Isothermal nanocrystallization kinetics during polymorphic transformation

The experimental value of Avrami exponent during polymorphic nanocrystallization deviates from the theoretical prediction of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) isothermal kinetics. The assumption of negligible nuclei volume, implicit in KJMA, is violated for all such transformations involving nano-sized grains. A discrete adaptation of the KJMA model is used to study the effect of the non-zero nuclei volume on nanocrystallization kinetics. Transformations initiated by homogeneous and heterogeneous nucleation are analyzed under constant nucleation and growth rate conditions. For homogeneous nucleation, a universal scaling relation with respect to finite nuclei size is found. In contrast to this, for the heterogeneous case a series of linear scaling relations are observed with respect to the nucleation conditions.     

晶核剂对锂锌硅系微晶玻璃析晶及显微结构的影响

采用差热分析方法研究了LZS系玻璃陶瓷的析晶动力学,讨论了晶核剂对微晶玻璃的晶相、显微结构及析晶动力学参数的影响.结果表明:与TiO2相比,P2O5能够更加有效地促进玻璃析晶,但两者效果相差不大.使用不同的晶核剂不会影响玻璃析出的晶相,但使用P2O5作为晶核剂能得到均匀细小的晶体.     

Cellular automata simulations on nanocrystallization processes: From instantaneous growth approximation to limited growth

Cellular automata simulations have been performed to simulate the crystallization process under a limited growth approximation. This approximation resembles several characteristics exhibited by nanocrystalline microstructures and nanocrystallization kinetics. Avrami exponent decreases from a value n = 4 indicating interface controlled growth and constant nucleation rate to a value n ~ 1 indicating absence of growth. A continuous change of the growth contribution to the Avrami exponent from zero to 3 is observed as the composition of the amorphous phase becomes richer in the element present in the crystalline phase.     

Instantaneous growth approximation describing the nanocrystallization process of amorphous alloys: A cellular automata model

A cellular automata simulation based on an instantaneous growth approximation is developed to model the nanocrystallization kinetics. In this frame, the time required for a nucleus to grow up to its maximum size is neglected in comparison with the time required for the crystallization process. This approach allows a simple interpretation of the very low values of Avrami exponent found for nanocrystallization processes, ?1, in the theoretical frame of Johnson-Mehl-Avrami-Kolmogorov theory. Kinetics and microstructure predictions from the simulations are compared with experimental data for FeCoNbB alloys and a good qualitative agreement is found.     

Crystallization kinetic of glass particles prepared from a mixture of coal ash and soda-lime cullet glass

The crystallization capability of a parent glass made from a mixture of coal ash (40 wt%) and soda-lime glass was investigated using differential thermal analysis (DTA), X-ray diffraction (XRD) and scanning electron microscopy. Different glass particle size distributions were considered in the range 20-500 μm. Two crystallization exotherms in DTA were attributed to the formation of both pyroxenes (diopside Ca(Mg,Al)(Si,Al)₂O₆ and augite Ca(Mg,Fe)Si₂O₆) and plagioclase (Na,Ca)(Si,Al)₄O₈. These phases were confirmed by XRD analyses. Analysis of non-isothermal DTA data yielded values of 545 kJ/mol and 1.8 for the activation energy of crystallization and the Avrami exponent, respectively. This value for the Avrami exponent was consistent with a decreasing nucleation rate and the observed dendritic morphology. The data on crystallization kinetics obtained in this study are relevant for the production of glass-ceramic materials by a sintering/crystallization method from powder compacts made of this parent glass.     

Determination of activation energies for nucleation and growth from isothermal differential scanning calorimetry data

Differential scanning calorimetry (DSC) is usually adopted to analyze solid-state phase transformation incorporating nucleation, growth and impingement. Then, for isothermal transformation, time-dependent Avrami exponent and overall effective activation energy can always be deduced using recipes, which are derived from an analytical phase transformation model. On this basis, a concise and reliable approach to determine time-independent activation energies for nucleation and growth is proposed. Numerical calculations have demonstrated that the new approach is sufficiently precise under different conditions of transformation (e.g. nucleation: mixed nucleation and Avrami nucleation; growth: interface-controlled growth and diffusion-controlled growth; impingement: randomly nuclei dispersed, anisotropic growth and non-random nuclei distributions). Application of the approach in crystallization of Zr₅₅Cu₃₀Al₁₀Ni₅, Zr₅₀Al₁₀Ni₄₀ and Cu₄₆Zr₄₅Al₇Y₂ bulk amorphous alloys as measured by isothermal DSC was performed.     

Crystallization of amorphous selenium and As0.005Se0.995

The effect of temperature on the crystallization kinetics of bulk amorphous selenium and the alloy As_0.005Se_0.995 has been studied using differential scanning calorimetry. A time-temperature-transformation (TTT) curve has been plotted from isothermal results over the temperature range 320 to 490 K, and shows the presence of two minima for both materials. Using the empirical Avrami expression for solid-state transformations, a number of kinetic parameters has been determined.     

Continuous cooling approximation for the formation of a glass

Non-isothermal equations describing the liquid-crystal transformation are derived using the isothermal Avrami equations. A theoretical expression for the critical cooling rate for the formation of a glass is found. Calculations based on this expression are in better agreement with experimental values than those derived from TTT (time-temperature-transformation) curves. A study performed on typical glass forming materials enables the glass forming ability (GFA) to be determined by experimentally measuring crystallization temperatures at different cooling rates which are easily accessible with commonly available technology. The behaviour of the rate constant for crystallization is also obtained from the same data in the experimental range considered. In both cases no previous knowledge of the parameters involved is needed.With some assumptions the values of the viscosity in the crystallization temperature range can be estimated.Although the study was performed for an Avrami index of 4 an extension to other values of n is made under some restricted conditions and a more general treatment is outlined.     

DSC Transformation Behaviour of a bcc Mg11Sm Phase Prepared by Rapid Solidification

The transformation behaviour of the bcc Mg₁₁Sm phase prepared by rapid solidification from the melt has been studied by DSC. The Kissinger and Ozawa equations led to the following activation energies of the first and the second phase transition: E ≈ 130 kJ/mol and E ≈ 194 kJ/mol, respectively. Isothermal Avrami kinetics of the first phase transition starts with an Avrami exponent n ≈ 2,5, dropping down at higher degrees of transformation to n ≈ 1.5. The data obtained have been compared with the parameters of the isothermal Avrami kinetics of decomposition of a rapidly quenched supersaturated MgYb_4.87 alloy.     

Probleme der Kinetik von Ordnungs-Unordnungs-Umwandlungen in kristallinen Festkörpern

A review is given on problems of the kinetic theory of order-disorder transformations in crystalline solids. These phase transformations especially include diffusion-like homogeneous transformations between crystals with superlattice structure (f. i. intermetallic compounds) and disordered substitutional solid solutions. At first the importance of order-disorder transformations for fundamental research in theoretical and solid state physics as well as for applied materials science is pointed out. Then the foundations of the electron theory and the statistical thermodynamics of order-disorder transformations in alloys are summarized. Problems, methods and results of the kinetics of ordering processes are discussed. A more detailed treatment is given for the kinetic Ising model (Glauber model). Finally, a general quantum statistical theory of homogeneous order-disorder transformations and its range of applicability are described.     

Crystallization kinetics of Fe73.5−xMnxCu1Nb3Si13.5B9 (x = 0, 1, 3, 5, 7) amorphous alloys

In this study, we have investigated the effect of substituting Mn for Fe on the crystallization kinetics of amorphous Fe_73.5−xMn_xCu₁Nb₃Si_13.5B₉ (x = 1, 3, 5, 7) alloys. The samples were annealed at 550 °C and 600 °C for 1 h under an argon atmosphere. The X-ray diffraction analyses showed only a crystalline peak belonging to the α-Fe(Si) phase, with the grain size ranging from 12.2 nm for x = 0 to 16.7 nm for x = 7. The activation energies of the alloys were calculated using Kissinger, Ozawa and Augis-Bennett models based on differential thermal analysis data. The Avrami exponent n was calculated from the Johnson-Mehl-Avrami equation. The activation energy increased up to x = 3, then decreased with increasing Mn content. The values of the Avrami exponent showed that the crystallization is typical diffusion-controlled three-dimensional growth at a constant nucleation rate.     

Stabilization processes of metastable crystalline phases in 2,5-dichlorothiophene

Three crystalline phases, two metastable and one most-stable phase, were found in 2,5-dichlorothiophene by differential scanning calorimetry (DSC). The relaxation processes from one metastable crystalline phase to another and from this metastable phase to the stable phase were investigated by tracing the enthalpy change for a long time under constant temperature using DSC. The Avrami index n, in the Avrami equation, was found to be approximately 2 for both relaxation processes.     

Thermal properties of chalcogenide glasses in the GeSe2–As2Se3–CdSe system

In the present work, thermal properties of GeSe₂–As₂Se₃–CdSe glasses were investigated via DSC measurements. The dependences of glass transition temperature and thermal stability on glass composition were discussed. XRD measurement was also performed to validate the effect of cadmium on the thermal properties of glasses. The calculated Avrami exponent was used to demonstrate the three-dimensional growth of crystals in the glass matrices. The crystallization kinetics for the glasses was studied by using the modified Kissinger and Ozawa equations.     

Influence of particle size on the crystallization kinetics of glasses produced from waste materials

The crystallization behavior and kinetics of glasses produced from coal fly ashes, red mud and silica fume were investigated by using differential thermal analysis, X-ray diffraction and scanning electron microscopy techniques. The kinetic parameters of the glass-crystallization transformation were estimated under non-isothermal conditions applying three different equations, namely, Kissinger, Matusuta-Sakka and Ozawa. Non-isothermal differential thermal analysis curves were obtained using both coarse and fine glass samples. The crystallization activation energies of coarse glasses are in the range of 233-439 kJ/mol while the activation energies of fine glasses change in the range of 369-450 kJ/mol. Avrami exponent, n, values of coarse glasses indicated the three-dimensional bulk crystallization. This result is in well agreement with the cross-sectional scanning electron microscopy investigations. The values of the n obtained experimentally are in the range of 1.24-1.36 for fine glasses which show the one-dimensional surface crystallization. The crystallized phase of the glass-ceramic samples produced from waste glasses by applying the controlled heat treatment process was identified as diopside by X-ray diffraction analysis.     

Static and dynamic crystallization in Mg–Cu–Y bulk metallic glass

The static and dynamic crystallization behavior of Mg₆₅Cu₂₅Y₁₀ bulk metallic glass was investigated by X-ray diffraction, differential scanning calorimetry and transmission electron microscopy. It was found that the kinetics of both anisothermal and isothermal crystallization were adequately represented by the Kissinger and KJMA relations, respectively. The apparent activation energy for crystallization was calculated to be 139 kJ/mol; this value is close to the self diffusion of Mg in both a crystalline and non-crystalline matrix. The Avrami exponent was found to vary from 2.2 to 2.5 with increasing annealing temperature which implies that, at high annealing temperatures, nucleation occurs at a constant rate accompanied by diffusion-controlled growth of spherical grains. Tensile straining in the supercooled liquid region indicated that crystallization is slightly accelerated compared with static crystallization; this phenomenon was found to adversely affect the ductility of the alloy.     

Formation of nanoporous and nanocrystalline anatase films by pyrolysis of PEO–TiO2 hybrid films

Poly(ethylene oxide)–titania (PEO–TiO₂) organic–inorganic hybrid films were synthesized through a sol–gel process and spin coating. The mixed precursor sols were aged for 6 and 12 h, respectively, prior to the spin coating. Hybrid films were crystallized to the anatase phase first and then further heat treated at elevated temperatures for different time periods to analyze the anatase-to-rutile phase transformation. Quantitative X-ray diffraction (Q-XRD) results were employed for Johnson–Mehl–Avrami (JMA) kinetic analyses and the Avrami exponent (n) was determined for each film. The Arrhenius plots were created based on the JMA plots and the activation energy (Q) values for the phase transformation were determined for each film. The difference in the phase transformation kinetics in the films was discussed based upon the difference in the activation energy values and thus the molecular structures of each hybrid film. Nanoporous and nanocrystalline anatase films were successfully achieved through the retarded phase transformation during the pyrolysis of the organic–inorganic hybrid films. Owing to the maximized surface area these nano-structured anatase films are highly expected to show the enhanced photocatalytic efficiency compared to common TiO₂ films as well as sintered bulk forms.     

Fracture in precursor-derived Si–C–N ceramics – Analysis of crack roughness and damage mechanisms

Roughness analysis of fracture in precursor-derived amorphous and phase segregated Si–C–N ceramics using fractal methods is reported, towards examining the possible correlations between fractal scaling of roughness and fracture properties as well as fracture damage mechanisms. Topography of the fracture surfaces created at a crack velocity of ～10^?4 m/s was recorded using atomic force microscopy, and analyzed using RMS roughness and second order height–height correlation functions. The evolution of roughness was well correlated with the evolution of structural and compositional inhomogeneities in the amorphous materials, and the formation of second phases in the phase segregated materials. All the investigated fracture surfaces displayed self-affine scaling with a correlation length of ～50–100 nm and a roughness exponent of 0.8 ± 0.1, commensurate with the universal exponent conjectured by Bouchaud et al. corresponding to dynamic damage regime. No correlation was observed between the roughness exponents and the fracture toughness of the corresponding materials. Examination of the crack opening near the tip region revealed no persistent damage cavities assignable to ‘plastic deformation’ preceding fracture, suggesting that the fracture in the Si–C–N ceramics proceeds in a brittle manner at the employed crack velocities.     

Analysis of the feasibility of Avrami equation to amino acid endcapped PPDO crystallization by using Malek and Mitsuhashi method

Typically, the crystallization kinetics behaviour of biodegradable polyester could be described by the Avrami equation; however, for the appropriate application of this equation, some assumptions are required. Under conventional conditions of isothermal crystallization without nucleating agents, homogeneous nucleation is the key factor for the compatibility of this equation. On account of structural characteristics, the homogeneous nucleation of polymers is possibly affected by several factors. In this study, we investigated the isothermal crystallization of four PPDOs end‐capped with amino acids, followed by the Avrami equation analysis. After employing the method reported by Malek and Mitsuhashi, the L‐Gly‐ end‐capped PPDO and L‐Leu‐, L‐Phe‐end‐capped PPDO crystallized at higher temperatures were not suitable for analysis by the Avrami equation. In addition, this result was substantiated by reasoning the polymer chains’ mobility which could be affected by the terminated amino acids’ steric hindrance and crystallization temperatures, subsequently affecting homogeneous nucleation.     

An analytical model to represent crystallization kinetics in materials with metastable phase formation

The aim of this article is to propose a simple analytical model that can describe the isothermal crystallization process in materials when the formation of a stable crystalline phase is preceded by the formation of a metastable phase. This model explains deviations from the well-known Johnson-Mehl-Avrami-Kolmogorov kinetics theory and predicts the three slopes in Avrami’s plot. The model predictions were compared with experimental results obtained from X-ray measurements in the chalcogenide glasses with composition of Ge₂Sb₂Te₅ (thin films) and in aqueous solutions of methylhydrazine monohydrate during isothermal phase transformations. In order to validate the proposed model to represent experimental results, a computer program was developed. This program uses experimental data from measurements of the total volume fraction at different times during isothermal transformations and fits the model parameters that best represent the kinetic behavior of the system.