetics of limestone decomposition in air (O2/N2) and oxy-fuel (O2/CO2) atmospheres

The non-isothermal experiments of limestone decomposition at multi-heating rates in O2/N2 and O2/CO2 atmospheres were studied using thermogravimetry. The limestone decomposition kinetic model function, kinetic parameters of apparent activation energy (E), and pre-exponential factor (A) were evaluated by Bagchi and Malek method. The results shown that in 20 % O2/80 % N2 atmosphere, the limestone decomposed slowly following the contracting sphere volume model controlled by boundary reaction (spherical symmetry) in two stages, and the E increased by about 50 kJ mol−1 in the second decomposition stage. But in 20 % O2/80 % CO2 atmosphere, the presence of high-concentration CO2 significantly inhibited the limestone decomposition, and made the decomposition process occur at high temperature with a rapid rate; the decomposition kinetics was divided into three stages, the first stage was an accelerated decomposition process following the Mampel Power law model with the exponential law equation, the second stage followed the nth order chemical reaction model as an α–t deceleration process, and the third stage belonged to the random nucleation and nuclei growth model with the Avrami–Erofeev equation. And with the heating rate increasing, the reaction order n showed a slight rise tendency. The E was about 1,245 kJ mol−1 in 20 % O2/80 % CO2 atmosphere, but was only about 175 kJ mol−1 in 20 % O2/80 % N2 atmosphere. The E and A increased markedly in the O2/CO2 atmosphere.

Thermal Decomposition Kinetics of Abietic Acid in Static Air

The thermal decomposition of abietic acid in air was investigated under non-isothermal condition using thermogravimetric analysis-differential thermal analysis (TGA-DTA) technique with heating rates of 5, 10, 15 and 25 K·min−1. The non-isothermal kinetic parameters were obtained via the analysis of the thermogravimetric and differential thermogravimetric (TG-DTG) curves by using Flynn-Wall-Ozawa method and Kissinger method. The thermal decomposition mechanism of abietic acid was studied with four integral methods (Šatava-Šesták, MacCallum-Tanner, ordinary integral and Agrawal). The results show that the thermal decomposition mechanism is nucleation and growth, and the mechanism function is Avrami-Erofeev equation with n equates 1/2. The activation energy and the pre-exponential factor are 64.04 kJ·mol−1 and 5.89×105 s−1, respectively.

Influence of Aluminum Particle Size on Thermal Decomposition of RDX

The effect of aluminum particle size (10.7 µm, 2.6 µm, and 40 nm) on the thermal decomposition of 1,3,5-trimethylene trinitramine (RDX) was investigated using differential scanning calorimetry (DSC), thermogravimetry–derivative thermogravimetry (TG-DTG), and DSC-TG–mass spectrometry (MS)–Fourier transform infrared (FTIR) spectroscopy, respectively. The results showed that the first exothermic peak (512 K) of RDX diminishes gradually with an increase in the nanosize aluminum content and is overcome by the second exothermic peak when the content of nano-Al reaches 30 wt%. The reaction mechanisms demonstrated by the nonisothermal kinetics of RDX in the absence and presence of 30 wt% Al were conformed to the Avrami-Erofeev equations for all of the RDX compositions. The nucleus growth factor for the RDX/40 nm Al mixture was found to be n = 2/3 compared to n = 3/4 for RDX with and without the microsized Al. The MS and FTIR analyses indicated that the thermal decomposition of RDX in the presence of Al nanopowders favors C-N bond cleavage over N-N bond cleavage as the rate determining step.

Enhanced apatite formation on Ti metal heated in PO2-controlled nitrogen atmosphere

The oxynitridation of biomedical titanium metal under a precisely regulated oxygen partial pressure (PO2) of 10−14Pa in nitrogen atmosphere at 973K for 1h strongly enhanced apatite formation compared with that on Ti heated in air. The factors governing the high apatite-forming ability are discussed from the viewpoint of the surface properties of Ti heated under a PO2 of 10−14Pa in nitrogen atmosphere determined from X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and zeta potential measurements. Nitrogen (N)-doped TiO2 (interstitial N) was formed on pure Ti heated under a PO2 of 10−14Pa in nitrogen atmosphere at 973K. The XPS O1s main peak shifted toward a lower binding energy upon heating under a PO2 of 10−14Pa. This shift may be due to the formation of oxygen vacancies. This Ti surface had a positive zeta potential of approximately 20mV. According to time-of-flight secondary ion mass spectroscopy results, PO43− ions were predominantly adsorbed on Ti soaked in simulated body fluid (SBF) after heat treatment, followed by calcium ions. It was concluded that the apatite formation kinetics can be described using the Avrami–Erofeev equation with an Avrami index of n=2, which implies the instantaneous nucleation of apatite on the surface of Ti soaked in SBF after heat treatment at 973K under a PO2 of 10−14Pa.

Chemism and kinetics of the oxidation of zinc-calcium oxysulfide

The sequence of phase transformations and the kinetics of the solid-phase (heating to 1273 K) oxidation of zinc-calcium oxysulfide CaZnSO with air are determined by thermodynamic, thermogravimetric, mass spectrometric, and X-ray diffraction analyses. The oxidation process is shown to be accompanied by the formation of the CaSO4 and ZnO phases depending on the heating conditions, as well as by the formation of CaO with SO2 evolution. The two-stage oxidation of CaZnSO is interpreted by the Avrami-Erofeev kinetic equations with activation energies of 190 and 422 kJ/mol.

Thermal decomposition mechanism of ammonium sulfate catalyzed by ferric oxide

The decomposition mechanism of ammonium sulfate catalyzed by ferric oxide was investigated in this paper. The decomposition kinetics parameters were determined via a global optimization of the Kissinger iterative method using the non-isothermal thermogravimetric analysis data. The products and intermediates were synchronously characterized by X-ray diffraction and mass spectrometry. The obtained results indicate that the decomposition process of ammonium sulfate catalyzed by ferric oxide can be divided into four stages of which the activation energies are 123.64, 126.58, 178.77 and 216.99 kJ·mol−1 respectively. The decomposition mechanisms at the first and the fourth stage both belong to Mample power theorem, the second stage belongs to Avrami-Erofeev equation and the third belongs to contracting sphere (volume) equation. The corresponding pre-exponential factors (A) are calculated simultaneously.

Hydrogen storage properties and thermal stability of amorphous Mg70(RE25Ni75)30 alloys

In this study, amorphous Mg70(RE25Ni75)30 (RE=La, Pr, Nd) alloys were produced by melt spinning, their hydrogen storage properties and the thermal stabilities have been studied by means of PCTPro2000 and Differential Scanning Calorimetry (DSC), respectively. After hydrogenation of Mg70(RE25Ni75)30 samples at 573K under 2MPa hydrogen pressure, XRD results indicate the formation of new phases of MgH2, Mg2NiH4, LaH3.01 (RE=La), PrH2.92 (RE=Pr) and Nd2H5 (RE=Nd). The experimental data of hydrogen desorption kinetics at 523K, 553K, 573K are well fitted through Avrami–Erofeev equation, and the hydrogen desorption kinetics were in the order of Pr>La>Nd. Based on the results of DSC analysis, dehydrogenation activation energies of these samples were determined to be 68.81±2.50kJ/mol (RE=La), 64.79±1.09kJ/mol (RE=Pr) and 73.37±3.23kJ/mol (RE=Nd), which are in accordance with the results of hydrogen desorption kinetics. As shown in the P–C isotherm curves, two hydrogen absorption plateaus at about 0.07MPa and 0.2MPa have been observed for Mg70(RE25Ni75)30 (RE=La, Pr) tested at 573K, while there is only one sloping hydrogen absorption plateau in the range of 0.06–0.3MPa for Mg70(Nd25Ni75)30 alloy. The maximum hydrogen absorption capacity is 4.21wt.% for Mg70(Nd25Ni75)30 and the maximum hydrogen desorption capacity is 2.74wt.% for Mg70(Pr25Ni75)30.

Thermal decomposition kinetics of glycine in nitrogen atmosphere

The non-isothermal decomposition kinetics of glycine was investigated using analyzer DTG-60. TG experiments were carried out under dynamic nitrogen atmosphere of 30mLmin−1 with heating rates of 10, 14, 18 and 22Kmin−1. The kinetic parameters such as activation energy (E), exponential factor (A) and reaction order (n) were evaluated by Flynn–Wall–Ozawa, Doyle, Kissinger and Šatava-Šesták methods. The results show that the non-isothermal decomposition mechanism of glycine corresponds to nucleation and growth, following the Avrami–Erofeev equation with n=1/3. Moreover, thermodynamic properties of the non-isothermal decomposition process such as the change in the values of enthalpy (ΔH), entropy (ΔS) and Gibbs free energy (ΔG) were calculated.

Evaluation of Crystallization Behavior on the Surface of Nifedipine Solid Dispersion Powder Using Inverse Gas Chromatography

To investigate crystallization behavior on the surface of amorphous solid dispersion powder using inverse gas chromatography (IGC) and to predict the physical stability at temperatures below the glass transition temperature (T (g)). Amorphous solid dispersion powder was prepared by melt-quenching of a mixture of crystalline nifedipine and polyvinylpyrrolidon (PVP) K-30. IGC was conducted by injecting undecane (probe gas) and methane (reference gas) repeatedly to the solid dispersion at temperatures below T (g). Surface crystallization was evaluated by the retention volume change of undecane based on the observation that the surface of the solid dispersion with crystallized nifedipine gives an increased retention volume. On applying the retention volume change to the Hancock-Sharp equation, surface crystallization was found to follow a two-dimensional growth of nuclei mechanism. Estimation of the crystallization rates at temperatures far below T (g) using the Avrami-Erofeev equation and Arrhenius equation showed that, to maintain its quality for at least three years, the solid dispersion should be stored at -20°C (T (g) - 65°C). IGC can be used to evaluate crystallization behavior on the surface of a solid dispersion powder, and, unlike traditional techniques, can also predict the stability of the solid dispersion based on the surface crystallization behavior.

Reaction Mechanism Study on Combustion of Micro Nanometer Iron Powder

Thermogravimetric curves of micro nanometer iron powder’s combustion were studied in different heating rates that were 10K/min, 20 K/min, 30 K/min and 40 K/min, and the particle sizes of iron were 100nm and 20μm. The iron’s kinetic parameters of combustion reaction were calculated by Coats-Redfern integral, differential and Kissinger methods, then the kinetic model was determined and the most probable mechanism function was verified by Popescu method. The results show that different heating rates, particle sizes and calculations can affect kinetic parameters and reaction mechanism. The activation energy of 100nm and 20μm iron powder’s combustion is 122.48 KJ/mol and 161.64 KJ/mol respectively. The combustion reaction of micro nanometer iron powder is controlled by random nucleation and subsequent growth model which is in agreement with Avrami-Erofeev equation. Rational control for the temperature and reaction time are conducive to optimize the combustion reaction of micro nanometer iron powder.

Effect of rapid solidification on phase structure and hydrogen storage properties of Mg70(Ni0.75La0.25)30 alloy

The hydrogen absorption/desorption kinetics and P–C isotherm of Mg70(Ni0.75La0.25)30 alloy, both the as-melt and rapid solidification were carried out on a sievert-type apparatus. The experimental data of initial hydrogen absorption and desorption kinetics at 573 K are in good agreement with Avrami–Erofeev equation, which indicated a three-dimensional interface reaction process of nucleation and growth for the initial hydrogenation kinetics and ‘‘geometrical contraction model’’ for dehydrogenation kinetics. However, the third absorption process seems to have a different hydriding mechanism as chemical reaction. P–C isotherm curves show that the as-melt alloy has two distinct hydrogen absorption plateaus, while the rapid solidification alloy has only one, which attribute to the absent of LaMg3 phase by rapid solidification. It can be confirmed by DSC analysis that the as-melt alloy has two endothermic peaks, compared to one for the rapid solidification alloy. The dehydrogenation activation energies of Mg70(Ni0.75La0.25)30 alloy were calculated by Kissinger method, showing the values of 128.60 ± 13.79 and 112.89 ± 9.94 kJ/mol for the as-melt sample and 61.09 ± 6.28 kJ/mol for rapid solidification alloy respectively.

A new methodology for the simulation of solid state phase transition kinetics by combination of nucleation and nuclei growth processes

A new methodology for the simulation of solid state phase transition kinetics has been developed by combining the influence of nucleation rate, nuclei growth rate and the power p characterizing the contact area between the growing particles. The equations used in this methodology were well known, and have been used previously for creating some of the most popular solid-state kinetic equations. The developed methodology made possible calculations of separate rate constants for two processes affecting the rate of phase transition—nucleation (described with K1) and nuclei growth (described with K2). Similar phase transitions were also approximated with the well-known single constant Avrami–Erofeev equation, but we successfully calculated both constants according to the new methodology, which allowed a separate evaluation of these two processes and explained the different induction periods. The effects of empirically adjusted constants on theoretically calculated kinetic curves were thus determined.